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Scientific Method

Science is an enormously successful human enterprise. The study of scientific method is the attempt to discern the activities by which that success is achieved. Among the activities often identified as characteristic of science are systematic observation and experimentation, inductive and deductive reasoning, and the formation and testing of hypotheses and theories. How these are carried out in detail can vary greatly, but characteristics like these have been looked to as a way of demarcating scientific activity from non-science, where only enterprises which employ some canonical form of scientific method or methods should be considered science (see also the entry on science and pseudo-science ). Others have questioned whether there is anything like a fixed toolkit of methods which is common across science and only science. Some reject privileging one view of method as part of rejecting broader views about the nature of science, such as naturalism (Dupré 2004); some reject any restriction in principle (pluralism).

Scientific method should be distinguished from the aims and products of science, such as knowledge, predictions, or control. Methods are the means by which those goals are achieved. Scientific method should also be distinguished from meta-methodology, which includes the values and justifications behind a particular characterization of scientific method (i.e., a methodology) — values such as objectivity, reproducibility, simplicity, or past successes. Methodological rules are proposed to govern method and it is a meta-methodological question whether methods obeying those rules satisfy given values. Finally, method is distinct, to some degree, from the detailed and contextual practices through which methods are implemented. The latter might range over: specific laboratory techniques; mathematical formalisms or other specialized languages used in descriptions and reasoning; technological or other material means; ways of communicating and sharing results, whether with other scientists or with the public at large; or the conventions, habits, enforced customs, and institutional controls over how and what science is carried out.

While it is important to recognize these distinctions, their boundaries are fuzzy. Hence, accounts of method cannot be entirely divorced from their methodological and meta-methodological motivations or justifications, Moreover, each aspect plays a crucial role in identifying methods. Disputes about method have therefore played out at the detail, rule, and meta-rule levels. Changes in beliefs about the certainty or fallibility of scientific knowledge, for instance (which is a meta-methodological consideration of what we can hope for methods to deliver), have meant different emphases on deductive and inductive reasoning, or on the relative importance attached to reasoning over observation (i.e., differences over particular methods.) Beliefs about the role of science in society will affect the place one gives to values in scientific method.

The issue which has shaped debates over scientific method the most in the last half century is the question of how pluralist do we need to be about method? Unificationists continue to hold out for one method essential to science; nihilism is a form of radical pluralism, which considers the effectiveness of any methodological prescription to be so context sensitive as to render it not explanatory on its own. Some middle degree of pluralism regarding the methods embodied in scientific practice seems appropriate. But the details of scientific practice vary with time and place, from institution to institution, across scientists and their subjects of investigation. How significant are the variations for understanding science and its success? How much can method be abstracted from practice? This entry describes some of the attempts to characterize scientific method or methods, as well as arguments for a more context-sensitive approach to methods embedded in actual scientific practices.

1. Overview and organizing themes

2. historical review: aristotle to mill, 3.1 logical constructionism and operationalism, 3.2. h-d as a logic of confirmation, 3.3. popper and falsificationism, 3.4 meta-methodology and the end of method, 4. statistical methods for hypothesis testing, 5.1 creative and exploratory practices.

• 5.2 Computer methods and the ‘new ways’ of doing science

6.1 “The scientific method” in science education and as seen by scientists

6.2 privileged methods and ‘gold standards’, 6.3 scientific method in the court room, 6.4 deviating practices, 7. conclusion, other internet resources, related entries.

This entry could have been given the title Scientific Methods and gone on to fill volumes, or it could have been extremely short, consisting of a brief summary rejection of the idea that there is any such thing as a unique Scientific Method at all. Both unhappy prospects are due to the fact that scientific activity varies so much across disciplines, times, places, and scientists that any account which manages to unify it all will either consist of overwhelming descriptive detail, or trivial generalizations.

The choice of scope for the present entry is more optimistic, taking a cue from the recent movement in philosophy of science toward a greater attention to practice: to what scientists actually do. This “turn to practice” can be seen as the latest form of studies of methods in science, insofar as it represents an attempt at understanding scientific activity, but through accounts that are neither meant to be universal and unified, nor singular and narrowly descriptive. To some extent, different scientists at different times and places can be said to be using the same method even though, in practice, the details are different.

Whether the context in which methods are carried out is relevant, or to what extent, will depend largely on what one takes the aims of science to be and what one’s own aims are. For most of the history of scientific methodology the assumption has been that the most important output of science is knowledge and so the aim of methodology should be to discover those methods by which scientific knowledge is generated.

Science was seen to embody the most successful form of reasoning (but which form?) to the most certain knowledge claims (but how certain?) on the basis of systematically collected evidence (but what counts as evidence, and should the evidence of the senses take precedence, or rational insight?) Section 2 surveys some of the history, pointing to two major themes. One theme is seeking the right balance between observation and reasoning (and the attendant forms of reasoning which employ them); the other is how certain scientific knowledge is or can be.

Section 3 turns to 20 th century debates on scientific method. In the second half of the 20 th century the epistemic privilege of science faced several challenges and many philosophers of science abandoned the reconstruction of the logic of scientific method. Views changed significantly regarding which functions of science ought to be captured and why. For some, the success of science was better identified with social or cultural features. Historical and sociological turns in the philosophy of science were made, with a demand that greater attention be paid to the non-epistemic aspects of science, such as sociological, institutional, material, and political factors. Even outside of those movements there was an increased specialization in the philosophy of science, with more and more focus on specific fields within science. The combined upshot was very few philosophers arguing any longer for a grand unified methodology of science. Sections 3 and 4 surveys the main positions on scientific method in 20 th century philosophy of science, focusing on where they differ in their preference for confirmation or falsification or for waiving the idea of a special scientific method altogether.

In recent decades, attention has primarily been paid to scientific activities traditionally falling under the rubric of method, such as experimental design and general laboratory practice, the use of statistics, the construction and use of models and diagrams, interdisciplinary collaboration, and science communication. Sections 4–6 attempt to construct a map of the current domains of the study of methods in science.

As these sections illustrate, the question of method is still central to the discourse about science. Scientific method remains a topic for education, for science policy, and for scientists. It arises in the public domain where the demarcation or status of science is at issue. Some philosophers have recently returned, therefore, to the question of what it is that makes science a unique cultural product. This entry will close with some of these recent attempts at discerning and encapsulating the activities by which scientific knowledge is achieved.

Attempting a history of scientific method compounds the vast scope of the topic. This section briefly surveys the background to modern methodological debates. What can be called the classical view goes back to antiquity, and represents a point of departure for later divergences. [ 1 ]

We begin with a point made by Laudan (1968) in his historical survey of scientific method:

Perhaps the most serious inhibition to the emergence of the history of theories of scientific method as a respectable area of study has been the tendency to conflate it with the general history of epistemology, thereby assuming that the narrative categories and classificatory pigeon-holes applied to the latter are also basic to the former. (1968: 5)

To see knowledge about the natural world as falling under knowledge more generally is an understandable conflation. Histories of theories of method would naturally employ the same narrative categories and classificatory pigeon holes. An important theme of the history of epistemology, for example, is the unification of knowledge, a theme reflected in the question of the unification of method in science. Those who have identified differences in kinds of knowledge have often likewise identified different methods for achieving that kind of knowledge (see the entry on the unity of science ).

Different views on what is known, how it is known, and what can be known are connected. Plato distinguished the realms of things into the visible and the intelligible ( The Republic , 510a, in Cooper 1997). Only the latter, the Forms, could be objects of knowledge. The intelligible truths could be known with the certainty of geometry and deductive reasoning. What could be observed of the material world, however, was by definition imperfect and deceptive, not ideal. The Platonic way of knowledge therefore emphasized reasoning as a method, downplaying the importance of observation. Aristotle disagreed, locating the Forms in the natural world as the fundamental principles to be discovered through the inquiry into nature ( Metaphysics Z , in Barnes 1984).

Aristotle is recognized as giving the earliest systematic treatise on the nature of scientific inquiry in the western tradition, one which embraced observation and reasoning about the natural world. In the Prior and Posterior Analytics , Aristotle reflects first on the aims and then the methods of inquiry into nature. A number of features can be found which are still considered by most to be essential to science. For Aristotle, empiricism, careful observation (but passive observation, not controlled experiment), is the starting point. The aim is not merely recording of facts, though. For Aristotle, science ( epistêmê ) is a body of properly arranged knowledge or learning—the empirical facts, but also their ordering and display are of crucial importance. The aims of discovery, ordering, and display of facts partly determine the methods required of successful scientific inquiry. Also determinant is the nature of the knowledge being sought, and the explanatory causes proper to that kind of knowledge (see the discussion of the four causes in the entry on Aristotle on causality ).

In addition to careful observation, then, scientific method requires a logic as a system of reasoning for properly arranging, but also inferring beyond, what is known by observation. Methods of reasoning may include induction, prediction, or analogy, among others. Aristotle’s system (along with his catalogue of fallacious reasoning) was collected under the title the Organon . This title would be echoed in later works on scientific reasoning, such as Novum Organon by Francis Bacon, and Novum Organon Restorum by William Whewell (see below). In Aristotle’s Organon reasoning is divided primarily into two forms, a rough division which persists into modern times. The division, known most commonly today as deductive versus inductive method, appears in other eras and methodologies as analysis/​synthesis, non-ampliative/​ampliative, or even confirmation/​verification. The basic idea is there are two “directions” to proceed in our methods of inquiry: one away from what is observed, to the more fundamental, general, and encompassing principles; the other, from the fundamental and general to instances or implications of principles.

The basic aim and method of inquiry identified here can be seen as a theme running throughout the next two millennia of reflection on the correct way to seek after knowledge: carefully observe nature and then seek rules or principles which explain or predict its operation. The Aristotelian corpus provided the framework for a commentary tradition on scientific method independent of science itself (cosmos versus physics.) During the medieval period, figures such as Albertus Magnus (1206–1280), Thomas Aquinas (1225–1274), Robert Grosseteste (1175–1253), Roger Bacon (1214/1220–1292), William of Ockham (1287–1347), Andreas Vesalius (1514–1546), Giacomo Zabarella (1533–1589) all worked to clarify the kind of knowledge obtainable by observation and induction, the source of justification of induction, and best rules for its application. [ 2 ] Many of their contributions we now think of as essential to science (see also Laudan 1968). As Aristotle and Plato had employed a framework of reasoning either “to the forms” or “away from the forms”, medieval thinkers employed directions away from the phenomena or back to the phenomena. In analysis, a phenomena was examined to discover its basic explanatory principles; in synthesis, explanations of a phenomena were constructed from first principles.

During the Scientific Revolution these various strands of argument, experiment, and reason were forged into a dominant epistemic authority. The 16 th –18 th centuries were a period of not only dramatic advance in knowledge about the operation of the natural world—advances in mechanical, medical, biological, political, economic explanations—but also of self-awareness of the revolutionary changes taking place, and intense reflection on the source and legitimation of the method by which the advances were made. The struggle to establish the new authority included methodological moves. The Book of Nature, according to the metaphor of Galileo Galilei (1564–1642) or Francis Bacon (1561–1626), was written in the language of mathematics, of geometry and number. This motivated an emphasis on mathematical description and mechanical explanation as important aspects of scientific method. Through figures such as Henry More and Ralph Cudworth, a neo-Platonic emphasis on the importance of metaphysical reflection on nature behind appearances, particularly regarding the spiritual as a complement to the purely mechanical, remained an important methodological thread of the Scientific Revolution (see the entries on Cambridge platonists ; Boyle ; Henry More ; Galileo ).

In Novum Organum (1620), Bacon was critical of the Aristotelian method for leaping from particulars to universals too quickly. The syllogistic form of reasoning readily mixed those two types of propositions. Bacon aimed at the invention of new arts, principles, and directions. His method would be grounded in methodical collection of observations, coupled with correction of our senses (and particularly, directions for the avoidance of the Idols, as he called them, kinds of systematic errors to which naïve observers are prone.) The community of scientists could then climb, by a careful, gradual and unbroken ascent, to reliable general claims.

Bacon’s method has been criticized as impractical and too inflexible for the practicing scientist. Whewell would later criticize Bacon in his System of Logic for paying too little attention to the practices of scientists. It is hard to find convincing examples of Bacon’s method being put in to practice in the history of science, but there are a few who have been held up as real examples of 16 th century scientific, inductive method, even if not in the rigid Baconian mold: figures such as Robert Boyle (1627–1691) and William Harvey (1578–1657) (see the entry on Bacon ).

It is to Isaac Newton (1642–1727), however, that historians of science and methodologists have paid greatest attention. Given the enormous success of his Principia Mathematica and Opticks , this is understandable. The study of Newton’s method has had two main thrusts: the implicit method of the experiments and reasoning presented in the Opticks, and the explicit methodological rules given as the Rules for Philosophising (the Regulae) in Book III of the Principia . [ 3 ] Newton’s law of gravitation, the linchpin of his new cosmology, broke with explanatory conventions of natural philosophy, first for apparently proposing action at a distance, but more generally for not providing “true”, physical causes. The argument for his System of the World ( Principia , Book III) was based on phenomena, not reasoned first principles. This was viewed (mainly on the continent) as insufficient for proper natural philosophy. The Regulae counter this objection, re-defining the aims of natural philosophy by re-defining the method natural philosophers should follow. (See the entry on Newton’s philosophy .)

To his list of methodological prescriptions should be added Newton’s famous phrase “ hypotheses non fingo ” (commonly translated as “I frame no hypotheses”.) The scientist was not to invent systems but infer explanations from observations, as Bacon had advocated. This would come to be known as inductivism. In the century after Newton, significant clarifications of the Newtonian method were made. Colin Maclaurin (1698–1746), for instance, reconstructed the essential structure of the method as having complementary analysis and synthesis phases, one proceeding away from the phenomena in generalization, the other from the general propositions to derive explanations of new phenomena. Denis Diderot (1713–1784) and editors of the Encyclopédie did much to consolidate and popularize Newtonianism, as did Francesco Algarotti (1721–1764). The emphasis was often the same, as much on the character of the scientist as on their process, a character which is still commonly assumed. The scientist is humble in the face of nature, not beholden to dogma, obeys only his eyes, and follows the truth wherever it leads. It was certainly Voltaire (1694–1778) and du Chatelet (1706–1749) who were most influential in propagating the latter vision of the scientist and their craft, with Newton as hero. Scientific method became a revolutionary force of the Enlightenment. (See also the entries on Newton , Leibniz , Descartes , Boyle , Hume , enlightenment , as well as Shank 2008 for a historical overview.)

Not all 18 th century reflections on scientific method were so celebratory. Famous also are George Berkeley’s (1685–1753) attack on the mathematics of the new science, as well as the over-emphasis of Newtonians on observation; and David Hume’s (1711–1776) undermining of the warrant offered for scientific claims by inductive justification (see the entries on: George Berkeley ; David Hume ; Hume’s Newtonianism and Anti-Newtonianism ). Hume’s problem of induction motivated Immanuel Kant (1724–1804) to seek new foundations for empirical method, though as an epistemic reconstruction, not as any set of practical guidelines for scientists. Both Hume and Kant influenced the methodological reflections of the next century, such as the debate between Mill and Whewell over the certainty of inductive inferences in science.

The debate between John Stuart Mill (1806–1873) and William Whewell (1794–1866) has become the canonical methodological debate of the 19 th century. Although often characterized as a debate between inductivism and hypothetico-deductivism, the role of the two methods on each side is actually more complex. On the hypothetico-deductive account, scientists work to come up with hypotheses from which true observational consequences can be deduced—hence, hypothetico-deductive. Because Whewell emphasizes both hypotheses and deduction in his account of method, he can be seen as a convenient foil to the inductivism of Mill. However, equally if not more important to Whewell’s portrayal of scientific method is what he calls the “fundamental antithesis”. Knowledge is a product of the objective (what we see in the world around us) and subjective (the contributions of our mind to how we perceive and understand what we experience, which he called the Fundamental Ideas). Both elements are essential according to Whewell, and he was therefore critical of Kant for too much focus on the subjective, and John Locke (1632–1704) and Mill for too much focus on the senses. Whewell’s fundamental ideas can be discipline relative. An idea can be fundamental even if it is necessary for knowledge only within a given scientific discipline (e.g., chemical affinity for chemistry). This distinguishes fundamental ideas from the forms and categories of intuition of Kant. (See the entry on Whewell .)

Clarifying fundamental ideas would therefore be an essential part of scientific method and scientific progress. Whewell called this process “Discoverer’s Induction”. It was induction, following Bacon or Newton, but Whewell sought to revive Bacon’s account by emphasising the role of ideas in the clear and careful formulation of inductive hypotheses. Whewell’s induction is not merely the collecting of objective facts. The subjective plays a role through what Whewell calls the Colligation of Facts, a creative act of the scientist, the invention of a theory. A theory is then confirmed by testing, where more facts are brought under the theory, called the Consilience of Inductions. Whewell felt that this was the method by which the true laws of nature could be discovered: clarification of fundamental concepts, clever invention of explanations, and careful testing. Mill, in his critique of Whewell, and others who have cast Whewell as a fore-runner of the hypothetico-deductivist view, seem to have under-estimated the importance of this discovery phase in Whewell’s understanding of method (Snyder 1997a,b, 1999). Down-playing the discovery phase would come to characterize methodology of the early 20 th century (see section 3 ).

Mill, in his System of Logic , put forward a narrower view of induction as the essence of scientific method. For Mill, induction is the search first for regularities among events. Among those regularities, some will continue to hold for further observations, eventually gaining the status of laws. One can also look for regularities among the laws discovered in a domain, i.e., for a law of laws. Which “law law” will hold is time and discipline dependent and open to revision. One example is the Law of Universal Causation, and Mill put forward specific methods for identifying causes—now commonly known as Mill’s methods. These five methods look for circumstances which are common among the phenomena of interest, those which are absent when the phenomena are, or those for which both vary together. Mill’s methods are still seen as capturing basic intuitions about experimental methods for finding the relevant explanatory factors ( System of Logic (1843), see Mill entry). The methods advocated by Whewell and Mill, in the end, look similar. Both involve inductive generalization to covering laws. They differ dramatically, however, with respect to the necessity of the knowledge arrived at; that is, at the meta-methodological level (see the entries on Whewell and Mill entries).

3. Logic of method and critical responses

The quantum and relativistic revolutions in physics in the early 20 th century had a profound effect on methodology. Conceptual foundations of both theories were taken to show the defeasibility of even the most seemingly secure intuitions about space, time and bodies. Certainty of knowledge about the natural world was therefore recognized as unattainable. Instead a renewed empiricism was sought which rendered science fallible but still rationally justifiable.

Analyses of the reasoning of scientists emerged, according to which the aspects of scientific method which were of primary importance were the means of testing and confirming of theories. A distinction in methodology was made between the contexts of discovery and justification. The distinction could be used as a wedge between the particularities of where and how theories or hypotheses are arrived at, on the one hand, and the underlying reasoning scientists use (whether or not they are aware of it) when assessing theories and judging their adequacy on the basis of the available evidence. By and large, for most of the 20 th century, philosophy of science focused on the second context, although philosophers differed on whether to focus on confirmation or refutation as well as on the many details of how confirmation or refutation could or could not be brought about. By the mid-20 th century these attempts at defining the method of justification and the context distinction itself came under pressure. During the same period, philosophy of science developed rapidly, and from section 4 this entry will therefore shift from a primarily historical treatment of the scientific method towards a primarily thematic one.

Advances in logic and probability held out promise of the possibility of elaborate reconstructions of scientific theories and empirical method, the best example being Rudolf Carnap’s The Logical Structure of the World (1928). Carnap attempted to show that a scientific theory could be reconstructed as a formal axiomatic system—that is, a logic. That system could refer to the world because some of its basic sentences could be interpreted as observations or operations which one could perform to test them. The rest of the theoretical system, including sentences using theoretical or unobservable terms (like electron or force) would then either be meaningful because they could be reduced to observations, or they had purely logical meanings (called analytic, like mathematical identities). This has been referred to as the verifiability criterion of meaning. According to the criterion, any statement not either analytic or verifiable was strictly meaningless. Although the view was endorsed by Carnap in 1928, he would later come to see it as too restrictive (Carnap 1956). Another familiar version of this idea is operationalism of Percy William Bridgman. In The Logic of Modern Physics (1927) Bridgman asserted that every physical concept could be defined in terms of the operations one would perform to verify the application of that concept. Making good on the operationalisation of a concept even as simple as length, however, can easily become enormously complex (for measuring very small lengths, for instance) or impractical (measuring large distances like light years.)

Carl Hempel’s (1950, 1951) criticisms of the verifiability criterion of meaning had enormous influence. He pointed out that universal generalizations, such as most scientific laws, were not strictly meaningful on the criterion. Verifiability and operationalism both seemed too restrictive to capture standard scientific aims and practice. The tenuous connection between these reconstructions and actual scientific practice was criticized in another way. In both approaches, scientific methods are instead recast in methodological roles. Measurements, for example, were looked to as ways of giving meanings to terms. The aim of the philosopher of science was not to understand the methods per se , but to use them to reconstruct theories, their meanings, and their relation to the world. When scientists perform these operations, however, they will not report that they are doing them to give meaning to terms in a formal axiomatic system. This disconnect between methodology and the details of actual scientific practice would seem to violate the empiricism the Logical Positivists and Bridgman were committed to. The view that methodology should correspond to practice (to some extent) has been called historicism, or intuitionism. We turn to these criticisms and responses in section 3.4 . [ 4 ]

Positivism also had to contend with the recognition that a purely inductivist approach, along the lines of Bacon-Newton-Mill, was untenable. There was no pure observation, for starters. All observation was theory laden. Theory is required to make any observation, therefore not all theory can be derived from observation alone. (See the entry on theory and observation in science .) Even granting an observational basis, Hume had already pointed out that one could not deductively justify inductive conclusions without begging the question by presuming the success of the inductive method. Likewise, positivist attempts at analyzing how a generalization can be confirmed by observations of its instances were subject to a number of criticisms. Goodman (1965) and Hempel (1965) both point to paradoxes inherent in standard accounts of confirmation. Recent attempts at explaining how observations can serve to confirm a scientific theory are discussed in section 4 below.

The standard starting point for a non-inductive analysis of the logic of confirmation is known as the Hypothetico-Deductive (H-D) method. In its simplest form, a sentence of a theory which expresses some hypothesis is confirmed by its true consequences. As noted in section 2 , this method had been advanced by Whewell in the 19 th century, as well as Nicod (1924) and others in the 20 th century. Often, Hempel’s (1966) description of the H-D method, illustrated by the case of Semmelweiss’ inferential procedures in establishing the cause of childbed fever, has been presented as a key account of H-D as well as a foil for criticism of the H-D account of confirmation (see, for example, Lipton’s (2004) discussion of inference to the best explanation; also the entry on confirmation ). Hempel described Semmelsweiss’ procedure as examining various hypotheses explaining the cause of childbed fever. Some hypotheses conflicted with observable facts and could be rejected as false immediately. Others needed to be tested experimentally by deducing which observable events should follow if the hypothesis were true (what Hempel called the test implications of the hypothesis), then conducting an experiment and observing whether or not the test implications occurred. If the experiment showed the test implication to be false, the hypothesis could be rejected. If the experiment showed the test implications to be true, however, this did not prove the hypothesis true. The confirmation of a test implication does not verify a hypothesis, though Hempel did allow that “it provides at least some support, some corroboration or confirmation for it” (Hempel 1966: 8). The degree of this support then depends on the quantity, variety and precision of the supporting evidence.

Another approach that took off from the difficulties with inductive inference was Karl Popper’s critical rationalism or falsificationism (Popper 1959, 1963). Falsification is deductive and similar to H-D in that it involves scientists deducing observational consequences from the hypothesis under test. For Popper, however, the important point was not the degree of confirmation that successful prediction offered to a hypothesis. The crucial thing was the logical asymmetry between confirmation, based on inductive inference, and falsification, which can be based on a deductive inference. (This simple opposition was later questioned, by Lakatos, among others. See the entry on historicist theories of scientific rationality. )

Popper stressed that, regardless of the amount of confirming evidence, we can never be certain that a hypothesis is true without committing the fallacy of affirming the consequent. Instead, Popper introduced the notion of corroboration as a measure for how well a theory or hypothesis has survived previous testing—but without implying that this is also a measure for the probability that it is true.

Popper was also motivated by his doubts about the scientific status of theories like the Marxist theory of history or psycho-analysis, and so wanted to demarcate between science and pseudo-science. Popper saw this as an importantly different distinction than demarcating science from metaphysics. The latter demarcation was the primary concern of many logical empiricists. Popper used the idea of falsification to draw a line instead between pseudo and proper science. Science was science because its method involved subjecting theories to rigorous tests which offered a high probability of failing and thus refuting the theory.

A commitment to the risk of failure was important. Avoiding falsification could be done all too easily. If a consequence of a theory is inconsistent with observations, an exception can be added by introducing auxiliary hypotheses designed explicitly to save the theory, so-called ad hoc modifications. This Popper saw done in pseudo-science where ad hoc theories appeared capable of explaining anything in their field of application. In contrast, science is risky. If observations showed the predictions from a theory to be wrong, the theory would be refuted. Hence, scientific hypotheses must be falsifiable. Not only must there exist some possible observation statement which could falsify the hypothesis or theory, were it observed, (Popper called these the hypothesis’ potential falsifiers) it is crucial to the Popperian scientific method that such falsifications be sincerely attempted on a regular basis.

The more potential falsifiers of a hypothesis, the more falsifiable it would be, and the more the hypothesis claimed. Conversely, hypotheses without falsifiers claimed very little or nothing at all. Originally, Popper thought that this meant the introduction of ad hoc hypotheses only to save a theory should not be countenanced as good scientific method. These would undermine the falsifiabililty of a theory. However, Popper later came to recognize that the introduction of modifications (immunizations, he called them) was often an important part of scientific development. Responding to surprising or apparently falsifying observations often generated important new scientific insights. Popper’s own example was the observed motion of Uranus which originally did not agree with Newtonian predictions. The ad hoc hypothesis of an outer planet explained the disagreement and led to further falsifiable predictions. Popper sought to reconcile the view by blurring the distinction between falsifiable and not falsifiable, and speaking instead of degrees of testability (Popper 1985: 41f.).

From the 1960s on, sustained meta-methodological criticism emerged that drove philosophical focus away from scientific method. A brief look at those criticisms follows, with recommendations for further reading at the end of the entry.

Thomas Kuhn’s The Structure of Scientific Revolutions (1962) begins with a well-known shot across the bow for philosophers of science:

History, if viewed as a repository for more than anecdote or chronology, could produce a decisive transformation in the image of science by which we are now possessed. (1962: 1)

The image Kuhn thought needed transforming was the a-historical, rational reconstruction sought by many of the Logical Positivists, though Carnap and other positivists were actually quite sympathetic to Kuhn’s views. (See the entry on the Vienna Circle .) Kuhn shares with other of his contemporaries, such as Feyerabend and Lakatos, a commitment to a more empirical approach to philosophy of science. Namely, the history of science provides important data, and necessary checks, for philosophy of science, including any theory of scientific method.

The history of science reveals, according to Kuhn, that scientific development occurs in alternating phases. During normal science, the members of the scientific community adhere to the paradigm in place. Their commitment to the paradigm means a commitment to the puzzles to be solved and the acceptable ways of solving them. Confidence in the paradigm remains so long as steady progress is made in solving the shared puzzles. Method in this normal phase operates within a disciplinary matrix (Kuhn’s later concept of a paradigm) which includes standards for problem solving, and defines the range of problems to which the method should be applied. An important part of a disciplinary matrix is the set of values which provide the norms and aims for scientific method. The main values that Kuhn identifies are prediction, problem solving, simplicity, consistency, and plausibility.

An important by-product of normal science is the accumulation of puzzles which cannot be solved with resources of the current paradigm. Once accumulation of these anomalies has reached some critical mass, it can trigger a communal shift to a new paradigm and a new phase of normal science. Importantly, the values that provide the norms and aims for scientific method may have transformed in the meantime. Method may therefore be relative to discipline, time or place

Feyerabend also identified the aims of science as progress, but argued that any methodological prescription would only stifle that progress (Feyerabend 1988). His arguments are grounded in re-examining accepted “myths” about the history of science. Heroes of science, like Galileo, are shown to be just as reliant on rhetoric and persuasion as they are on reason and demonstration. Others, like Aristotle, are shown to be far more reasonable and far-reaching in their outlooks then they are given credit for. As a consequence, the only rule that could provide what he took to be sufficient freedom was the vacuous “anything goes”. More generally, even the methodological restriction that science is the best way to pursue knowledge, and to increase knowledge, is too restrictive. Feyerabend suggested instead that science might, in fact, be a threat to a free society, because it and its myth had become so dominant (Feyerabend 1978).

An even more fundamental kind of criticism was offered by several sociologists of science from the 1970s onwards who rejected the methodology of providing philosophical accounts for the rational development of science and sociological accounts of the irrational mistakes. Instead, they adhered to a symmetry thesis on which any causal explanation of how scientific knowledge is established needs to be symmetrical in explaining truth and falsity, rationality and irrationality, success and mistakes, by the same causal factors (see, e.g., Barnes and Bloor 1982, Bloor 1991). Movements in the Sociology of Science, like the Strong Programme, or in the social dimensions and causes of knowledge more generally led to extended and close examination of detailed case studies in contemporary science and its history. (See the entries on the social dimensions of scientific knowledge and social epistemology .) Well-known examinations by Latour and Woolgar (1979/1986), Knorr-Cetina (1981), Pickering (1984), Shapin and Schaffer (1985) seem to bear out that it was social ideologies (on a macro-scale) or individual interactions and circumstances (on a micro-scale) which were the primary causal factors in determining which beliefs gained the status of scientific knowledge. As they saw it therefore, explanatory appeals to scientific method were not empirically grounded.

A late, and largely unexpected, criticism of scientific method came from within science itself. Beginning in the early 2000s, a number of scientists attempting to replicate the results of published experiments could not do so. There may be close conceptual connection between reproducibility and method. For example, if reproducibility means that the same scientific methods ought to produce the same result, and all scientific results ought to be reproducible, then whatever it takes to reproduce a scientific result ought to be called scientific method. Space limits us to the observation that, insofar as reproducibility is a desired outcome of proper scientific method, it is not strictly a part of scientific method. (See the entry on reproducibility of scientific results .)

By the close of the 20 th century the search for the scientific method was flagging. Nola and Sankey (2000b) could introduce their volume on method by remarking that “For some, the whole idea of a theory of scientific method is yester-year’s debate …”.

Despite the many difficulties that philosophers encountered in trying to providing a clear methodology of conformation (or refutation), still important progress has been made on understanding how observation can provide evidence for a given theory. Work in statistics has been crucial for understanding how theories can be tested empirically, and in recent decades a huge literature has developed that attempts to recast confirmation in Bayesian terms. Here these developments can be covered only briefly, and we refer to the entry on confirmation for further details and references.

Statistics has come to play an increasingly important role in the methodology of the experimental sciences from the 19 th century onwards. At that time, statistics and probability theory took on a methodological role as an analysis of inductive inference, and attempts to ground the rationality of induction in the axioms of probability theory have continued throughout the 20 th century and in to the present. Developments in the theory of statistics itself, meanwhile, have had a direct and immense influence on the experimental method, including methods for measuring the uncertainty of observations such as the Method of Least Squares developed by Legendre and Gauss in the early 19 th century, criteria for the rejection of outliers proposed by Peirce by the mid-19 th century, and the significance tests developed by Gosset (a.k.a. “Student”), Fisher, Neyman & Pearson and others in the 1920s and 1930s (see, e.g., Swijtink 1987 for a brief historical overview; and also the entry on C.S. Peirce ).

These developments within statistics then in turn led to a reflective discussion among both statisticians and philosophers of science on how to perceive the process of hypothesis testing: whether it was a rigorous statistical inference that could provide a numerical expression of the degree of confidence in the tested hypothesis, or if it should be seen as a decision between different courses of actions that also involved a value component. This led to a major controversy among Fisher on the one side and Neyman and Pearson on the other (see especially Fisher 1955, Neyman 1956 and Pearson 1955, and for analyses of the controversy, e.g., Howie 2002, Marks 2000, Lenhard 2006). On Fisher’s view, hypothesis testing was a methodology for when to accept or reject a statistical hypothesis, namely that a hypothesis should be rejected by evidence if this evidence would be unlikely relative to other possible outcomes, given the hypothesis were true. In contrast, on Neyman and Pearson’s view, the consequence of error also had to play a role when deciding between hypotheses. Introducing the distinction between the error of rejecting a true hypothesis (type I error) and accepting a false hypothesis (type II error), they argued that it depends on the consequences of the error to decide whether it is more important to avoid rejecting a true hypothesis or accepting a false one. Hence, Fisher aimed for a theory of inductive inference that enabled a numerical expression of confidence in a hypothesis. To him, the important point was the search for truth, not utility. In contrast, the Neyman-Pearson approach provided a strategy of inductive behaviour for deciding between different courses of action. Here, the important point was not whether a hypothesis was true, but whether one should act as if it was.

Similar discussions are found in the philosophical literature. On the one side, Churchman (1948) and Rudner (1953) argued that because scientific hypotheses can never be completely verified, a complete analysis of the methods of scientific inference includes ethical judgments in which the scientists must decide whether the evidence is sufficiently strong or that the probability is sufficiently high to warrant the acceptance of the hypothesis, which again will depend on the importance of making a mistake in accepting or rejecting the hypothesis. Others, such as Jeffrey (1956) and Levi (1960) disagreed and instead defended a value-neutral view of science on which scientists should bracket their attitudes, preferences, temperament, and values when assessing the correctness of their inferences. For more details on this value-free ideal in the philosophy of science and its historical development, see Douglas (2009) and Howard (2003). For a broad set of case studies examining the role of values in science, see e.g. Elliott & Richards 2017.

In recent decades, philosophical discussions of the evaluation of probabilistic hypotheses by statistical inference have largely focused on Bayesianism that understands probability as a measure of a person’s degree of belief in an event, given the available information, and frequentism that instead understands probability as a long-run frequency of a repeatable event. Hence, for Bayesians probabilities refer to a state of knowledge, whereas for frequentists probabilities refer to frequencies of events (see, e.g., Sober 2008, chapter 1 for a detailed introduction to Bayesianism and frequentism as well as to likelihoodism). Bayesianism aims at providing a quantifiable, algorithmic representation of belief revision, where belief revision is a function of prior beliefs (i.e., background knowledge) and incoming evidence. Bayesianism employs a rule based on Bayes’ theorem, a theorem of the probability calculus which relates conditional probabilities. The probability that a particular hypothesis is true is interpreted as a degree of belief, or credence, of the scientist. There will also be a probability and a degree of belief that a hypothesis will be true conditional on a piece of evidence (an observation, say) being true. Bayesianism proscribes that it is rational for the scientist to update their belief in the hypothesis to that conditional probability should it turn out that the evidence is, in fact, observed (see, e.g., Sprenger & Hartmann 2019 for a comprehensive treatment of Bayesian philosophy of science). Originating in the work of Neyman and Person, frequentism aims at providing the tools for reducing long-run error rates, such as the error-statistical approach developed by Mayo (1996) that focuses on how experimenters can avoid both type I and type II errors by building up a repertoire of procedures that detect errors if and only if they are present. Both Bayesianism and frequentism have developed over time, they are interpreted in different ways by its various proponents, and their relations to previous criticism to attempts at defining scientific method are seen differently by proponents and critics. The literature, surveys, reviews and criticism in this area are vast and the reader is referred to the entries on Bayesian epistemology and confirmation .

5. Method in Practice

Attention to scientific practice, as we have seen, is not itself new. However, the turn to practice in the philosophy of science of late can be seen as a correction to the pessimism with respect to method in philosophy of science in later parts of the 20 th century, and as an attempted reconciliation between sociological and rationalist explanations of scientific knowledge. Much of this work sees method as detailed and context specific problem-solving procedures, and methodological analyses to be at the same time descriptive, critical and advisory (see Nickles 1987 for an exposition of this view). The following section contains a survey of some of the practice focuses. In this section we turn fully to topics rather than chronology.

A problem with the distinction between the contexts of discovery and justification that figured so prominently in philosophy of science in the first half of the 20 th century (see section 2 ) is that no such distinction can be clearly seen in scientific activity (see Arabatzis 2006). Thus, in recent decades, it has been recognized that study of conceptual innovation and change should not be confined to psychology and sociology of science, but are also important aspects of scientific practice which philosophy of science should address (see also the entry on scientific discovery ). Looking for the practices that drive conceptual innovation has led philosophers to examine both the reasoning practices of scientists and the wide realm of experimental practices that are not directed narrowly at testing hypotheses, that is, exploratory experimentation.

Examining the reasoning practices of historical and contemporary scientists, Nersessian (2008) has argued that new scientific concepts are constructed as solutions to specific problems by systematic reasoning, and that of analogy, visual representation and thought-experimentation are among the important reasoning practices employed. These ubiquitous forms of reasoning are reliable—but also fallible—methods of conceptual development and change. On her account, model-based reasoning consists of cycles of construction, simulation, evaluation and adaption of models that serve as interim interpretations of the target problem to be solved. Often, this process will lead to modifications or extensions, and a new cycle of simulation and evaluation. However, Nersessian also emphasizes that

creative model-based reasoning cannot be applied as a simple recipe, is not always productive of solutions, and even its most exemplary usages can lead to incorrect solutions. (Nersessian 2008: 11)

Thus, while on the one hand she agrees with many previous philosophers that there is no logic of discovery, discoveries can derive from reasoned processes, such that a large and integral part of scientific practice is

the creation of concepts through which to comprehend, structure, and communicate about physical phenomena …. (Nersessian 1987: 11)

Similarly, work on heuristics for discovery and theory construction by scholars such as Darden (1991) and Bechtel & Richardson (1993) present science as problem solving and investigate scientific problem solving as a special case of problem-solving in general. Drawing largely on cases from the biological sciences, much of their focus has been on reasoning strategies for the generation, evaluation, and revision of mechanistic explanations of complex systems.

Addressing another aspect of the context distinction, namely the traditional view that the primary role of experiments is to test theoretical hypotheses according to the H-D model, other philosophers of science have argued for additional roles that experiments can play. The notion of exploratory experimentation was introduced to describe experiments driven by the desire to obtain empirical regularities and to develop concepts and classifications in which these regularities can be described (Steinle 1997, 2002; Burian 1997; Waters 2007)). However the difference between theory driven experimentation and exploratory experimentation should not be seen as a sharp distinction. Theory driven experiments are not always directed at testing hypothesis, but may also be directed at various kinds of fact-gathering, such as determining numerical parameters. Vice versa , exploratory experiments are usually informed by theory in various ways and are therefore not theory-free. Instead, in exploratory experiments phenomena are investigated without first limiting the possible outcomes of the experiment on the basis of extant theory about the phenomena.

The development of high throughput instrumentation in molecular biology and neighbouring fields has given rise to a special type of exploratory experimentation that collects and analyses very large amounts of data, and these new ‘omics’ disciplines are often said to represent a break with the ideal of hypothesis-driven science (Burian 2007; Elliott 2007; Waters 2007; O’Malley 2007) and instead described as data-driven research (Leonelli 2012; Strasser 2012) or as a special kind of “convenience experimentation” in which many experiments are done simply because they are extraordinarily convenient to perform (Krohs 2012).

5.2 Computer methods and ‘new ways’ of doing science

The field of omics just described is possible because of the ability of computers to process, in a reasonable amount of time, the huge quantities of data required. Computers allow for more elaborate experimentation (higher speed, better filtering, more variables, sophisticated coordination and control), but also, through modelling and simulations, might constitute a form of experimentation themselves. Here, too, we can pose a version of the general question of method versus practice: does the practice of using computers fundamentally change scientific method, or merely provide a more efficient means of implementing standard methods?

Because computers can be used to automate measurements, quantifications, calculations, and statistical analyses where, for practical reasons, these operations cannot be otherwise carried out, many of the steps involved in reaching a conclusion on the basis of an experiment are now made inside a “black box”, without the direct involvement or awareness of a human. This has epistemological implications, regarding what we can know, and how we can know it. To have confidence in the results, computer methods are therefore subjected to tests of verification and validation.

The distinction between verification and validation is easiest to characterize in the case of computer simulations. In a typical computer simulation scenario computers are used to numerically integrate differential equations for which no analytic solution is available. The equations are part of the model the scientist uses to represent a phenomenon or system under investigation. Verifying a computer simulation means checking that the equations of the model are being correctly approximated. Validating a simulation means checking that the equations of the model are adequate for the inferences one wants to make on the basis of that model.

A number of issues related to computer simulations have been raised. The identification of validity and verification as the testing methods has been criticized. Oreskes et al. (1994) raise concerns that “validiation”, because it suggests deductive inference, might lead to over-confidence in the results of simulations. The distinction itself is probably too clean, since actual practice in the testing of simulations mixes and moves back and forth between the two (Weissart 1997; Parker 2008a; Winsberg 2010). Computer simulations do seem to have a non-inductive character, given that the principles by which they operate are built in by the programmers, and any results of the simulation follow from those in-built principles in such a way that those results could, in principle, be deduced from the program code and its inputs. The status of simulations as experiments has therefore been examined (Kaufmann and Smarr 1993; Humphreys 1995; Hughes 1999; Norton and Suppe 2001). This literature considers the epistemology of these experiments: what we can learn by simulation, and also the kinds of justifications which can be given in applying that knowledge to the “real” world. (Mayo 1996; Parker 2008b). As pointed out, part of the advantage of computer simulation derives from the fact that huge numbers of calculations can be carried out without requiring direct observation by the experimenter/​simulator. At the same time, many of these calculations are approximations to the calculations which would be performed first-hand in an ideal situation. Both factors introduce uncertainties into the inferences drawn from what is observed in the simulation.

For many of the reasons described above, computer simulations do not seem to belong clearly to either the experimental or theoretical domain. Rather, they seem to crucially involve aspects of both. This has led some authors, such as Fox Keller (2003: 200) to argue that we ought to consider computer simulation a “qualitatively different way of doing science”. The literature in general tends to follow Kaufmann and Smarr (1993) in referring to computer simulation as a “third way” for scientific methodology (theoretical reasoning and experimental practice are the first two ways.). It should also be noted that the debates around these issues have tended to focus on the form of computer simulation typical in the physical sciences, where models are based on dynamical equations. Other forms of simulation might not have the same problems, or have problems of their own (see the entry on computer simulations in science ).

In recent years, the rapid development of machine learning techniques has prompted some scholars to suggest that the scientific method has become “obsolete” (Anderson 2008, Carrol and Goodstein 2009). This has resulted in an intense debate on the relative merit of data-driven and hypothesis-driven research (for samples, see e.g. Mazzocchi 2015 or Succi and Coveney 2018). For a detailed treatment of this topic, we refer to the entry scientific research and big data .

6. Discourse on scientific method

Despite philosophical disagreements, the idea of the scientific method still figures prominently in contemporary discourse on many different topics, both within science and in society at large. Often, reference to scientific method is used in ways that convey either the legend of a single, universal method characteristic of all science, or grants to a particular method or set of methods privilege as a special ‘gold standard’, often with reference to particular philosophers to vindicate the claims. Discourse on scientific method also typically arises when there is a need to distinguish between science and other activities, or for justifying the special status conveyed to science. In these areas, the philosophical attempts at identifying a set of methods characteristic for scientific endeavors are closely related to the philosophy of science’s classical problem of demarcation (see the entry on science and pseudo-science ) and to the philosophical analysis of the social dimension of scientific knowledge and the role of science in democratic society.

One of the settings in which the legend of a single, universal scientific method has been particularly strong is science education (see, e.g., Bauer 1992; McComas 1996; Wivagg & Allchin 2002). [ 5 ] Often, ‘the scientific method’ is presented in textbooks and educational web pages as a fixed four or five step procedure starting from observations and description of a phenomenon and progressing over formulation of a hypothesis which explains the phenomenon, designing and conducting experiments to test the hypothesis, analyzing the results, and ending with drawing a conclusion. Such references to a universal scientific method can be found in educational material at all levels of science education (Blachowicz 2009), and numerous studies have shown that the idea of a general and universal scientific method often form part of both students’ and teachers’ conception of science (see, e.g., Aikenhead 1987; Osborne et al. 2003). In response, it has been argued that science education need to focus more on teaching about the nature of science, although views have differed on whether this is best done through student-led investigations, contemporary cases, or historical cases (Allchin, Andersen & Nielsen 2014)

Although occasionally phrased with reference to the H-D method, important historical roots of the legend in science education of a single, universal scientific method are the American philosopher and psychologist Dewey’s account of inquiry in How We Think (1910) and the British mathematician Karl Pearson’s account of science in Grammar of Science (1892). On Dewey’s account, inquiry is divided into the five steps of

(i) a felt difficulty, (ii) its location and definition, (iii) suggestion of a possible solution, (iv) development by reasoning of the bearing of the suggestions, (v) further observation and experiment leading to its acceptance or rejection. (Dewey 1910: 72)

Similarly, on Pearson’s account, scientific investigations start with measurement of data and observation of their correction and sequence from which scientific laws can be discovered with the aid of creative imagination. These laws have to be subject to criticism, and their final acceptance will have equal validity for “all normally constituted minds”. Both Dewey’s and Pearson’s accounts should be seen as generalized abstractions of inquiry and not restricted to the realm of science—although both Dewey and Pearson referred to their respective accounts as ‘the scientific method’.

Occasionally, scientists make sweeping statements about a simple and distinct scientific method, as exemplified by Feynman’s simplified version of a conjectures and refutations method presented, for example, in the last of his 1964 Cornell Messenger lectures. [ 6 ] However, just as often scientists have come to the same conclusion as recent philosophy of science that there is not any unique, easily described scientific method. For example, the physicist and Nobel Laureate Weinberg described in the paper “The Methods of Science … And Those By Which We Live” (1995) how

The fact that the standards of scientific success shift with time does not only make the philosophy of science difficult; it also raises problems for the public understanding of science. We do not have a fixed scientific method to rally around and defend. (1995: 8)

Interview studies with scientists on their conception of method shows that scientists often find it hard to figure out whether available evidence confirms their hypothesis, and that there are no direct translations between general ideas about method and specific strategies to guide how research is conducted (Schickore & Hangel 2019, Hangel & Schickore 2017)

Reference to the scientific method has also often been used to argue for the scientific nature or special status of a particular activity. Philosophical positions that argue for a simple and unique scientific method as a criterion of demarcation, such as Popperian falsification, have often attracted practitioners who felt that they had a need to defend their domain of practice. For example, references to conjectures and refutation as the scientific method are abundant in much of the literature on complementary and alternative medicine (CAM)—alongside the competing position that CAM, as an alternative to conventional biomedicine, needs to develop its own methodology different from that of science.

Also within mainstream science, reference to the scientific method is used in arguments regarding the internal hierarchy of disciplines and domains. A frequently seen argument is that research based on the H-D method is superior to research based on induction from observations because in deductive inferences the conclusion follows necessarily from the premises. (See, e.g., Parascandola 1998 for an analysis of how this argument has been made to downgrade epidemiology compared to the laboratory sciences.) Similarly, based on an examination of the practices of major funding institutions such as the National Institutes of Health (NIH), the National Science Foundation (NSF) and the Biomedical Sciences Research Practices (BBSRC) in the UK, O’Malley et al. (2009) have argued that funding agencies seem to have a tendency to adhere to the view that the primary activity of science is to test hypotheses, while descriptive and exploratory research is seen as merely preparatory activities that are valuable only insofar as they fuel hypothesis-driven research.

In some areas of science, scholarly publications are structured in a way that may convey the impression of a neat and linear process of inquiry from stating a question, devising the methods by which to answer it, collecting the data, to drawing a conclusion from the analysis of data. For example, the codified format of publications in most biomedical journals known as the IMRAD format (Introduction, Method, Results, Analysis, Discussion) is explicitly described by the journal editors as “not an arbitrary publication format but rather a direct reflection of the process of scientific discovery” (see the so-called “Vancouver Recommendations”, ICMJE 2013: 11). However, scientific publications do not in general reflect the process by which the reported scientific results were produced. For example, under the provocative title “Is the scientific paper a fraud?”, Medawar argued that scientific papers generally misrepresent how the results have been produced (Medawar 1963/1996). Similar views have been advanced by philosophers, historians and sociologists of science (Gilbert 1976; Holmes 1987; Knorr-Cetina 1981; Schickore 2008; Suppe 1998) who have argued that scientists’ experimental practices are messy and often do not follow any recognizable pattern. Publications of research results, they argue, are retrospective reconstructions of these activities that often do not preserve the temporal order or the logic of these activities, but are instead often constructed in order to screen off potential criticism (see Schickore 2008 for a review of this work).

Philosophical positions on the scientific method have also made it into the court room, especially in the US where judges have drawn on philosophy of science in deciding when to confer special status to scientific expert testimony. A key case is Daubert vs Merrell Dow Pharmaceuticals (92–102, 509 U.S. 579, 1993). In this case, the Supreme Court argued in its 1993 ruling that trial judges must ensure that expert testimony is reliable, and that in doing this the court must look at the expert’s methodology to determine whether the proffered evidence is actually scientific knowledge. Further, referring to works of Popper and Hempel the court stated that

ordinarily, a key question to be answered in determining whether a theory or technique is scientific knowledge … is whether it can be (and has been) tested. (Justice Blackmun, Daubert v. Merrell Dow Pharmaceuticals; see Other Internet Resources for a link to the opinion)

But as argued by Haack (2005a,b, 2010) and by Foster & Hubner (1999), by equating the question of whether a piece of testimony is reliable with the question whether it is scientific as indicated by a special methodology, the court was producing an inconsistent mixture of Popper’s and Hempel’s philosophies, and this has later led to considerable confusion in subsequent case rulings that drew on the Daubert case (see Haack 2010 for a detailed exposition).

The difficulties around identifying the methods of science are also reflected in the difficulties of identifying scientific misconduct in the form of improper application of the method or methods of science. One of the first and most influential attempts at defining misconduct in science was the US definition from 1989 that defined misconduct as

fabrication, falsification, plagiarism, or other practices that seriously deviate from those that are commonly accepted within the scientific community . (Code of Federal Regulations, part 50, subpart A., August 8, 1989, italics added)

However, the “other practices that seriously deviate” clause was heavily criticized because it could be used to suppress creative or novel science. For example, the National Academy of Science stated in their report Responsible Science (1992) that it

wishes to discourage the possibility that a misconduct complaint could be lodged against scientists based solely on their use of novel or unorthodox research methods. (NAS: 27)

This clause was therefore later removed from the definition. For an entry into the key philosophical literature on conduct in science, see Shamoo & Resnick (2009).

The question of the source of the success of science has been at the core of philosophy since the beginning of modern science. If viewed as a matter of epistemology more generally, scientific method is a part of the entire history of philosophy. Over that time, science and whatever methods its practitioners may employ have changed dramatically. Today, many philosophers have taken up the banners of pluralism or of practice to focus on what are, in effect, fine-grained and contextually limited examinations of scientific method. Others hope to shift perspectives in order to provide a renewed general account of what characterizes the activity we call science.

One such perspective has been offered recently by Hoyningen-Huene (2008, 2013), who argues from the history of philosophy of science that after three lengthy phases of characterizing science by its method, we are now in a phase where the belief in the existence of a positive scientific method has eroded and what has been left to characterize science is only its fallibility. First was a phase from Plato and Aristotle up until the 17 th century where the specificity of scientific knowledge was seen in its absolute certainty established by proof from evident axioms; next was a phase up to the mid-19 th century in which the means to establish the certainty of scientific knowledge had been generalized to include inductive procedures as well. In the third phase, which lasted until the last decades of the 20 th century, it was recognized that empirical knowledge was fallible, but it was still granted a special status due to its distinctive mode of production. But now in the fourth phase, according to Hoyningen-Huene, historical and philosophical studies have shown how “scientific methods with the characteristics as posited in the second and third phase do not exist” (2008: 168) and there is no longer any consensus among philosophers and historians of science about the nature of science. For Hoyningen-Huene, this is too negative a stance, and he therefore urges the question about the nature of science anew. His own answer to this question is that “scientific knowledge differs from other kinds of knowledge, especially everyday knowledge, primarily by being more systematic” (Hoyningen-Huene 2013: 14). Systematicity can have several different dimensions: among them are more systematic descriptions, explanations, predictions, defense of knowledge claims, epistemic connectedness, ideal of completeness, knowledge generation, representation of knowledge and critical discourse. Hence, what characterizes science is the greater care in excluding possible alternative explanations, the more detailed elaboration with respect to data on which predictions are based, the greater care in detecting and eliminating sources of error, the more articulate connections to other pieces of knowledge, etc. On this position, what characterizes science is not that the methods employed are unique to science, but that the methods are more carefully employed.

Another, similar approach has been offered by Haack (2003). She sets off, similar to Hoyningen-Huene, from a dissatisfaction with the recent clash between what she calls Old Deferentialism and New Cynicism. The Old Deferentialist position is that science progressed inductively by accumulating true theories confirmed by empirical evidence or deductively by testing conjectures against basic statements; while the New Cynics position is that science has no epistemic authority and no uniquely rational method and is merely just politics. Haack insists that contrary to the views of the New Cynics, there are objective epistemic standards, and there is something epistemologically special about science, even though the Old Deferentialists pictured this in a wrong way. Instead, she offers a new Critical Commonsensist account on which standards of good, strong, supportive evidence and well-conducted, honest, thorough and imaginative inquiry are not exclusive to the sciences, but the standards by which we judge all inquirers. In this sense, science does not differ in kind from other kinds of inquiry, but it may differ in the degree to which it requires broad and detailed background knowledge and a familiarity with a technical vocabulary that only specialists may possess.

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• Blackmun opinion , in Daubert v. Merrell Dow Pharmaceuticals (92–102), 509 U.S. 579 (1993).
• Scientific Method at philpapers. Darrell Rowbottom (ed.).
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What is the Scientific Method: How does it work and why is it important?

The scientific method is a systematic process involving steps like defining questions, forming hypotheses, conducting experiments, and analyzing data. It minimizes biases and enables replicable research, leading to groundbreaking discoveries like Einstein's theory of relativity, penicillin, and the structure of DNA. This ongoing approach promotes reason, evidence, and the pursuit of truth in science.

Updated on November 18, 2023

Beginning in elementary school, we are exposed to the scientific method and taught how to put it into practice. As a tool for learning, it prepares children to think logically and use reasoning when seeking answers to questions.

Rather than jumping to conclusions, the scientific method gives us a recipe for exploring the world through observation and trial and error. We use it regularly, sometimes knowingly in academics or research, and sometimes subconsciously in our daily lives.

In this article we will refresh our memories on the particulars of the scientific method, discussing where it comes from, which elements comprise it, and how it is put into practice. Then, we will consider the importance of the scientific method, who uses it and under what circumstances.

What is the scientific method?

The scientific method is a dynamic process that involves objectively investigating questions through observation and experimentation . Applicable to all scientific disciplines, this systematic approach to answering questions is more accurately described as a flexible set of principles than as a fixed series of steps.

The following representations of the scientific method illustrate how it can be both condensed into broad categories and also expanded to reveal more and more details of the process. These graphics capture the adaptability that makes this concept universally valuable as it is relevant and accessible not only across age groups and educational levels but also within various contexts.

Steps in the scientific method

While the scientific method is versatile in form and function, it encompasses a collection of principles that create a logical progression to the process of problem solving:

• Define a question : Constructing a clear and precise problem statement that identifies the main question or goal of the investigation is the first step. The wording must lend itself to experimentation by posing a question that is both testable and measurable.
• Gather information and resources : Researching the topic in question to find out what is already known and what types of related questions others are asking is the next step in this process. This background information is vital to gaining a full understanding of the subject and in determining the best design for experiments. 
• Form a hypothesis : Composing a concise statement that identifies specific variables and potential results, which can then be tested, is a crucial step that must be completed before any experimentation. An imperfection in the composition of a hypothesis can result in weaknesses to the entire design of an experiment.
• Perform the experiments : Testing the hypothesis by performing replicable experiments and collecting resultant data is another fundamental step of the scientific method. By controlling some elements of an experiment while purposely manipulating others, cause and effect relationships are established.
• Analyze the data : Interpreting the experimental process and results by recognizing trends in the data is a necessary step for comprehending its meaning and supporting the conclusions. Drawing inferences through this systematic process lends substantive evidence for either supporting or rejecting the hypothesis.
• Report the results : Sharing the outcomes of an experiment, through an essay, presentation, graphic, or journal article, is often regarded as a final step in this process. Detailing the project's design, methods, and results not only promotes transparency and replicability but also adds to the body of knowledge for future research.
• Retest the hypothesis : Repeating experiments to see if a hypothesis holds up in all cases is a step that is manifested through varying scenarios. Sometimes a researcher immediately checks their own work or replicates it at a future time, or another researcher will repeat the experiments to further test the hypothesis.

Where did the scientific method come from?

Oftentimes, ancient peoples attempted to answer questions about the unknown by:

• Making simple observations
• Discussing the possibilities with others deemed worthy of a debate
• Drawing conclusions based on dominant opinions and preexisting beliefs

For example, take Greek and Roman mythology. Myths were used to explain everything from the seasons and stars to the sun and death itself.

However, as societies began to grow through advancements in agriculture and language, ancient civilizations like Egypt and Babylonia shifted to a more rational analysis for understanding the natural world. They increasingly employed empirical methods of observation and experimentation that would one day evolve into the scientific method . 

In the 4th century, Aristotle, considered the Father of Science by many, suggested these elements , which closely resemble the contemporary scientific method, as part of his approach for conducting science:

• Study what others have written about the subject.
• Look for the general consensus about the subject.
• Perform a systematic study of everything even partially related to the topic.

By continuing to emphasize systematic observation and controlled experiments, scholars such as Al-Kindi and Ibn al-Haytham helped expand this concept throughout the Islamic Golden Age . 

In his 1620 treatise, Novum Organum , Sir Francis Bacon codified the scientific method, arguing not only that hypotheses must be tested through experiments but also that the results must be replicated to establish a truth. Coming at the height of the Scientific Revolution, this text made the scientific method accessible to European thinkers like Galileo and Isaac Newton who then put the method into practice.

As science modernized in the 19th century, the scientific method became more formalized, leading to significant breakthroughs in fields such as evolution and germ theory. Today, it continues to evolve, underpinning scientific progress in diverse areas like quantum mechanics, genetics, and artificial intelligence.

Why is the scientific method important?

The history of the scientific method illustrates how the concept developed out of a need to find objective answers to scientific questions by overcoming biases based on fear, religion, power, and cultural norms. This still holds true today.

By implementing this standardized approach to conducting experiments, the impacts of researchers’ personal opinions and preconceived notions are minimized. The organized manner of the scientific method prevents these and other mistakes while promoting the replicability and transparency necessary for solid scientific research.

The importance of the scientific method is best observed through its successes, for example: 

• “ Albert Einstein stands out among modern physicists as the scientist who not only formulated a theory of revolutionary significance but also had the genius to reflect in a conscious and technical way on the scientific method he was using.” Devising a hypothesis based on the prevailing understanding of Newtonian physics eventually led Einstein to devise the theory of general relativity .
• Howard Florey “Perhaps the most useful lesson which has come out of the work on penicillin has been the demonstration that success in this field depends on the development and coordinated use of technical methods.” After discovering a mold that prevented the growth of Staphylococcus bacteria, Dr. Alexander Flemimg designed experiments to identify and reproduce it in the lab, thus leading to the development of penicillin .
• James D. Watson “Every time you understand something, religion becomes less likely. Only with the discovery of the double helix and the ensuing genetic revolution have we had grounds for thinking that the powers held traditionally to be the exclusive property of the gods might one day be ours. . . .” By using wire models to conceive a structure for DNA, Watson and Crick crafted a hypothesis for testing combinations of amino acids, X-ray diffraction images, and the current research in atomic physics, resulting in the discovery of DNA’s double helix structure .

Final thoughts

As the cases exemplify, the scientific method is never truly completed, but rather started and restarted. It gave these researchers a structured process that was easily replicated, modified, and built upon. 

While the scientific method may “end” in one context, it never literally ends. When a hypothesis, design, methods, and experiments are revisited, the scientific method simply picks up where it left off. Each time a researcher builds upon previous knowledge, the scientific method is restored with the pieces of past efforts.

By guiding researchers towards objective results based on transparency and reproducibility, the scientific method acts as a defense against bias, superstition, and preconceived notions. As we embrace the scientific method's enduring principles, we ensure that our quest for knowledge remains firmly rooted in reason, evidence, and the pursuit of truth.

The AJE Team

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Science and the scientific method: Definitions and examples

Here's a look at the foundation of doing science — the scientific method.

The scientific method

Hypothesis, theory and law, a brief history of science, additional resources, bibliography.

Science is a systematic and logical approach to discovering how things in the universe work. It is also the body of knowledge accumulated through the discoveries about all the things in the universe. 

The word "science" is derived from the Latin word "scientia," which means knowledge based on demonstrable and reproducible data, according to the Merriam-Webster dictionary . True to this definition, science aims for measurable results through testing and analysis, a process known as the scientific method. Science is based on fact, not opinion or preferences. The process of science is designed to challenge ideas through research. One important aspect of the scientific process is that it focuses only on the natural world, according to the University of California, Berkeley . Anything that is considered supernatural, or beyond physical reality, does not fit into the definition of science.

When conducting research, scientists use the scientific method to collect measurable, empirical evidence in an experiment related to a hypothesis (often in the form of an if/then statement) that is designed to support or contradict a scientific theory .

"As a field biologist, my favorite part of the scientific method is being in the field collecting the data," Jaime Tanner, a professor of biology at Marlboro College, told Live Science. "But what really makes that fun is knowing that you are trying to answer an interesting question. So the first step in identifying questions and generating possible answers (hypotheses) is also very important and is a creative process. Then once you collect the data you analyze it to see if your hypothesis is supported or not."

The steps of the scientific method go something like this, according to Highline College :

• Make an observation or observations.
• Form a hypothesis — a tentative description of what's been observed, and make predictions based on that hypothesis.
• Test the hypothesis and predictions in an experiment that can be reproduced.
• Analyze the data and draw conclusions; accept or reject the hypothesis or modify the hypothesis if necessary.
• Reproduce the experiment until there are no discrepancies between observations and theory. "Replication of methods and results is my favorite step in the scientific method," Moshe Pritsker, a former post-doctoral researcher at Harvard Medical School and CEO of JoVE, told Live Science. "The reproducibility of published experiments is the foundation of science. No reproducibility — no science."

Some key underpinnings to the scientific method:

• The hypothesis must be testable and falsifiable, according to North Carolina State University . Falsifiable means that there must be a possible negative answer to the hypothesis.
• Research must involve deductive reasoning and inductive reasoning . Deductive reasoning is the process of using true premises to reach a logical true conclusion while inductive reasoning uses observations to infer an explanation for those observations.
• An experiment should include a dependent variable (which does not change) and an independent variable (which does change), according to the University of California, Santa Barbara .
• An experiment should include an experimental group and a control group. The control group is what the experimental group is compared against, according to Britannica .

The process of generating and testing a hypothesis forms the backbone of the scientific method. When an idea has been confirmed over many experiments, it can be called a scientific theory. While a theory provides an explanation for a phenomenon, a scientific law provides a description of a phenomenon, according to The University of Waikato . One example would be the law of conservation of energy, which is the first law of thermodynamics that says that energy can neither be created nor destroyed. 

A law describes an observed phenomenon, but it doesn't explain why the phenomenon exists or what causes it. "In science, laws are a starting place," said Peter Coppinger, an associate professor of biology and biomedical engineering at the Rose-Hulman Institute of Technology. "From there, scientists can then ask the questions, 'Why and how?'"

Laws are generally considered to be without exception, though some laws have been modified over time after further testing found discrepancies. For instance, Newton's laws of motion describe everything we've observed in the macroscopic world, but they break down at the subatomic level.

This does not mean theories are not meaningful. For a hypothesis to become a theory, scientists must conduct rigorous testing, typically across multiple disciplines by separate groups of scientists. Saying something is "just a theory" confuses the scientific definition of "theory" with the layperson's definition. To most people a theory is a hunch. In science, a theory is the framework for observations and facts, Tanner told Live Science.

The earliest evidence of science can be found as far back as records exist. Early tablets contain numerals and information about the solar system , which were derived by using careful observation, prediction and testing of those predictions. Science became decidedly more "scientific" over time, however.

1200s: Robert Grosseteste developed the framework for the proper methods of modern scientific experimentation, according to the Stanford Encyclopedia of Philosophy. His works included the principle that an inquiry must be based on measurable evidence that is confirmed through testing.

1400s: Leonardo da Vinci began his notebooks in pursuit of evidence that the human body is microcosmic. The artist, scientist and mathematician also gathered information about optics and hydrodynamics.

1500s: Nicolaus Copernicus advanced the understanding of the solar system with his discovery of heliocentrism. This is a model in which Earth and the other planets revolve around the sun, which is the center of the solar system.

1600s: Johannes Kepler built upon those observations with his laws of planetary motion. Galileo Galilei improved on a new invention, the telescope, and used it to study the sun and planets. The 1600s also saw advancements in the study of physics as Isaac Newton developed his laws of motion.

1700s: Benjamin Franklin discovered that lightning is electrical. He also contributed to the study of oceanography and meteorology. The understanding of chemistry also evolved during this century as Antoine Lavoisier, dubbed the father of modern chemistry , developed the law of conservation of mass.

1800s: Milestones included Alessandro Volta's discoveries regarding electrochemical series, which led to the invention of the battery. John Dalton also introduced atomic theory, which stated that all matter is composed of atoms that combine to form molecules. The basis of modern study of genetics advanced as Gregor Mendel unveiled his laws of inheritance. Later in the century, Wilhelm Conrad Röntgen discovered X-rays , while George Ohm's law provided the basis for understanding how to harness electrical charges.

1900s: The discoveries of Albert Einstein , who is best known for his theory of relativity, dominated the beginning of the 20th century. Einstein's theory of relativity is actually two separate theories. His special theory of relativity, which he outlined in a 1905 paper, " The Electrodynamics of Moving Bodies ," concluded that time must change according to the speed of a moving object relative to the frame of reference of an observer. His second theory of general relativity, which he published as " The Foundation of the General Theory of Relativity ," advanced the idea that matter causes space to curve.

In 1952, Jonas Salk developed the polio vaccine , which reduced the incidence of polio in the United States by nearly 90%, according to Britannica . The following year, James D. Watson and Francis Crick discovered the structure of DNA , which is a double helix formed by base pairs attached to a sugar-phosphate backbone, according to the National Human Genome Research Institute .

2000s: The 21st century saw the first draft of the human genome completed, leading to a greater understanding of DNA. This advanced the study of genetics, its role in human biology and its use as a predictor of diseases and other disorders, according to the National Human Genome Research Institute .

• This video from City University of New York delves into the basics of what defines science.
• Learn about what makes science science in this book excerpt from Washington State University .
• This resource from the University of Michigan — Flint explains how to design your own scientific study.

Merriam-Webster Dictionary, Scientia. 2022. https://www.merriam-webster.com/dictionary/scientia

University of California, Berkeley, "Understanding Science: An Overview." 2022. ​​ https://undsci.berkeley.edu/article/0_0_0/intro_01  

Highline College, "Scientific method." July 12, 2015. https://people.highline.edu/iglozman/classes/astronotes/scimeth.htm  

North Carolina State University, "Science Scripts." https://projects.ncsu.edu/project/bio183de/Black/science/science_scripts.html  

University of California, Santa Barbara. "What is an Independent variable?" October 31,2017. http://scienceline.ucsb.edu/getkey.php?key=6045  

Encyclopedia Britannica, "Control group." May 14, 2020. https://www.britannica.com/science/control-group  

The University of Waikato, "Scientific Hypothesis, Theories and Laws." https://sci.waikato.ac.nz/evolution/Theories.shtml  

Stanford Encyclopedia of Philosophy, Robert Grosseteste. May 3, 2019. https://plato.stanford.edu/entries/grosseteste/  

Encyclopedia Britannica, "Jonas Salk." October 21, 2021. https://www.britannica.com/ biography /Jonas-Salk

National Human Genome Research Institute, "​Phosphate Backbone." https://www.genome.gov/genetics-glossary/Phosphate-Backbone  

National Human Genome Research Institute, "What is the Human Genome Project?" https://www.genome.gov/human-genome-project/What  

‌ Live Science contributor Ashley Hamer updated this article on Jan. 16, 2022.

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Steps of the Scientific Method 2

The scientific method is a system scientists and other people use to ask and answer questions about the natural world. In a nutshell, the scientific method works by making observations, asking a question or identifying a problem, and then designing and analyzing an experiment to test a prediction of what you expect will happen. It’s a powerful analytical tool because once you draw conclusions, you may be able to answer a question and make predictions about future events.

These are the steps of the scientific method:

• Make observations.

Sometimes this step is omitted in the list, but you always make observations before asking a question, whether you recognize it or not. You always have some background information about a topic. However, it’s a good idea to be systematic about your observations and to record them in a lab book or another way. Often, these initial observations can help you identify a question. Later on, this information may help you decide on another area of investigation of a topic.

• Ask a question, identify a problem, or state an objective.

There are various forms of this step. Sometimes you may want to state an objective and a problem and then phrase it in the form of a question. The reason it’s good to state a question is because it’s easiest to design an experiment to answer a question. A question helps you form a hypothesis, which focuses your study.

• Research the topic.

You should conduct background research on your topic to learn as much as you can about it. This can occur both before and after you state an objective and form a hypothesis. In fact, you may find yourself researching the topic throughout the entire process.

• Formulate a hypothesis.

A hypothesis is a formal prediction. There are two forms of a hypothesis that are particularly easy to test. One is to state the hypothesis as an “if, then” statement. An example of an if-then hypothesis is: “If plants are grown under red light, then they will be taller than plants grown under white light.” Another good type of hypothesis is what is called a “ null hypothesis ” or “no difference” hypothesis. An example of a null hypothesis is: “There is no difference in the rate of growth of plants grown under red light compared with plants grown under white light.”

• Design and perform an experiment to test the hypothesis.

Once you have a hypothesis, you need to find a way to test it. This involves an experiment . There are many ways to set up an experiment. A basic experiment contains variables, which are factors you can measure. The two main variables are the independent variable (the one you control or change) and the dependent variable (the one you measure to see if it is affected when you change the independent variable).

• Record and analyze the data you obtain from the experiment.

It’s a good idea to record notes alongside your data, stating anything unusual or unexpected. Once you have the data, draw a chart, table, or graph to present your results. Next, analyze the results to understand what it all means.

• Determine whether you accept or reject the hypothesis.

Do the results support the hypothesis or not? Keep in mind, it’s okay if the hypothesis is not supported, especially if you are testing a null hypothesis. Sometimes excluding an explanation answers your question! There is no “right” or “wrong” here. However, if you obtain an unexpected result, you might want to perform another experiment.

• Draw a conclusion and report the results of the experiment.

What good is knowing something if you keep it to yourself? You should report the outcome of the experiment, even if it’s just in a notebook. What did you learn from the experiment?

How Many Steps Are There?

You may be asked to list the 5 steps of the scientific method or the 6 steps of the method or some other number. There are different ways of grouping together the steps outlined here, so it’s a good idea to learn the way an instructor wants you to list the steps. No matter how many steps there are, the order is always the same.

Related Posts

2 thoughts on “ steps of the scientific method ”.

You raise a valid point, but peer review has its limitations. Consider the case of Galileo, for example.

That’s a good point too. But that was a rare limitation due to religion, and scientific consensus prevailed in the end. It’s nowhere near a reason to doubt scientific consensus in general. I’m thinking about issues such as climate change where so many people are skeptical despite 97% consensus among climate scientists. I was just surprised to see that this is not included as an important part of the process.

Comments are closed.

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2.1: The Scientific Method

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Hypothesis Testing and The scientific Method

The scientific method is a process of research with defined steps that include data collection and careful observation. The scientific method was used even in ancient times, but it was first documented by England’s Sir Francis Bacon (1561–1626) (Figure \(\PageIndex{5}\)), who set up inductive methods for scientific inquiry.

Observation

Scientific advances begin with observations . This involves noticing a pattern, either directly or indirectly from the literature. An example of a direct observation is noticing that there have been a lot of toads in your yard ever since you turned on the sprinklers, where as an indirect observation would be reading a scientific study reporting high densities of toads in urban areas with watered lawns.

During the Vietnam War (figure \(\PageIndex{6}\)), press reports from North Vietnam documented an increasing rate of birth defects. While this credibility of this information was initially questioned by the U.S., it evoked questions about what could be causing these birth defects. Furthermore, increased incidence of certain cancers and other diseases later emerged in Vietnam veterans who had returned to the U.S. This leads us to the next step of the scientific method, the question.

Figure \(\PageIndex{6}\): A map of Vietnam 1954-1975. Image from Bureau of Public Affairs U.S. Government Printing Office (public domain).

The question step of the scientific method is simply asking, what explains the observed pattern? Multiple questions can stem from a single observation. Scientists and the public began to ask, what is causing the birth defects in Vietnam and diseases in Vietnam veterans? Could it be associated with the widespread military use of the herbicide Agent Orange to clear the forests (figure \(\PageIndex{7-8}\)), which helped identify enemies more easily?

Figure \(\PageIndex{7}\): Agent Orange drums in Vietnam. Image by U.S. Government (public domain).

Figure \(\PageIndex{8}\): A healthy mangrove forest (top), and another forest after application of Agent Orange. Image by unknown author (public domain).

Hypothesis and Prediction

The hypothesis is the expected answer to the question. The best hypotheses state the proposed direction of the effect (increases, decreases, etc.) and explain why the hypothesis could be true.

• OK hypothesis: Agent Orange influences rates of birth defects and disease.
• Better hypothesis: Agent Orange increases the incidence of birth defects and disease.
• Best hypothesis: Agent Orange increases the incidence of birth defects and disease because these health problems have been frequently reported by individuals exposed to this herbicide.

If two or more hypotheses meet this standard, the simpler one is preferred.

Predictions stem from the hypothesis. The prediction explains what results would support hypothesis. The prediction is more specific than the hypothesis because it references the details of the experiment. For example, "If Agent Orange causes health problems, then mice experimentally exposed to TCDD, a contaminant of Agent Orange, during development will have more frequent birth defects than control mice" (figure \(\PageIndex{9}\)).

Figure \(\PageIndex{9}\): The chemical structure of TCDD (2,3,7,8-tetrachlorodibenzo-p-dioxin), which is produced when synthesizing the chemicals in Agent Orange. It contaminates Agent Orange at low but harmful concentrations. Image by Emeldir (public domain).

Hypotheses and predictions must be testable to ensure that it is valid. For example, a hypothesis that depends on what a bear thinks is not testable, because it can never be known what a bear thinks. It should also be falsifiable , meaning that they have the capacity to be tested and demonstrated to be untrue. An example of an unfalsifiable hypothesis is “Botticelli’s Birth of Venus is beautiful.” There is no experiment that might show this statement to be false. To test a hypothesis, a researcher will conduct one or more experiments designed to eliminate one or more of the hypotheses. This is important. A hypothesis can be disproven, or eliminated, but it can never be proven. Science does not deal in proofs like mathematics. If an experiment fails to disprove a hypothesis, then we find support for that explanation, but this is not to say that down the road a better explanation will not be found, or a more carefully designed experiment will be found to falsify the hypothesis.

Hypotheses are tentative explanations and are different from scientific theories. A scientific theory is a widely-accepted, thoroughly tested and confirmed explanation for a set of observations or phenomena. Scientific theory is the foundation of scientific knowledge. In addition, in many scientific disciplines (less so in biology) there are scientific laws , often expressed in mathematical formulas, which describe how elements of nature will behave under certain specific conditions, but they do not offer explanations for why they occur.

Design an Experiment

Next, a scientific study (experiment) is planned to test the hypothesis and determine whether the results match the predictions. Each experiment will have one or more variables. The explanatory variable is what scientists hypothesize might be causing something else. In a manipulative experiment (see below), the explanatory variable is manipulated by the scientist. The response variable is the response, the variable ultimately measured in the study. Controlled variables (confounding factors) might affect the response variable, but they are not the focus of the study. Scientist attempt to standardize the controlled variables so that they do not influence the results. In our previous example, exposure to Agent Orange is the explanatory variable. It is hypothesized to cause a change in health (likelihood of having children with birth defects or developing a disease), the response variable. Many other things could affect health, including diet, exercise, and family history. These are the controlled variables.

There are two main types of scientific studies: experimental studies (manipulative experiments) and observational studies.

In a manipulative experiment , the explanatory variable is altered by the scientists, who then observe the response. In other words, the scientists apply a treatment . An example would be exposing developing mice to TCDD and comparing the rate of birth defects to a control group. The control group is group of test subjects that are as similar as possible to all other test subjects, with the exception that they don’t receive the experimental treatment (those that do receive it are known as the experimental, treatment, or test group ). The purpose of the control group is to establish what the dependent variable would be under normal conditions, in the absence of the experimental treatment. It serves as a baseline to which the test group can be compared. In this example, the control group would contain mice that were not exposed to TCDD but were otherwise handled the same way as the other mice (figure \(\PageIndex{10}\))

Figure \(\PageIndex{10}\): Laboratory mice. In a proper scientific study, the treatment would be applied to multiple mice. Another group of mice would not receive the treatment (the control group). Image by Aaron Logan ( CC-BY ).

In an observational study , scientists examine multiple samples with and without the presumed cause. An example would be monitoring the health of veterans who had varying levels of exposure to Agent Orange.

Scientific studies contain many replicates. Multiple samples ensure that any observed pattern is due to the treatment rather than naturally occurring differences between individuals. A scientific study should also be repeatable , meaning that if it is conducted again, following the same procedure, it should reproduce the same general results. Additionally, multiple studies will ultimately test the same hypothesis.

Finally, the data are collected and the results are analyzed. As described in the Math Blast chapter, statistics can be used to describe the data and summarize data. They also provide a criterion for deciding whether the pattern in the data is strong enough to support the hypothesis.

The manipulative experiment in our example found that mice exposed to high levels of 2,4,5-T (a component of Agent Orange) or TCDD (a contaminant found in Agent Orange) during development had a cleft palate birth defect more frequently than control mice (figure \(\PageIndex{11}\)). Mice embryos were also more likely to die when exposed to TCDD compared to controls.

Figure \(\PageIndex{11}\): Cleft lip and palate, a birth defect in which these structures are split. Image by James Heilman, MD ( CC-BY-SA ).

An observational study found that self-reported exposure to Agent Orange was positively correlated with incidence of multiple diseases in Korean veterans of the Vietnam War, including various cancers, diseases of the cardiovascular and nervous systems, skin diseases, and psychological disorders. Note that a positive correlation simply means that the independent and dependent variables both increase or decrease together, but further data, such as the evidence provided by manipulative experiments is needed to document a cause-and-effect relationship . (A negative correlation occurs when one variable increases as the other decreases.)

Lastly, scientists make a conclusion regarding whether the data support the hypothesis. In the case of Agent Orange, the data, that mice exposed to TCDD and 2,4,5-T had higher frequencies of cleft palate, matches the prediction. Additionally, veterans exposed to Agent Orange had higher rates of certain diseases, further supporting the hypothesis. We can thus accept the hypothesis that Agent Orange increases the incidence of birth defects and disease.

Scientific Method in Practice

In practice, the scientific method is not as rigid and structured as it might first appear. Sometimes an experiment leads to conclusions that favor a change in approach; often, an experiment brings entirely new scientific questions to the puzzle. Many times, science does not operate in a linear fashion; instead, scientists continually draw inferences and make generalizations, finding patterns as their research proceeds (figure \(\PageIndex{12}\)). Even if the hypothesis was supported, scientists may still continue to test it in different ways. For example, scientists explore the impacts of Agent Orange, examining long-term health impacts as Vietnam veterans age.

Scientific findings can influence decision making. In response to evidence regarding the effect of Agent Orange on human health, compensation is now available for Vietnam veterans who were exposed to Agent Orange and develop certain diseases. The use of Agent Orange is also banned in the U.S. Finally, the U.S. has began cleaning sites in Vietnam that are still contaminated with TCDD.

As another simple example, an experiment might be conducted to test the hypothesis that phosphate limits the growth of algae in freshwater ponds. A series of artificial ponds are filled with water and half of them are treated by adding phosphate each week, while the other half are treated by adding a salt that is known not to be used by algae. The variable here is the phosphate (or lack of phosphate), the experimental or treatment cases are the ponds with added phosphate and the control ponds are those with something inert added, such as the salt. Just adding something is also a control against the possibility that adding extra matter to the pond has an effect. If the treated ponds show lesser growth of algae, then we have found support for our hypothesis. If they do not, then we reject our hypothesis. Be aware that rejecting one hypothesis does not determine whether or not the other hypotheses can be accepted; it simply eliminates one hypothesis that is not valid (Figure \(\PageIndex{12}\)). Using the scientific method, the hypotheses that are inconsistent with experimental data are rejected.

Institute of Medicine (US) Committee to Review the Health Effects in Vietnam Veterans of Exposure to Herbicides. Veterans and Agent Orange: Health Effects of Herbicides Used in Vietnam . Washington (DC): National Academies Press (US); 1994. 2, History of the Controversy Over the Use of Herbicides.

Neubert, D., Dillmann, I. Embryotoxic effects in mice treated with 2,4,5-trichlorophenoxyacetic acid and 2,3,7,8-tetrachlorodibenzo-p-dioxin . Naunyn-Schmiedeberg's Arch. Pharmacol. 272, 243–264 (1972).

Stellman, J. M., & Stellman, S. D. (2018). Agent Orange During the Vietnam War: The Lingering Issue of Its Civilian and Military Health Impact . American journal of public health , 108 (6), 726–728.

Yi, S. W., Ohrr, H., Hong, J. S., & Yi, J. J. (2013). Agent Orange exposure and prevalence of self-reported diseases in Korean Vietnam veterans . Journal of preventive medicine and public health = Yebang Uihakhoe chi , 46 (5), 213–225.

American Association for the Advancement of Science (AAAS). 1990. Science for All Americans. AAAS, Washington, DC.

Barnes, B. 1985. About Science. Blackwell Ltd ,London, UK.

Giere, R.N. 2005. Understanding Scientific Reasoning. 5th ed. Wadsworth Publishing, New York, NY.

Kuhn, T.S. 1996. The Structure of Scientific Revolutions. 3rd ed. University of Chicago Press, Chicago, IL.

McCain, G. and E.M. Siegal. 1982. The Game of Science. Holbrook Press Inc., Boston, MA.

Moore, J.A. 1999. Science as a Way of Knowing. Harvard University Press, Boston, MA.

Popper, K. 1979. Objective Knowledge: An Evolutionary Approach. Clarendon Press, Oxford, UK.

Raven, P.H., G.B. Johnson, K.A. Mason, and J. Losos. 2013. Biology. 10th ed. McGraw-Hill, Columbus, OH.

Silver, B.L. 2000. The Ascent of Science. Oxford University Press, Oxford, UK.

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• Modified by Kyle Whittinghill (University of Pittsburgh)

Samantha Fowler (Clayton State University), Rebecca Roush (Sandhills Community College), James Wise (Hampton University). Original content by OpenStax (CC BY 4.0; Access for free at https://cnx.org/contents/b3c1e1d2-83...4-e119a8aafbdd ).

• Modified by Melissa Ha
• 1.2: The Process of Science by OpenStax , is licensed CC BY
• What is Science? from An Introduction to Geology by Chris Johnson et al. (licensed under CC-BY-NC-SA )
• The Process of Science from Environmental Biology by Matthew R. Fisher (licensed under CC-BY )
• Scientific Methods from Biology by John W. Kimball (licensed under CC-BY )
• Scientific Papers from Biology by John W. Kimball ( CC-BY )
• Environmental Science: A Canadian perspective by Bill Freedman Chapter 2: Science as a Way of Understanding the Natural World

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Scientific Method Steps in Psychology Research

Steps, Uses, and Key Terms

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Emily is a board-certified science editor who has worked with top digital publishing brands like Voices for Biodiversity, Study.com, GoodTherapy, Vox, and Verywell.

Verywell / Theresa Chiechi

How do researchers investigate psychological phenomena? They utilize a process known as the scientific method to study different aspects of how people think and behave.

When conducting research, the scientific method steps to follow are:

• Observe what you want to investigate
• Ask a research question and make predictions
• Test the hypothesis and collect data
• Examine the results and draw conclusions
• Report and share the results 

This process not only allows scientists to investigate and understand different psychological phenomena but also provides researchers and others a way to share and discuss the results of their studies.

Generally, there are five main steps in the scientific method, although some may break down this process into six or seven steps. An additional step in the process can also include developing new research questions based on your findings.

What Is the Scientific Method?

What is the scientific method and how is it used in psychology?

The scientific method consists of five steps. It is essentially a step-by-step process that researchers can follow to determine if there is some type of relationship between two or more variables.

By knowing the steps of the scientific method, you can better understand the process researchers go through to arrive at conclusions about human behavior.

Scientific Method Steps

While research studies can vary, these are the basic steps that psychologists and scientists use when investigating human behavior.

The following are the scientific method steps:

Step 1. Make an Observation

Before a researcher can begin, they must choose a topic to study. Once an area of interest has been chosen, the researchers must then conduct a thorough review of the existing literature on the subject. This review will provide valuable information about what has already been learned about the topic and what questions remain to be answered.

A literature review might involve looking at a considerable amount of written material from both books and academic journals dating back decades.

The relevant information collected by the researcher will be presented in the introduction section of the final published study results. This background material will also help the researcher with the first major step in conducting a psychology study: formulating a hypothesis.

Step 2. Ask a Question

Once a researcher has observed something and gained some background information on the topic, the next step is to ask a question. The researcher will form a hypothesis, which is an educated guess about the relationship between two or more variables

For example, a researcher might ask a question about the relationship between sleep and academic performance: Do students who get more sleep perform better on tests at school?

In order to formulate a good hypothesis, it is important to think about different questions you might have about a particular topic.

You should also consider how you could investigate the causes. Falsifiability is an important part of any valid hypothesis. In other words, if a hypothesis was false, there needs to be a way for scientists to demonstrate that it is false.

Step 3. Test Your Hypothesis and Collect Data

Once you have a solid hypothesis, the next step of the scientific method is to put this hunch to the test by collecting data. The exact methods used to investigate a hypothesis depend on exactly what is being studied. There are two basic forms of research that a psychologist might utilize: descriptive research or experimental research.

Descriptive research is typically used when it would be difficult or even impossible to manipulate the variables in question. Examples of descriptive research include case studies, naturalistic observation , and correlation studies. Phone surveys that are often used by marketers are one example of descriptive research.

Correlational studies are quite common in psychology research. While they do not allow researchers to determine cause-and-effect, they do make it possible to spot relationships between different variables and to measure the strength of those relationships. 

Experimental research is used to explore cause-and-effect relationships between two or more variables. This type of research involves systematically manipulating an independent variable and then measuring the effect that it has on a defined dependent variable .

One of the major advantages of this method is that it allows researchers to actually determine if changes in one variable actually cause changes in another.

While psychology experiments are often quite complex, a simple experiment is fairly basic but does allow researchers to determine cause-and-effect relationships between variables. Most simple experiments use a control group (those who do not receive the treatment) and an experimental group (those who do receive the treatment).

Step 4. Examine the Results and Draw Conclusions

Once a researcher has designed the study and collected the data, it is time to examine this information and draw conclusions about what has been found.  Using statistics , researchers can summarize the data, analyze the results, and draw conclusions based on this evidence.

So how does a researcher decide what the results of a study mean? Not only can statistical analysis support (or refute) the researcher’s hypothesis; it can also be used to determine if the findings are statistically significant.

When results are said to be statistically significant, it means that it is unlikely that these results are due to chance.

Based on these observations, researchers must then determine what the results mean. In some cases, an experiment will support a hypothesis, but in other cases, it will fail to support the hypothesis.

So what happens if the results of a psychology experiment do not support the researcher's hypothesis? Does this mean that the study was worthless?

Just because the findings fail to support the hypothesis does not mean that the research is not useful or informative. In fact, such research plays an important role in helping scientists develop new questions and hypotheses to explore in the future.

After conclusions have been drawn, the next step is to share the results with the rest of the scientific community. This is an important part of the process because it contributes to the overall knowledge base and can help other scientists find new research avenues to explore.

Step 5. Report the Results

The final step in a psychology study is to report the findings. This is often done by writing up a description of the study and publishing the article in an academic or professional journal. The results of psychological studies can be seen in peer-reviewed journals such as  Psychological Bulletin , the  Journal of Social Psychology ,  Developmental Psychology , and many others.

The structure of a journal article follows a specified format that has been outlined by the  American Psychological Association (APA) . In these articles, researchers:

• Provide a brief history and background on previous research
• Present their hypothesis
• Identify who participated in the study and how they were selected
• Provide operational definitions for each variable
• Describe the measures and procedures that were used to collect data
• Explain how the information collected was analyzed
• Discuss what the results mean

Why is such a detailed record of a psychological study so important? By clearly explaining the steps and procedures used throughout the study, other researchers can then replicate the results. The editorial process employed by academic and professional journals ensures that each article that is submitted undergoes a thorough peer review, which helps ensure that the study is scientifically sound.

Once published, the study becomes another piece of the existing puzzle of our knowledge base on that topic.

Before you begin exploring the scientific method steps, here's a review of some key terms and definitions that you should be familiar with:

• Falsifiable : The variables can be measured so that if a hypothesis is false, it can be proven false
• Hypothesis : An educated guess about the possible relationship between two or more variables
• Variable : A factor or element that can change in observable and measurable ways
• Operational definition : A full description of exactly how variables are defined, how they will be manipulated, and how they will be measured

Uses for the Scientific Method

The  goals of psychological studies  are to describe, explain, predict and perhaps influence mental processes or behaviors. In order to do this, psychologists utilize the scientific method to conduct psychological research. The scientific method is a set of principles and procedures that are used by researchers to develop questions, collect data, and reach conclusions.

Goals of Scientific Research in Psychology

Researchers seek not only to describe behaviors and explain why these behaviors occur; they also strive to create research that can be used to predict and even change human behavior.

Psychologists and other social scientists regularly propose explanations for human behavior. On a more informal level, people make judgments about the intentions, motivations , and actions of others on a daily basis.

While the everyday judgments we make about human behavior are subjective and anecdotal, researchers use the scientific method to study psychology in an objective and systematic way. The results of these studies are often reported in popular media, which leads many to wonder just how or why researchers arrived at the conclusions they did.

Examples of the Scientific Method

Now that you're familiar with the scientific method steps, it's useful to see how each step could work with a real-life example.

Say, for instance, that researchers set out to discover what the relationship is between psychotherapy and anxiety .

• Step 1. Make an observation : The researchers choose to focus their study on adults ages 25 to 40 with generalized anxiety disorder.
• Step 2. Ask a question : The question they want to answer in their study is: Do weekly psychotherapy sessions reduce symptoms in adults ages 25 to 40 with generalized anxiety disorder?
• Step 3. Test your hypothesis : Researchers collect data on participants' anxiety symptoms . They work with therapists to create a consistent program that all participants undergo. Group 1 may attend therapy once per week, whereas group 2 does not attend therapy.
• Step 4. Examine the results : Participants record their symptoms and any changes over a period of three months. After this period, people in group 1 report significant improvements in their anxiety symptoms, whereas those in group 2 report no significant changes.
• Step 5. Report the results : Researchers write a report that includes their hypothesis, information on participants, variables, procedure, and conclusions drawn from the study. In this case, they say that "Weekly therapy sessions are shown to reduce anxiety symptoms in adults ages 25 to 40."

Of course, there are many details that go into planning and executing a study such as this. But this general outline gives you an idea of how an idea is formulated and tested, and how researchers arrive at results using the scientific method.

Erol A. How to conduct scientific research ? Noro Psikiyatr Ars . 2017;54(2):97-98. doi:10.5152/npa.2017.0120102

University of Minnesota. Psychologists use the scientific method to guide their research .

Shaughnessy, JJ, Zechmeister, EB, & Zechmeister, JS. Research Methods In Psychology . New York: McGraw Hill Education; 2015.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Scientific Method

Illustration by J.R. Bee. ThoughtCo. 

• Cell Biology
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• A.S., Nursing, Chattahoochee Technical College

The scientific method is a series of steps followed by scientific investigators to answer specific questions about the natural world. It involves making observations, formulating a hypothesis , and conducting scientific experiments . Scientific inquiry starts with an observation followed by the formulation of a question about what has been observed. The steps of the scientific method are as follows:

Observation

The first step of the scientific method involves making an observation about something that interests you. This is very important if you are doing a science project because you want your project to be focused on something that will hold your attention. Your observation can be on anything from plant movement to animal behavior, as long as it is something you really want to know more about.​ This is where you come up with the idea for your science project.

Once you've made your observation, you must formulate a question about what you have observed. Your question should tell what it is that you are trying to discover or accomplish in your experiment. When stating your question you should be as specific as possible.​ For example, if you are doing a project on plants , you may want to know how plants interact with microbes. Your question may be: Do plant spices inhibit bacterial growth ?

The hypothesis is a key component of the scientific process. A hypothesis is an idea that is suggested as an explanation for a natural event, a particular experience, or a specific condition that can be tested through definable experimentation. It states the purpose of your experiment, the variables used, and the predicted outcome of your experiment. It is important to note that a hypothesis must be testable. That means that you should be able to test your hypothesis through experimentation .​ Your hypothesis must either be supported or falsified by your experiment. An example of a good hypothesis is: If there is a relation between listening to music and heart rate, then listening to music will cause a person's resting heart rate to either increase or decrease.

Once you've developed a hypothesis, you must design and conduct an experiment that will test it. You should develop a procedure that states very clearly how you plan to conduct your experiment. It is important that you include and identify a controlled variable or dependent variable in your procedure. Controls allow us to test a single variable in an experiment because they are unchanged. We can then make observations and comparisons between our controls and our independent variables (things that change in the experiment) to develop an accurate conclusion.​

The results are where you report what happened in the experiment. That includes detailing all observations and data made during your experiment. Most people find it easier to visualize the data by charting or graphing the information.​

The final step of the scientific method is developing a conclusion. This is where all of the results from the experiment are analyzed and a determination is reached about the hypothesis. Did the experiment support or reject your hypothesis? If your hypothesis was supported, great. If not, repeat the experiment or think of ways to improve your procedure.

• Null Hypothesis Examples
• Examples of Independent and Dependent Variables
• The 10 Most Important Lab Safety Rules
• Difference Between Independent and Dependent Variables
• Six Steps of the Scientific Method
• Scientific Method Flow Chart
• What Is an Experiment? Definition and Design
• Scientific Method Lesson Plan
• How To Design a Science Fair Experiment
• Science Projects for Every Subject
• How to Do a Science Fair Project
• What Are the Elements of a Good Hypothesis?
• How to Write a Lab Report
• What Is a Hypothesis? (Science)
• Understanding Simple vs Controlled Experiments
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The scientific method and climate change: How scientists know

By Holly Shaftel, NASA's Jet Propulsion Laboratory

The scientific method is the gold standard for exploring our natural world. You might have learned about it in grade school, but here’s a quick reminder: It’s the process that scientists use to understand everything from animal behavior to the forces that shape our planet—including climate change.

“The way science works is that I go out and study something, and maybe I collect data or write equations, or I run a big computer program,” said Josh Willis, principal investigator of NASA’s Oceans Melting Greenland (OMG) mission and oceanographer at NASA’s Jet Propulsion Laboratory. “And I use it to learn something about how the world works.”

Using the scientific method, scientists have shown that humans are extremely likely the dominant cause of today’s climate change. The story goes back to the late 1800s, but in 1958, for example, Charles Keeling of the Mauna Loa Observatory in Waimea, Hawaii, started taking meticulous measurements of carbon dioxide (CO 2 ) in the atmosphere, showing the first significant evidence of rapidly rising CO 2 levels and producing the Keeling Curve climate scientists know today.

“The way science works is that I go out and study something, and maybe I collect data or write equations, or I run a big computer program, and I use it to learn something about how the world works.”- Josh Willis, NASA oceanographer and Oceans Melting Greenland principal investigator

Since then, thousands of peer-reviewed scientific papers have come to the same conclusion about climate change, telling us that human activities emit greenhouse gases into the atmosphere, raising Earth’s average temperature and bringing a range of consequences to our ecosystems.

“The weight of all of this information taken together points to the single consistent fact that humans and our activity are warming the planet,” Willis said.

The scientific method’s steps

The exact steps of the scientific method can vary by discipline, but since we have only one Earth (and no “test” Earth), climate scientists follow a few general guidelines to better understand carbon dioxide levels, sea level rise, global temperature and more.

• Form a hypothesis (a statement that an experiment can test)
• Make observations (conduct experiments and gather data)
• Analyze and interpret the data
• Draw conclusions
• Publish results that can be validated with further experiments (rinse and repeat)

As you can see, the scientific method is iterative (repetitive), meaning that climate scientists are constantly making new discoveries about the world based on the building blocks of scientific knowledge.

“The weight of all of this information taken together points to the single consistent fact that humans and our activity are warming the planet." - Josh Willis, NASA oceanographer and Oceans Melting Greenland principal investigator

The scientific method at work.

How does the scientific method work in the real world of climate science? Let’s take NASA’s Oceans Melting Greenland (OMG) campaign, a multi-year survey of Greenland’s ice melt that’s paving the way for improved sea level rise estimates, as an example.

• Form a hypothesis OMG hypothesizes that the oceans are playing a major role in Greenland ice loss.
• Make observations Over a five-year period, OMG will survey Greenland by air and ship to collect ocean temperature and salinity (saltiness) data and take ice thinning measurements to help climate scientists better understand how the ice and warming ocean interact with each other. OMG will also collect data on the sea floor’s shape and depth, which determines how much warm water can reach any given glacier.
• Analyze and interpret data As the OMG crew and scientists collect data around 27,000 miles (over 43,000 kilometers) of Greenland coastline over that five-year period, each year scientists will analyze the data to see how much the oceans warmed or cooled and how the ice changed in response.
• Draw conclusions In one OMG study , scientists discovered that many Greenland glaciers extend deeper (some around 1,000 feet, or about 300 meters) beneath the ocean’s surface than once thought, making them quite vulnerable to the warming ocean. They also discovered that Greenland’s west coast is generally more vulnerable than its east coast.
• Publish results Scientists like Willis write up the results, send in the paper for peer review (a process in which other experts in the field anonymously critique the submission), and then those peers determine whether the information is correct and valuable enough to be published in an academic journal, such as Nature or Earth and Planetary Science Letters . Then it becomes another contribution to the well-substantiated body of climate change knowledge, which evolves and grows stronger as scientists gather and confirm more evidence. Other scientists can take that information further by conducting their own studies to better understand sea level rise.

All in all, the scientific method is “a way of going from observations to answers,” NASA terrestrial ecosystem scientist Erika Podest, based at JPL, said. It adds clarity to our way of thinking and shows that scientific knowledge is always evolving.

Related Terms

• Climate Change
• Climate Science
• Earth Science

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The Scientific Method: A Need for Something Better?

Here is the last part of the triptych that started with the “Perspectives” on brainstorming that was followed by the one on verbal overshadowing. I have decided to keep this for last because it deals with and in many ways attempts to debunk the use of the scientific method as the Holy Grail of research. Needless to say, the topic is controversial and will anger some.

In the “natural sciences,” advances occur through research that employs the scientific method. Just imagine trying to publish an original investigation or getting funds for a project without using it! Although research in the pure (fundamental) sciences (eg, biology, physics, and chemistry) must adhere to it, investigations pertaining to soft (a pejorative term) sciences (eg, sociology, economics, and anthropology) do not use it and yet produce valid ideas important enough to be published in peer-reviewed journals and even win Nobel Prizes.

The scientific method is better thought of as a set of “methods” or different techniques used to prove or disprove 1 or more hypotheses. A hypothesis is a proposed explanation for observed phenomena. These phenomena are, in general, empirical—that is, they are gathered by observation and/or experimentation. “Hypothesis” is a term often confused with “theory.” A theory is the end result of a previously tested hypothesis, meaning a proved set of principles that explain observed phenomena. Thus, a hypothesis is sometimes called a “working hypothesis,” to avoid this confusion. A working hypothesis needs to be proved or disproved by investigation. The entire approach employed to validate a hypothesis is more broadly called the “hypothetico-deductivism” method. Not all hypotheses are proved by empirical testing, and most of what we know and accept as truth about the economy and ancient civilizations is solely based on … just observation and thoughts. Conversely, the deep thinkers in the non-natural disciplines see many things wrong with the scientific method because it does not entirely reflect the chaotic environment that we live in—that is, the scientific method is rigid and constrained in its design and produces results that are isolated from real environments and that only address specific issues.

One of the most important features of the scientific method is its repeatability. The experiments performed to prove a working hypothesis must clearly record all details so that others may replicate them and eventually allow the hypothesis to become widely accepted. Objectivity must be used in experiments to reduce bias. “Bias” refers to the inclination to favor one perspective over others. The opposite of bias is “neutrality,” and all experiments (and their peer review) need to be devoid of bias and be neutral. In medicine, bias is also a part of conflict of interest and produces corrupt results. In medicine, conflict of interest is often due to relationships with the pharmaceutical/device industries. The American Journal of Neuroradiology ( AJNR ), as do most other serious journals, requires that contributors fill out the standard disclosure form regarding conflict of interest proposed by the International Committee of Medical Journal Editors, and it publishes these at the end of articles. 1

Like many other scientific advances, the scientific method originated in the Muslim world. About 1000 years ago, the Iraqi mathematician Ibn al-Haytham was already using it. In the Western world, the scientific method was first welcomed by astronomers such as Galileo and Kepler, and after the 17th century, its use became widespread. As we now know it, the scientific method dates only from the 1930s. The first step in the scientific method is observation from which one formulates a question. From that question, the hypothesis is generated. A hypothesis must be phrased in a way that it can be proved or disproved (“falsifiable”). The so-called “null hypothesis” represents the default position. For example, if you are trying to prove the relationship between 2 phenomena, the null hypothesis may be a statement that there is no relationship between the observed phenomena. The next step is to test the hypothesis via 1 or more experiments. The best experiments, at least in medicine, are those that are blinded and accompanied by control groups (not submitted to the same experiments). Third is the analysis of the data obtained. The results may support the working hypothesis or “falsify” (disprove) it, leading to the creation of a new hypothesis again to be tested scientifically. Not surprising, the structure of abstracts and articles published in AJNR and other scientific journals reflects the 4 steps in the scientific method (Background and Purpose, Materials and Methods, Results, and Conclusions). Another way in which our journals adhere to the scientific method is peer review—that is, every part of the article must be open to review by others who look for possible mistakes and biases. The last part of the modern scientific method is publication.

Despite its rigid structure, the scientific method still depends on the most human capabilities: creativity, imagination, and intelligence; and without these, it cannot exist. Documentation of experiments is always flawed because everything cannot be recorded. One of the most significant problems with the scientific method is the lack of importance placed on observations that lie outside of the main hypothesis (related to lateral thinking). No matter how carefully you record what you observe, if these observations are not also submitted to the method, they cannot be accepted. This is a common problem found by paleontologists who really have no way of testing their observations; yet many of their observations (primary and secondary) are accepted as valid. Also, think about the works of Sigmund Freud that led to improved understanding of psychological development and related disorders; most were based just on observations. Many argue that because the scientific method discards observations extemporaneous to it, this actually limits the growth of scientific knowledge. Because a hypothesis only reflects current knowledge, data that contradict it may be discarded only to later become important.

Because the scientific method is basically a “trial-and-error” scheme, progress is slow. In older disciplines, there may not have been enough knowledge to develop good theories, which led to the creation of bad theories that have resulted in significant delay of progress. It can also be said that progress is many times fortuitous; while one is trying to test a hypothesis, completely unexpected and often accidental results lead to new discoveries. Just imagine how many important data have been discarded because the results did not fit the initial hypothesis.

A lot of time goes into the trial-and-error phase of an experiment, so why do it when we already know perfectly well what to expect from the results? Just peruse AJNR , and most proposed hypotheses are proved true! Hypotheses proved false are never sexy, and journals are generally not interested in publishing such studies. In the scientific method, unexpected results are not trusted, while expected and understood ones are immediately trusted. The fact that we do “this” to observe “that” may be very misleading in the long run. 2 However, in reality, many controversies could have been avoided if instead of calling it “The Scientific Method,” we simply would have called it “A Scientific Method,” leaving space for development of other methods and acceptance of those used by other disciplines. Some argue that it was called “scientific” because the ones who invented it were arrogant and pretentious.

The term “science” comes from the Latin “scientia,” meaning knowledge. Aristotle equated science with reliability because it could be rationally and logically explained. Curiously, science was, for many centuries, a part of the greater discipline of philosophy. In the 14th and 15th centuries, “natural philosophy” was born; by the start of the 17th century, it had become “natural sciences.” It was during the 16th century that Francis Bacon popularized the inductive reasoning methods that would thereafter become known as the scientific method. Western reasoning is based on our faith in truth, many times absolute truth. Beginning assumptions that then become hypotheses are subjectively accepted as being true; thus, the scientific method took longer to be accepted by Eastern civilizations whose concept of truth differs from ours. It is possible that the scientific method is the greatest unifying activity of the human race. Although medicine and philosophy have been separated from each other by centuries, there is a current trend to unite both again.

The specialty of psychiatry did not become “scientific” until the widespread use of medications and therapeutic procedures offered the possibility of being examined by the scientific method. In the United States and Europe, the number of psychoanalysts has progressively declined; and most surprising, philosophers are taking their place. 3 The benefits philosophy offers are that it puts patients first, supports new models of service delivery, and reconnects researchers in different disciplines (it is the advances in neurosciences that demand answers to the more abstract questions that define a human “being”). Philosophy provides psychiatrists with much-needed generic thinking skills; and because philosophy is more widespread than psychiatry and recognizes its importance, it provides a more universal and open environment. 4 This is an example of a soft discipline merging with a hard one (medicine) for the improvement of us all. However, this is not the case in other areas.

For about 10 years, the National Science Foundation has sponsored the “Empirical Implications of Theoretical Models” initiative in political science. 5 A major complaint is that most political science literature consists of noncumulative empirical studies and very few have a “formal” component. The formal part refers to accumulation of data and use of statistics to prove or disprove an observation (thus, the use of the scientific method). For academics in political science, the problem is that some journals no longer accept publications that are based on unproven theoretic models, and this poses a significant problem to the “non-natural” sciences. 6 In this case, the social sciences try to emulate the “hard” sciences, and this may not be the best approach. These academics and others think that using the scientific method in such instances emphasizes predictions rather than ideas, focuses learning on material activities rather than on a deep understanding of a subject, and lacks epistemic framing relevant to a discipline. 7 So, is there a better approach than the scientific method?

A provocative method called “model-based inquiry” respects the precepts of the scientific method (that knowledge is testable, revisable, explanatory, conjectural, and generative). 7 While the scientific method attempts to find patterns in natural phenomena, the model-based inquiry method attempts to develop defensible explanations. This new system sees models as tools for explanations and not explanations proper and allows going beyond data; thus, new hypotheses, new concepts, and new predictions can be generated at any point along the inquiry, something not allowed within the rigidity of the traditional scientific method.

In a different approach, the National Science Foundation charged scientists, philosophers, and educators from the University of California at Berkeley to come up with a “dynamic” alternative to the scientific method. 8 The proposed method accepts input from serendipitous occurrences and emphasizes that science is a dynamic process engaging many individuals and activities. Unlike the traditional scientific method, this new one accepts data that do not fit into organized and neat conclusions. Science is about discovery, not the justifications it seems to emphasize. 9

Obviously, I am not proposing that we immediately get rid of the traditional scientific method. Until another one is proved better, it should continue to be the cornerstone of our endeavors. However, in a world where information will grow more in the next 50 years than in the past 400 years, where the Internet has 1 trillion links, where 300 billion e-mail messages are generated every day, and 200 million Tweets occur daily, ask yourself whether it is still valid to use the same scientific method that was invented nearly 400 years ago?

The Scientific Method

Introduction.

There are many scientific disciplines that address topics from medicine and astrophysics to agriculture and zoology. In each discipline, modern scientists use a process called the "Scientific Method" to advance their knowledge and understanding. This publication describes the method scientists use to conduct research and describe and explain nature, ultimately trying prove or disprove theories.

Scientists all over the world conduct research using the Scientific Method. The University of Nevada Cooperative Extension exists to provide unbiased, research-based information on topics important and relevant to society. The scientific research efforts, analyses, and subsequent information disseminated by Cooperative Extension is driven by careful review and synthesis of relevant scientific research. Cooperative Extension presents useful information based on the best science available, and today that science is based on knowledge obtained by application of the Scientific Method.

The Scientific Method – What it’s Not

The Scientific Method is a process for explaining the world we see. It is:

• Not a formula

The Scientific Method – What is it?

The Scientific Method is a process used to validate observations while minimizing observer bias. Its goal is for research to be conducted in a fair, unbiased and repeatable manner.

Long ago, people viewed the workings of nature and believed that the events and phenomena they observed were associated with the intrinsic nature of the beings or things being observed (Ackoff 1962, Wilson 1937). Today we view events and phenomena as having been caused , and science has evolved as a process to ask how and why things and events happen. Scientists seek to understand the relationships and intricacies between cause and effect in order to predict outcomes of future or similar events. To answer these questions and to help predict future happenings, scientists use the Scientific Method - a series of steps that lead to answers that accurately describe the things we observe, or at least improve our understanding of them.

The Scientific Method is not the only way, but is the best-known way to discover how and why the world works, without our knowledge being tainted by religious, political, or philosophical values. This method provides a means to formulate questions about general observations and devise theories of explanation. The approach lends itself to answering questions in fair and unbiased statements, as long as questions are posed correctly, in a hypothetical form that can be tested.

Definitions

It is important to understand three important terms before describing the Scientific Method.

This is a statement made by a researcher that is a working assumption to be tested and proven. It is something "considered true for the purpose of investigation" (Webster’s Dictionary 1995). An example might be “The earth is round.”

general principles drawn from facts that explain observations and can be used to predict new events. An example would be Newton’s theory of gravitation or Einstein’s theory of relativity. Each is based on falsifiable hypotheses of phenomenon we observe.

Falsifiable/ Null Hypothesis

to prove to be false (Webster’s Dictionary 1995). The hypothesis that is generated must be able to be tested, and either accepted or rejected. Scientists make hypotheses that they want to disprove in order that they may prove the working assumption describing the observed phenomena. This is done by declaring the statement or hypothesis as falsifiable . So, we would state the above hypothesis as “the earth is not round,” or “the earth is square” making it a working statement to be disproved.

The Scientific Method is not a formula, but rather a process with a number of sequential steps designed to create an explainable outcome that increases our knowledge base. This process is as follows:

STEP 1. Make an OBSERVATION

gather and assimilate information about an event, phenomenon, process, or an exception to a previous observation, etc.

STEP 2. Define the PROBLEM

ask questions about the observation that are relevant and testable. Define the null hypothesis to provide unbiased results.

STEP 3: Form the HYPOTHESIS

create an explanation, or educated guess, for the observation that is testable and falsifiable.

STEP 4: Conduct the EXPERIMENT

devise and perform an experiment to test the hypothesis.

STEP 5: Derive a THEORY

create a statement based in the outcome of the experiment that explains the observation(s) and predicts the likelihood of future observations.

Replication

Using the Scientific Method to answer questions about events or phenomena we observe can be repeated to fine-tune our theories. For example, if we conduct research using the Scientific Method and think we have answered a question, but different results occur the next time we make an observation, we may have to ask new questions and formulate new hypotheses that are tested by another experiment. Sometimes scientists must perform many experiments over many years or even decades using the Scientific Method to prove or disprove theories that are generated from one initial question. Numerous studies are often necessary to fully test the broad range of results that occur in order that scientists can formulate theories that truly account for the variation we see in our natural environment.

The Scientific Method – Is it worth all the effort?

Scientific knowledge can only advance when all scientists systematically use the same process to discover and disseminate new information. The advantage of all scientific research using the Scientific Method is that the experiments are repeatable by anyone, anywhere. When similar results occur in each experiment, these facts make the case for the theory stronger. If the same experiment is performed many times in many different locations, under a broad range of conditions, then the theory derived from these experiments is considered strong and widely applicable. If the questions are posed as testable hypotheses that rely on inductive reasoning and empiricism – that is, observations and data collection – then experiments can be devised to generate logical theories that explain the things we see. If we understand why the observed results occur, then we can accurately apply concepts derived from the experiment to other situations.

What do we need to consider when using the Scientific Method?

The Scientific Method requires that we ask questions and perform experiments to prove or disprove questions in ways that will lead to unbiased answers. Experiments must be well designed to provide accurate and repeatable (precise) results. If we test hypotheses correctly, then we can prove the cause of a phenomenon and determine the likelihood (probability) of the events to happen again. This provides predictive power. The Scientific Method enables us to test a hypothesis and distinguish between the correlation of two or more things happening in association with each other and the actual cause of the phenomenon we observe.

Correlation of two variables cannot explain the cause and effect of their relationship. Scientists design experiments using a number of methods to ensure the results reveal the likelihood of the observation happening (probability). Controlled experiments are used to analyze these relationships and develop cause and effect relationships. Statistical analysis is used to determine whether differences between treatments can be attributed to the treatment applied, if they are artifacts of the experimental design, or of natural variation.

In summary, the Scientific Method produces answers to questions posed in the form of a working hypothesis that enables us to derive theories about what we observe in the world around us. Its power lies in its ability to be repeated, providing unbiased answers to questions to derive theories. This information is powerful and offers opportunity to predict future events and phenomena.

Bibliography

• Ackoff, R. 1962. Scientific Method, Optimizing Applied Research Decisions. Wiley and Sons, New York, NY.
• Wilson, F. 1937. The Logic and Methodology of Science in Early Modern Thought. University of Toronto Press. Buffalo, NY.
• Committee on Science, Engineering, and Public Policy. Experimental Error. 1995. From: On Being a Scientist: Responsible Conduct in Research. Second Edition.
• The Gale Group. The Scientific Method. 2001. Gale Encyclopedia of Psychology. Second Edition.

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Case Study Research Method in Psychology

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

Case studies are in-depth investigations of a person, group, event, or community. Typically, data is gathered from various sources using several methods (e.g., observations & interviews).

The case study research method originated in clinical medicine (the case history, i.e., the patient’s personal history). In psychology, case studies are often confined to the study of a particular individual.

The information is mainly biographical and relates to events in the individual’s past (i.e., retrospective), as well as to significant events that are currently occurring in his or her everyday life.

The case study is not a research method, but researchers select methods of data collection and analysis that will generate material suitable for case studies.

Freud (1909a, 1909b) conducted very detailed investigations into the private lives of his patients in an attempt to both understand and help them overcome their illnesses.

This makes it clear that the case study is a method that should only be used by a psychologist, therapist, or psychiatrist, i.e., someone with a professional qualification.

There is an ethical issue of competence. Only someone qualified to diagnose and treat a person can conduct a formal case study relating to atypical (i.e., abnormal) behavior or atypical development.

 Famous Case Studies

• Anna O – One of the most famous case studies, documenting psychoanalyst Josef Breuer’s treatment of “Anna O” (real name Bertha Pappenheim) for hysteria in the late 1800s using early psychoanalytic theory.
• Little Hans – A child psychoanalysis case study published by Sigmund Freud in 1909 analyzing his five-year-old patient Herbert Graf’s house phobia as related to the Oedipus complex.
• Bruce/Brenda – Gender identity case of the boy (Bruce) whose botched circumcision led psychologist John Money to advise gender reassignment and raise him as a girl (Brenda) in the 1960s.
• Genie Wiley – Linguistics/psychological development case of the victim of extreme isolation abuse who was studied in 1970s California for effects of early language deprivation on acquiring speech later in life.
• Phineas Gage – One of the most famous neuropsychology case studies analyzes personality changes in railroad worker Phineas Gage after an 1848 brain injury involving a tamping iron piercing his skull.

Clinical Case Studies

• Studying the effectiveness of psychotherapy approaches with an individual patient
• Assessing and treating mental illnesses like depression, anxiety disorders, PTSD
• Neuropsychological cases investigating brain injuries or disorders

Child Psychology Case Studies

• Studying psychological development from birth through adolescence
• Cases of learning disabilities, autism spectrum disorders, ADHD
• Effects of trauma, abuse, deprivation on development

Types of Case Studies

• Explanatory case studies : Used to explore causation in order to find underlying principles. Helpful for doing qualitative analysis to explain presumed causal links.
• Exploratory case studies : Used to explore situations where an intervention being evaluated has no clear set of outcomes. It helps define questions and hypotheses for future research.
• Descriptive case studies : Describe an intervention or phenomenon and the real-life context in which it occurred. It is helpful for illustrating certain topics within an evaluation.
• Multiple-case studies : Used to explore differences between cases and replicate findings across cases. Helpful for comparing and contrasting specific cases.
• Intrinsic : Used to gain a better understanding of a particular case. Helpful for capturing the complexity of a single case.
• Collective : Used to explore a general phenomenon using multiple case studies. Helpful for jointly studying a group of cases in order to inquire into the phenomenon.

Where Do You Find Data for a Case Study?

There are several places to find data for a case study. The key is to gather data from multiple sources to get a complete picture of the case and corroborate facts or findings through triangulation of evidence. Most of this information is likely qualitative (i.e., verbal description rather than measurement), but the psychologist might also collect numerical data.

1. Primary sources

• Interviews – Interviewing key people related to the case to get their perspectives and insights. The interview is an extremely effective procedure for obtaining information about an individual, and it may be used to collect comments from the person’s friends, parents, employer, workmates, and others who have a good knowledge of the person, as well as to obtain facts from the person him or herself.
• Observations – Observing behaviors, interactions, processes, etc., related to the case as they unfold in real-time.
• Documents & Records – Reviewing private documents, diaries, public records, correspondence, meeting minutes, etc., relevant to the case.

2. Secondary sources

• News/Media – News coverage of events related to the case study.
• Academic articles – Journal articles, dissertations etc. that discuss the case.
• Government reports – Official data and records related to the case context.
• Books/films – Books, documentaries or films discussing the case.

3. Archival records

Searching historical archives, museum collections and databases to find relevant documents, visual/audio records related to the case history and context.

Public archives like newspapers, organizational records, photographic collections could all include potentially relevant pieces of information to shed light on attitudes, cultural perspectives, common practices and historical contexts related to psychology.

4. Organizational records

Organizational records offer the advantage of often having large datasets collected over time that can reveal or confirm psychological insights.

Of course, privacy and ethical concerns regarding confidential data must be navigated carefully.

However, with proper protocols, organizational records can provide invaluable context and empirical depth to qualitative case studies exploring the intersection of psychology and organizations.

• Organizational/industrial psychology research : Organizational records like employee surveys, turnover/retention data, policies, incident reports etc. may provide insight into topics like job satisfaction, workplace culture and dynamics, leadership issues, employee behaviors etc.
• Clinical psychology : Therapists/hospitals may grant access to anonymized medical records to study aspects like assessments, diagnoses, treatment plans etc. This could shed light on clinical practices.
• School psychology : Studies could utilize anonymized student records like test scores, grades, disciplinary issues, and counseling referrals to study child development, learning barriers, effectiveness of support programs, and more.

How do I Write a Case Study in Psychology?

Follow specified case study guidelines provided by a journal or your psychology tutor. General components of clinical case studies include: background, symptoms, assessments, diagnosis, treatment, and outcomes. Interpreting the information means the researcher decides what to include or leave out. A good case study should always clarify which information is the factual description and which is an inference or the researcher’s opinion.

1. Introduction

• Provide background on the case context and why it is of interest, presenting background information like demographics, relevant history, and presenting problem.
• Compare briefly to similar published cases if applicable. Clearly state the focus/importance of the case.

2. Case Presentation

• Describe the presenting problem in detail, including symptoms, duration,and impact on daily life.
• Include client demographics like age and gender, information about social relationships, and mental health history.
• Describe all physical, emotional, and/or sensory symptoms reported by the client.
• Use patient quotes to describe the initial complaint verbatim. Follow with full-sentence summaries of relevant history details gathered, including key components that led to a working diagnosis.
• Summarize clinical exam results, namely orthopedic/neurological tests, imaging, lab tests, etc. Note actual results rather than subjective conclusions. Provide images if clearly reproducible/anonymized.
• Clearly state the working diagnosis or clinical impression before transitioning to management.

3. Management and Outcome

• Indicate the total duration of care and number of treatments given over what timeframe. Use specific names/descriptions for any therapies/interventions applied.
• Present the results of the intervention,including any quantitative or qualitative data collected.
• For outcomes, utilize visual analog scales for pain, medication usage logs, etc., if possible. Include patient self-reports of improvement/worsening of symptoms. Note the reason for discharge/end of care.

4. Discussion

• Analyze the case, exploring contributing factors, limitations of the study, and connections to existing research.
• Analyze the effectiveness of the intervention,considering factors like participant adherence, limitations of the study, and potential alternative explanations for the results.
• Identify any questions raised in the case analysis and relate insights to established theories and current research if applicable. Avoid definitive claims about physiological explanations.
• Offer clinical implications, and suggest future research directions.

5. Additional Items

• Thank specific assistants for writing support only. No patient acknowledgments.
• References should directly support any key claims or quotes included.
• Use tables/figures/images only if substantially informative. Include permissions and legends/explanatory notes.
• Provides detailed (rich qualitative) information.
• Provides insight for further research.
• Permitting investigation of otherwise impractical (or unethical) situations.

Case studies allow a researcher to investigate a topic in far more detail than might be possible if they were trying to deal with a large number of research participants (nomothetic approach) with the aim of ‘averaging’.

Because of their in-depth, multi-sided approach, case studies often shed light on aspects of human thinking and behavior that would be unethical or impractical to study in other ways.

Research that only looks into the measurable aspects of human behavior is not likely to give us insights into the subjective dimension of experience, which is important to psychoanalytic and humanistic psychologists.

Case studies are often used in exploratory research. They can help us generate new ideas (that might be tested by other methods). They are an important way of illustrating theories and can help show how different aspects of a person’s life are related to each other.

The method is, therefore, important for psychologists who adopt a holistic point of view (i.e., humanistic psychologists ).

Limitations

• Lacking scientific rigor and providing little basis for generalization of results to the wider population.
• Researchers’ own subjective feelings may influence the case study (researcher bias).
• Difficult to replicate.
• Time-consuming and expensive.
• The volume of data, together with the time restrictions in place, impacted the depth of analysis that was possible within the available resources.

Because a case study deals with only one person/event/group, we can never be sure if the case study investigated is representative of the wider body of “similar” instances. This means the conclusions drawn from a particular case may not be transferable to other settings.

Because case studies are based on the analysis of qualitative (i.e., descriptive) data , a lot depends on the psychologist’s interpretation of the information she has acquired.

This means that there is a lot of scope for Anna O , and it could be that the subjective opinions of the psychologist intrude in the assessment of what the data means.

For example, Freud has been criticized for producing case studies in which the information was sometimes distorted to fit particular behavioral theories (e.g., Little Hans ).

This is also true of Money’s interpretation of the Bruce/Brenda case study (Diamond, 1997) when he ignored evidence that went against his theory.

Breuer, J., & Freud, S. (1895).  Studies on hysteria . Standard Edition 2: London.

Curtiss, S. (1981). Genie: The case of a modern wild child .

Diamond, M., & Sigmundson, K. (1997). Sex Reassignment at Birth: Long-term Review and Clinical Implications. Archives of Pediatrics & Adolescent Medicine , 151(3), 298-304

Freud, S. (1909a). Analysis of a phobia of a five year old boy. In The Pelican Freud Library (1977), Vol 8, Case Histories 1, pages 169-306

Freud, S. (1909b). Bemerkungen über einen Fall von Zwangsneurose (Der “Rattenmann”). Jb. psychoanal. psychopathol. Forsch ., I, p. 357-421; GW, VII, p. 379-463; Notes upon a case of obsessional neurosis, SE , 10: 151-318.

Harlow J. M. (1848). Passage of an iron rod through the head.  Boston Medical and Surgical Journal, 39 , 389–393.

Harlow, J. M. (1868).  Recovery from the Passage of an Iron Bar through the Head .  Publications of the Massachusetts Medical Society. 2  (3), 327-347.

Money, J., & Ehrhardt, A. A. (1972).  Man & Woman, Boy & Girl : The Differentiation and Dimorphism of Gender Identity from Conception to Maturity. Baltimore, Maryland: Johns Hopkins University Press.

Money, J., & Tucker, P. (1975). Sexual signatures: On being a man or a woman.

Further Information

• Case Study Approach
• Case Study Method
• Enhancing the Quality of Case Studies in Health Services Research
• “We do things together” A case study of “couplehood” in dementia
• Using mixed methods for evaluating an integrative approach to cancer care: a case study

Related Articles

Research Methodology

Qualitative Data Coding

What Is a Focus Group?

Cross-Cultural Research Methodology In Psychology

What Is Internal Validity In Research?

Research Methodology , Statistics

What Is Face Validity In Research? Importance & How To Measure

Criterion Validity: Definition & Examples

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• Published: 27 May 2024

Research on safety condition assessment methodology for single tower steel box girder suspension bridges over the sea based on improved AHP-fuzzy comprehensive evaluation

• Huifeng Su 1 , 2 ,
• Cheng Guo 1 ,
• Ziyi Wang 3 ,
• Tao Han 4 ,
• David Bonfils Kamanda 1 ,
• Fengzhao Su 1 &
• Liuhong Shang 1  

Scientific Reports volume  14 , Article number:  12079 ( 2024 ) Cite this article

Metrics details

• Engineering
• Mathematics and computing

In order to propose a reliable method for assessing the safety condition for single-tower steel box girder Suspension bridges over the sea, a condition monitoring system is established by installing sensors on the bridge structure. The system is capable of gathering monitoring data that influence the safety status of the bridge. These include cable tension, load on the main tower and pylon, bearing displacement, wind direction, wind speed, and ambient temperature and humidity. Furthermore, an improved Analytic Hierarchy Process (AHP) algorithm is developed by integrating a hybrid triangular fuzzy number logic structure. This improvement, coupled with comprehensive fuzzy evaluation methods, improves the consistency, weight determination, and security evaluation capabilities of the AHP algorithm. Finally, taking the No.2 Channel Bridge as an example and based on the data collected by the health monitoring system, the application of the safety assessment method proposed in this paper provides favorable results in evaluating the overall safety status of the bridge in practical engineering applications. This provides a basis for management decisions by bridge maintenance departments. This project confirms that the research results can provide a reliable method for assessing the security status of relevant areas.

Introduction

With the in-depth implementation of the strategy to strengthen national transport, the development of transport infrastructure has entered a new phase of rapid development. It is expected that China could lead the world in the number of bridges by the 2030s 1 . As the service life of bridges increases, damage to various structures and components can have an impact on the safe operation of bridges. In some cases, the failure of a particular component can result in a complete loss of bridge safety. In order to be able to assess the safety status of bridges intuitively and quickly, it is usually necessary to carry out safety assessments. There are two main methods for assessing bridge safety: using bridge monitoring data and using manual inspections along with standardized criteria. Currently, the assessment and early warning of the safety status of bridge structures is largely carried out by installing sensors and monitoring devices on bridge structures. This enables long-term real-time monitoring of the operating status and relevant physical parameters of the bridge 2 , 3 . For single-tower steel box girder suspension bridges over the sea, traditional manual inspection methods suffer from subjectivity, low efficiency and high labor costs due to their high pylons and structural complexity, so they cannot meet maintenance requirements. Therefore, in order to capture the safety operation status of bridge structures in real time, it is particularly important to conduct safety status assessments for single-tower steel box girder suspension bridges over the sea using health monitoring systems.

Bao et al. 4 In order to carry out an effective risk assessment in the construction of long-span bridges and determine the optimal construction scheme using the Analytic Hierarchy Process, the AHP was integrated with the Gray Correlation method. They created a multi-level comprehensive assessment model and used the AHP to provide weights for the factors that influence the assessment indicators. Yang et al. 5 based on a comprehensive analysis of the safety factors associated with existing bridges crossing municipal roads, proposed a comprehensive fuzzy evaluation method of Analytic Hierarchy Process to evaluate the impact of road construction on the safety of existing bridges. Yang et al. 6 proposed a novel comprehensive condition assessment method that considers the uncertainty of the measured data intervals and the influence of conflicting measured data. By comparing the condition assessment results with the actual state of components or the entire bridge, they verified the advantages of the proposed method over existing AHP assessment methods and traditional combination methods. Liu et al. 7 presented a reliability assessment method for a precast reinforced concrete hollow slab bridge system considering damage to joint nodes based on an improved Analytic Hierarchy Process. Tan et al. 8 addressed the optimization selection problem of retrofit solutions for old bridges and introduced a decision method based on fuzzy Analytic Hierarchy Process weights and gray relational analysis. Lu et al. 9 proposed a method for risk assessment of Suspension bridges and cable systems based on cloud model, which effectively combines the randomness and uncertainty of risk information. Wang et al. 10 , 11 outlined the research trends in main cable safety assessment and emphasized the importance of improving the safety of main cables to ensure the structural safety of long-span, multi-tower suspension bridges. Andrić et al. 12 combined the Fuzzy Analytic Hierarchy Process (FAHP) with fuzzy knowledge representation and fuzzy logic techniques, proposing a novel framework for disaster risk assessment. This method proves its practicality and efficiency in analyzing and evaluating multi-hazard risks for bridges. Ji et al. 13 introduced a large-scale risk assessment method for complex bridge structures based on Delphi-enhanced Fuzzy Analytic Hierarchy Process (FAHP) factor analysis. The approach was validated through a comparative study with practical engineering cases and the Analytic Hierarchy Process, confirming its feasibility and practicality. It serves as a reference for later risk prevention in bridge. Liang 14 presented a multi-level evaluation system suitable for assessing the health status of prestressed continuous concrete bridges. This innovative rating system effectively supports bridge management and maintenance. Deng et al. 15 developed a comprehensive assessment method for the safety and reliability of existing railway bridges. The method serves as a theoretical basis for the maintenance and strengthening of the Songhua River Bridge on the Binbei Line. Ma et al. 16 proposed a systematic safety assessment for overwater bridge transportation, a technology that significantly increases the safety of bridges during sea transportation. Maljaars et al. 17 developed an evaluation method to determine the actual safety level of highway bridges and viaducts. This method focuses on assessing the impact of traffic behavior and consists of several levels. Zhu et al. 18 conducted an in-depth study on the safety assessment methods for Bridge Health Monitoring Systems (BHMS) using comprehensive fuzzy assessment techniques. They developed a novel Bridge Health Monitoring System based on safety assessment vectors. Li et al. 19 introduced a new security assessment method that combines Monte Carlo simulation (MCS) and Bayesian theory. This method enables reliable assessment and back-diagnosis of the overall safety performance of reinforced concrete bridges in cold regions. Fu et al. 20 used multi-source data from the construction and dismantling of a large-span reinforced concrete arch bridge in China. They applied the Analytic Hierarchy Process AHP to analyze the data from multiple sources and set a safety alarm threshold for the bridge during construction. Miyamoto et al. 21 proposed an early warning method for bridge safety using wireless sensor network technology. The method showed satisfactory results in various performance indicators such as flood delay, energy efficiency and throughput. Li et al. 22 established a risk assessment index system for safety in the operational phase of highway bridges. They then used cloud entropy weighting to objectively weigh various risk indicators and applied cloud model theory to risk assessment, emphasizing the objectivity of the assigned values. Feng et al. 23 presented an innovative approach that combines the Analytic Hierarchy Process (AHP) with the Finite Element Method (FEM). This approach highlighted the potential risk of influence of uncertain factors on the environment. Li et al. 24 proposed a probabilistic performance evaluation framework for a Suspension bridge, which considers factors such as wind speed, wind direction, bridge orientation, wind-wave correlation and parameter uncertainty. This framework provides a comprehensive and practical method for evaluating the performance and optimizing the design of SCBs under wind and wave loads. Xu et al. 25 presented a cloud-based Analytic Hierarchy Process (C-AHP) scoring system for determining inspection intervals. The proposed C-AHP rating system not only takes into account the vagueness of the AHP rating system, but also addresses its randomness and provides more stringent time intervals for routine inspections of long-span suspension bridges compared to the F-AHP rating system. Prasetyo et al. 26 used AHP and Promethee II methods to analyze and prioritize the ideal weight criteria for bridge handling. This approach makes the priority weighting process more dynamic and manageable.

In summary, there exists a paucity of research both domestically and internationally concerning the safety assessment of single tower suspension bridges featuring a steel box girder structure spanning over open sea expanses. In the field of safety assessment analysis for bridge structures, the traditional AHP is commonly used. In the traditional AHP framework, assessment matrices are created based on pairwise comparisons of selected criteria. However, the requirement for precise numerical values ​​within these matrices requires respondents to have a thorough understanding of the relative importance of each choice. In practice, due to the complexity of objective phenomena and the human mind's use of fuzzy concepts, describing relative importance with precise numbers (such as 3, 1/9, etc.) becomes challenging. This leads to low credibility of weight calculation, cumbersome calculations, and weakened ability to comprehensively evaluate. Further refinements and improvements are required to determine the weights and improve the scoring matrix in a more meaningful way. Given this background, the present study improves the judgment matrix through a hybrid triangular fuzzy number logic structure with the aim of accounting for the uncertainty inherent in human analysis and cognition. This extension includes specifying the upper and lower limits of the possibility intervals as well as the most likely central values. By using the membership function of triangular fuzzy numbers, the study derives the possibilities of various parameters within the entire interval range. This method improves the determination of weights in the AHP, thereby improving its consistency and weight solution capabilities. By combining the improved AHP method with comprehensive fuzzy evaluation, the study proposes an improved AHP-fuzzy comprehensive evaluation approach to evaluate the safety status of a single-tower steel box girder suspension bridge over the sea. This approach increases the accuracy and rationality of the assessment results and aims to address the shortcomings in the safety assessment research of such bridge structures and provide valuable insights for the safety assessment of bridges.

Method for assessing the safety status of a single tower steel box girder suspension bridges over the sea

Basic principles of improved analytic hierarchy process.

The Analytic Hierarchy Process, introduced by American operations research professor Saaty in the 1970s 27 , is an effective method that converts semi-qualitative and semi-quantitative problems into quantitative calculations. AHP is known for its simplicity, rigorous mathematical foundation, and widespread application in analysis and decision making of complex systems. It serves as a practical, multi-criteria decision-making method and offers advantages such as systematicity, conciseness, flexibility and usefulness.

In traditional AHP, judgment matrices are determined through pairwise comparisons of selected criteria, which requires respondents to have a clear understanding of the relative importance of each selection. However, in practice, due to the large number of evaluation criteria in the AHP evaluation process, the complexity of objective phenomena and the application of fuzzy concepts in human thinking, experts find it difficult to give an accurate value when evaluating pairwise comparison indicators. Restricting the evaluation of importance levels to fixed and finite numbers ignores the fuzziness of experts' thought processes during evaluation, which leads to inconsistency problems in the evaluation matrices and to some extent limits the accuracy of the evaluations. To address this problem, this study integrates the triangular fuzzy number method, improves the weight determination method in the analytical hierarchy process, and improves its consistency and weight solution capabilities. Triangular fuzzy numbers represent a range concept that specifies the upper and lower limits of a probability interval as well as the maximum probability value. By using the membership function of triangular fuzzy numbers, the probabilities of various parameters within the entire interval range can be determined.

When constructing the judgment matrix \(A = \left( {a_{ij} } \right)_{n \times n}\) , we depart from the conventional method of using a single precise numerical value to represent the importance of two indicators, and instead employ the method of triangular fuzzy numbers to indicate the interrelationships between pairs of indicators. First, the most probable value “m” is determined, which represents the basic assessment of the relationship between the two indicators, followed by the establishment of the upper and lower limits, denoted “a” and “b”. The lower bound represents the minimum rating that experts consider possible, while the upper bound represents the maximum possible rating. Finally, an importance interval is provided, denoted as \(a_{ij} = \left[ {a_{ij} ,m_{ij} ,b_{ij} } \right]\) , where “ \(a\) ” represents the minimum importance value in the comparison of the two indicators, “ \(m\) ” denotes the most likely value in the comparison. and “ \(b\) ” denotes the maximum importance value in the comparison.

Using formula ( 1 ), transform the interval form of importance into specific precise numerical values-and obtain a consistent judgment matrix without the need for consistency checks.

Regarding formula ( 1 ), Professor Hua Luogeng has previously provided explanations for similar formulas: The probability of “ \(a_{ij}\) ” taking the minimum value, “ \(a\) ” and “ \(b\) ” taking the maximum value is relatively small, and the probability distribution closely follows the normal distribution distribution pattern. Therefore, assuming that “ \(a_{ij}\) ” takes the most likely value “ \(m\) ” is twice as likely as assuming that “ \(a\) ” takes the minimum value and “ \(b\) ” takes the maximum value. The weighted average algorithm produces the following results:

For example, if an expert's assessment of the relative weights of Indicator 1 and Indicator 2 is (2/3, 1, 3/2), then that expert's assessment of the weight of Indicator 1 relative to Indicator 2 is:

Improving the basic steps of the analytic hierarchy process

Clearly define the basic problems and relevant influencing factors

At the initial stage, it is important to have a comprehensive understanding of the problems being studied and the problems to be solved. The aim is to clearly identify the overarching problem, i.e. the end goal. After defining the basic problem, it is then a matter of identifying the relevant influencing factors that can play a role in solving the problem. These include both primary and secondary factors.

Establishing a hierarchical structure

Establishing a hierarchical structure is a crucial step in the AHP, especially when assessing the comprehensive safety status of bridges. The initial phase involves systematically categorizing the research problem and organizing it into hierarchical layers and thus constructing an evaluative indicator system or model. Within this system or model, the research problem is delineated into different indicator elements at different levels. These indicator elements are further classified based on their unique properties. In particular, each set of indicators at a lower level should be subordinate to the indicators at the level above. To improve the overall rationality of the hierarchical system or model, the division of hierarchical levels should conform to principles such as security, simplicity, independence and objectivity. The hierarchical structure can basically be divided into three levels:

Top level (target level): This level is also called the target level and contains only one indicator element. In the context of this document, the top level is the comprehensive safety assessment of the 2nd canal bridge.

Intermediate level (criterion level): This level is also called the criterion level and can contain several indicator elements. Each indicator at this level is constrained by and subordinate to the top level indicator. The indicators at this level should share common attributes. For example, in the case of a suspension bridge, the central indicators may include components such as main beams, main tower, main cables, hanging rods, etc.

Bottom level (alternative level): This level is also called alternative level and can also contain several indicator elements. These indicators represent various solution measures for achieving the goal. Each indicator at this level should have an influencing factor on the security status of the higher-level indicators. For example, within the “main beam” indicator at the middle level, the indicators at the lowest level could include the stress and displacement of the main beam. Stress and displacement can be further divided based on different locations and directions.

An ideal typical analytic hierarchy model is shown in Fig.  1 .

Ideal typical AHP model.

Construction of a triangular judgment matrix in fuzzy number form

Within the same hierarchy, different indicator elements are categorized into multiple levels based on their respective excellence or importance. Quantitative values are assigned to represent these levels. If the precision requirements are low, a 5-step quantitative method can be used, using the integers 1, 3, 5, 7 and 9 to express the importance of one indicator element over another. This is called the 5-stage quantitative method, where a higher number indicates greater importance of the former over the latter. To express the former as less important than the latter, the reciprocal of 1, 3, 5, 7 and 9 can be used. If higher precision in level division is required, interpolation can be applied within the 5 level method by introducing 2, 4, 6 and 8, creating a 9 level quantitative method. The meaning of the scale from 1 to 9 is shown in Table 1 .

Distribute evaluation matrix evaluation sheets to relevant experts and guide them to evaluate the scale table using the hierarchical analysis method described above. They are expected to perform pairwise comparisons of the indicators and then assign importance values. Summarize the assessments of each expert and create the evaluation matrix in the form of triangular fuzzy numbers, as shown in ( 2 ).

The approximation of the consistency of the matrix “A” leads to the generation of the consistency assessment matrix \(M = \left( {m_{ij} } \right)_{n \times n}\) , whereby the parameter \(m_{ij}\) is calculated as follows:

Based on the consistency judgment matrix, calculate the weights of each indicator

Start by calculating the nth root of the product of the elements in each row of the consistency judgment matrix.

where \(M_{i} \prod\nolimits_{j = 1}^{n} {m_{ij} }, \;\; \left( {i = 1,2, \ldots n} \right)\) .

Orthogonalize the above calculation results to obtain coefficients for each evaluation indicator.

\(W_{i} = \left( {W_{1} ,W_{2} , \ldots ,W_{n} } \right)^{T}\) therefore denotes the weight coefficients determined for the respective evaluation indicators.

Basic principle of the comprehensive fuzzy evaluation method

In 1965, Professor L.A. Zadeh from the United States published an article on fuzzy logic in an international journal in which he established the concept of fuzzy set theory and marked the birth of fuzzy mathematics 28 . Fuzzy or uncertain entities can be described using fuzzy mathematics. The term “fuzzy” refers to the variability between objective units that arises from the uncertainty in classifying units due to subjective differences. It is a form of description for concepts that are clearly defined but have unclear boundaries. In practical life, many concepts are vague, such as: youth, early morning, cold, etc. Due to subjective and objective limitations, each individual has different mental limits for these phenomena, which reflect people's subjective factors. When the fundamental concepts are unclear, accurate identification of an object is unrealistic. Instead, one can only assess the extent to which the object is likely to correspond to the concept.

Fuzzy sets and membership functions

In classical set theory, for a given element “ \({\text{x}}\) ”, its membership in the classical set “ \({\text{A}}\) ” is clear. The relationship between the two is binary, either belonging or not belonging, a clear distinction represented by either \({\text{x}} \in A\) or \({\text{x}} \notin A\) . This relationship can be described using a characteristic function. However, for certain indefinite quantities or units, their values cannot be determined precisely. Therefore, it becomes necessary to apply fuzzy set theory to handle such cases.

In fuzzy set theory, the transformation of the characteristic function into a membership function is used to solve problems. Membership degrees are used to reflect the degree of membership of a fuzzy set to a fuzzy set. Assuming a discourse universe “ \({\text{U}}\) ” and a set “ \({\text{A}}\) ”, for each element \({\text{x}} \in A\) , a function \(\mu_{A} \left( {\text{x}} \right) \in \left[ {01} \right]\) can be used to represent the degree to which element “ \({\text{x}}\) ” belongs to the set “ \({\text{A}}\) ”, as follows:

In the context of fuzzy set theory, the range “ \({\text{U}}\) ” is called the set of elements, while the set “ \({\text{A}}\) ” is called a fuzzy set. The function \(\mu_{A} \left( {\text{x}} \right)\) , called the membership function, serves as the membership function for “A”. In this scenario, a fuzzy set can be fully represented by a corresponding fuzzy function. The membership function \(\mu_{A} \left( {\text{x}} \right)\) assigns values ranging from 0 to 1, where the value is to 1, the higher the degree of membership of the element “ \({\text{x}}\) ” to a fuzzy set in the fuzzy set” \({\text{A}}\) ”; the closer it is to 0, the lower the degree of membership of the element “ \({\text{x}}\) ” to a fuzzy quantity in the fuzzy set ” \({\text{A}}\) ”.

Methods for determining membership functions

Fuzzy set and membership function are inextricably linked. The fuzzy set is represented by the membership function. The membership function is also the implementation of fuzzy set operations. Using the correct membership function is the basis for applying fuzzy set theory to solve practical problems. This article uses fuzzy statistics to determine the membership function.

Fuzzy statistics are used to represent the membership function in a similar way to probability statistics to determine the degree of membership. The basic steps are as follows: First, a fuzzy set “A” and a discourse area “U” are determined. Then, based on their personal experience, several experts or scientists judge which fuzzy set or which fuzzy evaluation interval of a specific element “ \({\text{x}}_{0}\) ” in the discourse area ”U” belongs to the fuzzy set “A” The expression of the membership function can be expressed as follows:

where “n” is the number of experts or scientists. In this way, the membership level is determined by the statistical membership frequency. When “n” experts are invited to an experiment, the membership frequency “ \(\mu\) ” tends to the stable value as the “n” value increases, and the stable frequency value is the membership degree of the element “ \({\text{x}}_{0}\) ” belonging to the fuzzy set “A”.

Basic steps of first-level comprehensive fuzzy evaluation

Identification of the factor set

When conducting fuzzy assessments, the first step is to identify the various factors that affect the target's assessment results. For example, in a comprehensive safety assessment of a suspension bridge, the influencing factors include the main girder, main tower, main cables, hanging rods and others. The totality of these individual factors is called a factor set and is usually denoted by the symbol “U”. This can be expressed as follows:

Determine the factor weight vector

In the determined factor set \({\text{U}} = \left\{ {\mu_{{1}} ,\mu_{{2}} , \ldots ,\mu_{{\text{n}}} } \right\}\) , each factor has a different influence on the evaluation goal. Therefore, it is necessary to meaningfully divide the weight of each factor and assign a corresponding weight value, which can be determined through an analytical hierarchy process. The weight value of each factor can be converted into a weight vector, generally expressed by “A”:

In the formula, \(a_{1} ,a_{2} , \ldots a_{n}\) represents the weight value corresponding to the factor \(u_{1} ,u_{2} , \ldots u_{n}\) , and \(0 \le a_{i} \le 1\) .

Determine the amount of fuzzy comments

After determining the factor set \({\text{U}} = \left\{ {\mu_{{1}} ,\mu_{{2}} , \ldots ,\mu_{{\text{n}}} } \right\}\) , a corresponding fuzzy comment set needs to be created so that the evaluator can achieve specific judgment results for each element in the factor set. For example, according to the classification of the technical condition of a bridge, the bridge can be divided into categories 1, 2, 3, 4 and 5, and the corresponding fuzzy comments on the bridge status include intact, good, fairly good, poor and dangerous. The set of fuzzy evaluation is called fuzzy evaluation theorem and is generally used in the “V” representation, that is:

In the equation, \({\text{v}}_{1} ,{\text{v}}_{2} , \ldots ,{\text{v}}_{m}\) represents “m” fuzzy evaluations created for each factor.

Single factor evaluation

The single factor evaluation refers to the individual evaluation of each factor within the factor set “U”. This process determines the degree of membership of each factor to different ratings in the fuzzy rating set “V”. For example, when evaluating the “i”-th factor \(\mu_{{\text{i}}}\) within the factor set “U”, the degree of membership of this factor to the “j”-th evaluation “V” in the fuzzy evaluation set \({\text{v}}_{{\text{j}}}\) can be specified as \({\text{r}}_{{{\text{ij}}}}\) . The membership degrees obtained for the \({\text{i}}\) th factor \(\mu_{{\text{i}}}\) can be represented as \(r_{j}\) , which in the context of bridge building can be expressed as follows:

In the equation, \({\text{r}}_{{{\text{i1}}}} ,{\text{r}}_{{{\text{i2}}}} , \ldots ,{\text{r}}_{{{\text{im}}}}\) represents the membership degrees of the \({\text{i}}\) th factor to \({\text{m}}\) fuzzy evaluations, where \(0 \le {\text{r}}_{{{\text{im}}}} \le 1\) .

Building a comprehensive fuzzy evaluation matrix

When evaluating a goal with multiple influencing factors, the aggregation of the membership degree sets resulting from the evaluation of all factors within the factor set \({\text{U}}\) leads to the creation of a comprehensive assessment matrix for the evaluation goal. This matrix is usually represented by the symbol \({\text{R}}\) . It can be expressed as:

Fuzzy comprehensive evaluation

After determining the weight vector \(A_{1 \times n}\) for each factor and constructing the comprehensive judgment matrix \(R_{{{\text{n}} \times {\text{m}}}}\) , fuzzy transformation is applied to both using fuzzy operators. This process produces a fuzzy valuation vector \({\text{B}} = \left( {{\text{b}}_{{1}} ,{\text{b}}_{{2}} , \ldots ,{\text{b}}_{{\text{m}}} } \right)\) , the calculation formula of which is expressed as follows:

In the equation, " \(\circ\) " represents the fuzzy operator.

Fuzzy operator

In the process of fuzzy transformation, fuzzy operators generally include primary factor determination type, primary factor prominence type, unbalanced average type and weighted average type, among others. The weighted average operator is characterized by clear weighting effects and high completeness. Therefore, this article uses the weighted average type operator for calculation. The specific calculation is as follows:

Handling evaluation results

After the calculation process of comprehensive fuzzy evaluation, the final evaluation result “B” is obtained. At this stage it is necessary to process the assessment indicators. This article uses the maximum membership degree principle to process the fuzzy, comprehensive evaluation results and derive explicit evaluation results. The specific calculation method for the maximum membership degree principle is as follows:

Then the comprehensive assessment results of \({\text{i}}_{0}\) levels are determined. This operating method is relatively straightforward, with the majority of comprehensive evaluation approaches typically employing the maximum membership degree principle.

Multi-level fuzzy comprehensive evaluation

Typically, when evaluating a complex system, it's necessary to consider the influences of various factors, which may also include sub-factors. Therefore, a comprehensive assessment of membership degrees across different factor levels is needed. In such cases, a multi-level assessment must be conducted in conjunction with the situation of each factor layer. When there are numerous influencing factors affecting the evaluation object, it is difficult to meaningfully assign the weights, which means that it is difficult to determine the hierarchy of individual factors within the overall assessment. In such situations, a multi-level fuzzy comprehensive assessment method is needed for determination.

For example, when assessing the condition of a bridge, a bridge is divided into superstructure, substructure, auxiliary structure and bridge deck system according to its structure. Each structure is first subjected to a comprehensive assessment, and the assessment results then serve as single-factor assessments at a higher level. The weights of these four structures are denoted by A, and a comprehensive second-level fuzzy evaluation is performed. The calculation process is as follows.

In the above equation, “C” represents the comprehensive evaluation result of the bridge condition. In cases with multiple influencing factors, it's advisable to first stratify and classify the factors, and then proceed with multi-level fuzzy comprehensive evaluation.

Improved AHP-fuzzy comprehensive evaluation model for single tower steel box girder suspension bridges over the sea

The safety evaluation of single-tower steel box girder bridges over the sea includes various factors, including the steel box girder, concrete main tower, main cables, suspension rods and others, making it a typical multi-dimensional evaluation challenge. In the improved AHP method, although there are weights for each indicator, there is still a subjective element in the expert evaluation process. Therefore, it is crucial to further improve the quality of quantitative assessment through comprehensive fuzzy assessment methods. The evaluation model for single-tower steel box girder oversea suspension bridges based on the improved AHP-Fuzzy Comprehensive Evaluation is shown in Fig.  2 .

Schematic diagram of the evaluation model for single-tower steel box girder suspension bridges over the sea based on the improved AHP-fuzzy comprehensive evaluation.

Health monitoring of a cross-sea single tower steel box girder suspension bridge

The condition monitoring of steel box girder suspension bridges with a tower over the sea primarily requires the installation of various types of sensors on site. These sensors collect monitoring data that reflects the structural safety status. By analyzing and processing this monitoring data, the health status of the structure is determined. This process creates a solid foundation for conducting bridge safety assessments and provides reference and decision support for bridge maintenance and management.

Overview of the bridge health monitoring system

The condition monitoring system for the steel box girder tower suspension bridge over the sea consists of five main subsystems: the sensor subsystem, the data acquisition and transmission subsystem, the data storage and management subsystem, the data processing and analysis subsystem and the structure monitoring. Early warning and security assessment subsystem. These subsystems are integrated using system integration technologies to coordinate the operation of hardware and software components. The configuration of the bridge condition monitoring system is shown in Fig.  3 .

Structure of the health monitoring system of a single tower steel box girder suspension bridge over the sea.

Bridge health monitoring project and sensor placement

According to the structural characteristics of the 2nd Canal Bridge and taking into account the traffic volume and investment scale, the monitoring system for the 2nd Canal Bridge includes the following monitoring projects: wind speed and direction, structure temperature, deflection, cable saddle displacement, temperature and humidity, cable forces, anchor displacement, ship collision seismicity, preload force, cable clamping and vibration. The arrangement of the sensors is shown in Fig.  4 , and a summary of the measurement points can be found in Table 2 . The sampling frequency, units and data volume for each monitoring indicator are shown in Table 3 .

Schematic diagram of the monitoring point layout.

Validation of engineering cases

Project overview.

Bridge No. 2 is an important part of a northern coastal bridge and serves as an important sea connection between the eastern and western parts of the Bay City. It plays an important role in the Qinglan Expressway network. Bridge No. 2 is designed as a continuous, self-anchored steel box girder suspension bridge with a tower and a main span of 260 m. It is equipped with two main cables and 58 hanging rods. The span is 80 + 190 + 260 + 80 m with a total length of 610 m. The main and side panels utilize a suspension design with a continuous, semi-floating four panel system, as shown in Fig.  5 . The tower of Bridge No. 2 consists of a single-column concrete tower and the main girder is made of segmented steel box girder construction. Both the main and side spans are configured as suspension systems, with a main span aspect ratio of 1/12.53 and a side span aspect ratio of 1/18.04.

General structure of the bridge.

Application of the improved AHP in Bridge No. 2

Structure of the evaluation index system.

Based on the structural form, characteristics and monitored content of Bridge No. 2, the AHP was used to hierarchize the structural system of Bridge No. 2. This led to the creation of a rating index system with corresponding hierarchical divisions. The highest level, the target level, refers to the comprehensive assessment of the safety status of Bridge No. 2. The middle level consists of primary indicators, a total of 8, and the lowest level includes secondary indicators, a total of 29. The hierarchical assessment The system for Bridge No. 2 is listed in Table 4 .

In order to obtain the evaluation matrix for each indicator level of the suspension bridge, a survey questionnaire is developed, which is based on the created evaluation indicator system for Bridge No.2 and involves the 9-stage quantitative method for establishing evaluation criteria for each indicator, determining the hierarchical relationships and weight comparisons between the Indicators. Surveys on the No.2 Bridge Evaluation Indicator System were distributed to experts or scientists familiar with suspension bridge designs, and then promptly collected and analyzed.

Construction of an assessment matrix in the form of triangular fuzzy numbers for primary indicators and weight calculation

Based on the ratings assigned from the expert survey questionnaires, coupled with the finite element model analysis of Bridge No. 2, various monitoring values from the health monitoring system and with reference to the “Technical Condition Assessment Standards for Highway Bridges” (JTG/TH21-2011) a comprehensive calculation results in the assessment matrix shown in Table 5 .

The assessment matrix is subjected to a consistency approximation in order to obtain a consistency judgment matrix:

Calculate the nth root of the product of the elements in each row of the consistency judgment matrix:

The above calculation results are orthogonalized to obtain the weight coefficient of each evaluation index: \(W_{i} = \frac{{\overline{{W_{i} }} }}{{\sum\nolimits_{j = 1}^{n} {w_{j} } }}\)

Through the above calculation, the weights of the first level index steel box beam, concrete main tower, main cable system, suspension system, anchor bar, substructure, auxiliary facilities and environmental factors can be found as follows: 0.0978, 0.0978, 0, 3121, 0.2067, 0.2067, 0.0581, 0.0104, 0.0104, which shows that the weight value of the main cable is the largest and the weight value of the auxiliary facilities and environmental factors is the smallest.

Calculation of secondary indicator weights

Calculation of the secondary indicator weights for the primary evaluation criteria of the first-level box girder

The method of constructing the judgment matrix in the triangular fuzzy number form for same-level indicators is consistent, and the comprehensive results are presented in the following matrix, as shown in Table 6 .

Similarly, the weights for the primary box girder evaluation criteria corresponding to main girder deflection, main girder stress, main girder lateral displacement, main girder longitudinal displacement, and vibration frequency can be determined. The results are shown in Table 7 .

According to Table 7 , it can be observed that the weight value for the vibration frequency of the box girder is the highest, whereas the weight values for main girder stress and main girder longitudinal displacement are the lowest.

Calculation of secondary criterion weights corresponding to the primary evaluation criteria for a concrete main tower

The method of constructing the judgment matrix in the triangular fuzzy number form for same-level indicators is consistent, and the comprehensive results are presented in the following matrix, as shown in Table 8 .

Similarly, the weight values for the primary evaluation criteria corresponding to main tower stress, main tower longitudinal displacement, and main tower lateral displacement can be obtained, as shown in Table 9 .

From Table 9 , it can be inferred that the weight assigned to the longitudinal displacement of the main tower is the highest, while the weight for the stress on the main tower is the lowest.

Calculation of secondary criterion weights corresponding to primary evaluation criteria for primary cable system

The method of constructing the judgment matrix in the triangular fuzzy number form for same-level indicators is consistent, and the comprehensive results are presented in the following matrix, as shown in Table 10 .

Similarly, the weight values for the primary evaluation criteria can be determined according to the main cable force, main cable protection layer, clamping force and saddle displacement, as shown in Table 11 .

From Table 11 , it can be observed that the weight value for the main cable force is the highest, while the weight value for the clamp force is the smallest.

Calculation of secondary indicator weights corresponding to primary suspension rod system evaluation criteria

The method of constructing the judgment matrix in the triangular fuzzy number form for same-level indicators is consistent, and the comprehensive results are presented in the following matrix, as shown in Table 12 .

Similarly, the weights for the evaluation criteria of the primary suspension rod system can be calculated according to the suspension rod tension, the suspension rod protective layer and the damper, as shown in Table 13 .

From Table 13 , it can be seen that the weight value for the tension of the suspender cable is the highest, while the weight value for the protective layer of the suspender cable is the lowest.

Calculation of weights for secondary indicators that correspond to the primary anchoring evaluation criteria.

The method of constructing the judgment matrix in the triangular fuzzy number form for same-level indicators is consistent, and the comprehensive results are presented in the following matrix, as shown in Table 14 .

Similarly, the weight values for the displacement of the primary anchoring system and the concrete strength evaluation criteria can be calculated as shown in Table 15 .

From Table 15 , it can be concluded that the weight value for anchor displacement is the highest, while the weight value for concrete strength is the lowest.

Calculation of weight for secondary indicators corresponding to the primary evaluation criteria for the substructure.

The method of constructing the judgment matrix in the triangular fuzzy number form for indicators at the same level is consistent, and the comprehensive results are presented in the following matrix, as shown in Table 16 .

Similarly, the weight values for the primary substructure assessment criteria corresponding to support displacement, foundation settlement, and concrete strength can be calculated, as shown in Table 17 .

From Table 17 , it can be seen that the weighting value for foundation settlement is the largest, while the weighting value for concrete strength is the smallest.

Calculation of weighting values for secondary indicators that correspond to the primary assessment criteria for ancillary facilities.

The method of constructing the judgment matrix in the triangular fuzzy number form for same-level indicators is consistent, and the comprehensive results are presented in the following matrix, as shown in Table 18 .

Similarly, weight values can be calculated for the primary assessment criteria for ancillary facilities relating to bridge decking, expansion joints, drainage systems, lighting systems and railings, as shown in Table 19 .

From Table 19 , it can be seen that the weight values for bridge deck and expansion joints are the highest, while the weight value for railings is the lowest.

Calculation of weight values for secondary indicators that correspond to the assessment criteria for primary environmental factors.

The method of constructing the judgment matrix in the triangular fuzzy number form for same-level indicators is consistent, and the comprehensive results are presented in the following matrix, as shown in Table 20 .

Similarly, the weight values for wind speed, temperature and humidity can be determined, which correspond to the primary evaluation criteria for environmental factors. As shown in Table 21 :

From Table 21 , it can be concluded that the weight value for CL ions is the highest, while the weight value for temperature is the lowest.

Safety assessment of Canal Bridge No. 2 based on an improved comprehensive AHP + Fuzzy assessment

In accordance with the improved AHP applied to the evaluation criteria system for the components of Bridge No. 2, it is divided into three levels: the highest level (objective level), the intermediate level (first-level indicators), and the lowest level (second-level indicators). In this paper, the eight first-level indicators at the intermediate level are designated as the first layer of the factor set, denoted as \(U_{1}\) , and the 28 s-level indicators at the lowest level are designated as the second layer of the factor set, denoted as \(U_{2}\) , The weight values of each level's factors are determined based on the calculations presented in " Bridge health monitoring project and sensor placement " section of this paper.

Fuzzy statistical method is employed in this study to determine the membership functions. A survey questionnaire is distributed to relevant experts or scholars to individually evaluate and score all the factors in the third layer of factors set \(U_{2}\) . The recipients of the survey questionnaire include the users of Bridge No. 2, maintenance managers, and individuals involved in the bridge load testing. Fuzzy evaluations in this paper are primarily based on relevant specifications, combined with finite element simulation responses, actual data from health monitoring systems, and the real condition of the bridge. The fuzzy evaluations are classified into five levels: "Intact," "Good," "Fairly Good," "Poor," and "Dangerous," denoted as V1 = Intact, V2 = Good, V3 = Fairly Good, V4 = Poor, V5 = Dangerous. The set of fuzzy evaluations is represented as V = {Intact, Good, Fairly Good, Poor, Dangerous}.

Statistical analysis was performed on the distributed and collected expert questionnaires to determine the membership frequencies or membership degrees for each factor indicator. The statistical results are shown in Table 22 .

Index evaluation of the primary index layer of the No. 2 Channel bridge

Evaluation of steel box girder indicator

The fuzzy matrix corresponding to the indicators of the second level of the steel box girder is:

The weights of the second level indicators corresponding to the steel box girder criteria are as follows:

The degree of membership defined for the steel box girder indicators is:

According to the principle of maximum membership degree, the highest membership degree of 0.6213 is selected as the comprehensive evaluation result for the steel box girder indicators. Therefore, when assessing its indicators, it must be assumed that it is in an intact state.

Evaluation of the concrete main tower indicator

The fuzzy matrix corresponding to the secondary indicators of the main concrete tower is:

The weights associated with the secondary indicators of the main concrete tower are:

The membership set for the primary indicators of the steel box girder main tower is:

According to the maximum membership degree principle, the highest membership degree of 0.7427 should be selected as the comprehensive evaluation result for the concrete main tower indicators to judge it as being in good condition.

Main cable system

The fuzzy matrix corresponding to the secondary indicators of the main cable system is as follows:

The weights of the secondary indicators corresponding to the main criteria of the cable system are as follows:

The membership degree set for the main cable system indicators is as follows:

According to the maximum membership degree principle, the highest membership degree of 0.7110 is selected as the comprehensive evaluation result for the main indicators of the cable system, and the system is judged to be in good condition.

Suspension rod system

The fuzzy matrix corresponding to the secondary indicators of the suspension rod system is as follows:

The weights of the secondary indicators corresponding to the suspension rod system are as follows:

The degree of membership established for the indicators of the suspension rod system is as follows:

According to the maximum membership degree principle, taking a maximum membership degree of 0.4097 as the comprehensive evaluation result for the suspension rod system indicators, the system should be judged to be in good condition.

Anchor block

The fuzzy matrix corresponding to the secondary indicators of the anchor block is as follows:

The weights of the secondary indicators that correspond to the anchor block criteria are as follows:

The membership degree set for the anchor block criteria is as follows:

According to the maximum membership degree principle, and taking the maximum membership degree of 0.8000 as the comprehensive assessment result for the anchor block criteria, the indicators should be judged to be relatively good.

Substructure

The fuzzy matrix corresponding to the secondary indicators of the substructure criteria is as follows:

The weights of the secondary indicators that correspond to the sub-structural criteria are:

The membership degree set for the substructure criteria is:

According to the maximum membership degree principle, taking the highest membership degree of 0.5073 as the comprehensive evaluation result for the substructure criteria, the indicators should be judged to be in a sound condition.

Auxiliary facilities

The fuzzy matrix corresponding to the secondary indicators of the auxiliary facilities criteria is:

The weights of the secondary indicators corresponding to the criteria for auxiliary facilities are:

The membership degree set for the criteria for auxiliary facilities is:

According to the maximum membership degree principle, selecting the highest membership degree of 0.4108 as the comprehensive assessment result for the aid facility criteria indicates that the indicators are in good condition.

Environmental factors

The fuzzy matrix corresponding to the secondary indicators of the environmental factors criteria is:

The weights of the secondary indicators corresponding to the criteria for environmental factors are:

The degree of membership established for the environmental factors criteria is:

According to the maximum membership degree principle and choosing the highest membership degree of 0.5070 as the comprehensive evaluation result for the environmental factor criteria, the indicators should be evaluated as being in good condition.

Overall safety assessment of Bridge No. 2

The fuzzy matrix corresponding to the primary indicators of Bridge No. 2 is as follows:

The weights of the primary indicators corresponding to Bridge No. 2 are:

The membership degree set for Bridge No. 2 is:

According to the maximum membership degree principle, selecting the highest membership degree of 0.6413 as the result of the comprehensive safety assessment for Bridge No. 2 indicates that the overall safety assessment is in a solid state.

Based on the above, the comprehensive safety assessment results of various systems and the overall structure of Bridge No. 2 are shown in Table 23 .

The safety status assessment of Bridge No. 2 relied on the improved AHP-fuzzy comprehensive evaluation method proposed in this study and showed favorable results. The introduced improved AHP-Fuzzy comprehensive evaluation method for bridge safety evaluation has certain significance for technical guidance.

Conclusions

Using the triangular fuzzy number method, improvements have been made to the judgment matrix, allowing experts to rate the importance of indicators without being confined to providing an exact numerical value; instead, they need only provide a score range. This reduces the influence of subjective factors on the evaluation results, ensures the consistency of the judgment matrix, and improves the performance of determining the AHP indicator weight.

By combining the improved AHP with a comprehensive fuzzy assessment, a model is constructed to evaluate the safety status of a single-tower steel box girder suspension bridge over the sea. Building on the determination of the weights of various evaluation indicators using the improved AHP, the comprehensive fuzzy evaluation method is applied to calculate the membership degrees of each indicator, thereby evaluating the safety status of the bridge, resulting in a more reasonable and reliable evaluation result.

The assessment of the safety status of the No. 2 Channel Bridge shows that the bridge is currently in good condition overall and should undergo routine maintenance in the future. It was found that the main cable system of the suspension bridge has the highest weight values, while the weightage of auxiliary facilities and environmental factors is the lowest. Among the environmental factors, chloride ions (CL) were assigned the highest weightage, which can corrode the concrete structure of the bridge, requiring increased additional anti-corrosion measures.

The assessment of the safety status of the No. 2 Channel Bridge shows that the proposed method is effective in assessing bridges under the condition that data from health monitoring systems are collected, so as to determine the safety status of the bridge. This method also accurately evaluates the index system and is of considerable importance for engineering guidance.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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This research was funded by the research project (2022QDFZYG02) grant from Shandong Expressway Qingdao Development Corporation.

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Huifeng Su, Cheng Guo, David Bonfils Kamanda, Fengzhao Su & Liuhong Shang

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Conceptualization, H.S.; methodology, C.G.; software, C.G.; validation, C.G. and H.S.; formal analysis, Z.W.; investigation, C.G. and Z.W.; resource, F.S. and L.S.; data curation, T.H.; writing—original draft preparation, H.S.; writing—review and editing, C.G., D.K. and L.S.; visualization, C.G. and D.K.; supervision, H.S.; project administration, H.S.; funding acquisition, T.H. All authors have read and agreed to the published version of the manuscript.

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Su, H., Guo, C., Wang, Z. et al. Research on safety condition assessment methodology for single tower steel box girder suspension bridges over the sea based on improved AHP-fuzzy comprehensive evaluation. Sci Rep 14 , 12079 (2024). https://doi.org/10.1038/s41598-024-61579-1

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Improving statistical methods to protect wildlife populations

Threats affecting more and more species

In human populations, it is relatively easy to calculate demographic trends and make projections of the future if data on basic processes such as births and immigration is known. The data, given by individuals, can be also death and emigration, which subtract. In the wild, on the other hand, understanding the processes that determine wildlife demographic patterns is a highly complex challenge for the scientific community. Although a wide range of methods are now available to estimate births and deaths in wildlife, quantifying emigration and immigration has historically been difficult or impossible in many populations of interest, particularly in the case of threatened species.

A paper published in the journal Biological Conservation warns that missing data on emigration and immigration movements in wildlife can lead to significant biases in species' demographic projections. As a result, projections about the short-, medium- and long-term future of study populations may be inadequate. This puts their survival at risk due to the implementation of erroneous or ineffective conservation strategies. The authors of the new study are Joan Real, Jaume A. Badia-Boher and Antonio Hernández-Matías, from the Conservation Biology team of the Faculty of Biology of the University of Barcelona and the Institute for Research on Biodiversity (IRBio).

More reliable population predictions

This new study on population biology is based on data collected from 2008 to 2020 on the population of the Bonelli's eagle ( Aquila fasciata ), a threatened species that can be found in Catalonia in the coastal and pre-coastal mountain ranges, from the Empordà to Terres de L'Ebre. In the study, the team emphasises the precision of the population viability analysis (PVA) methodology to improve the management and conservation of long-lived species in the natural environment.

"Population viability analyses are a set of methods that allow us to project the demography of a species into the future, mainly to quantify the probability of extinction of a given species or population of interest," says Joan Real, professor at the Department of Evolutionary Biology, Ecology and Environmental Sciences and head of the Conservation Biology team.

"To date -- he continues -- these projections have mostly been carried out only with data on births and deaths, so that migration processes were ignored because of the difficulty of obtaining these data. In other words, we are trying to make demographic projections without considering two key demographic processes."

In the study of wildlife, population models that do not incorporate immigration or emigration "have a considerable probability of leading to biased projections of future population trends. However, explicitly considering migratory processes allows us to consider all the key demographic processes that determine the future trend of a population," says expert Jaume A. Badia-Boher, first author of the study. "This allows us to be much more precise when making demographic predictions, and therefore also when planning future conservation strategies," he adds.

The development of new and more sophisticated statistical methods over the last decade has made it possible to estimate emigration and immigration in a much more accessible way than before. Including these processes in population viability analyses is therefore relatively straightforward, the paper details.

"This new perspective may imply a relevant advance in the reliability of population viability analyses, which will allow us to estimate the future trend of populations more accurately and propose conservation actions more efficiently," notes Professor Antonio Hernández-Matías. "This is of great importance given that in the current context of global change the extinction rates of species are increasing, and more and more species require urgent and effective conservation actions to reverse their decline," the expert says.

Applying methodological developments to conserve biodiversity

Introducing changes in the structure and modelling of population viability analyses can lead to multiple benefits in many areas of biodiversity research and conservation. "Methodological advances are effective when they are applied. For this reason, the application of the new methodology in populations and species of conservation interest should be promoted. It is a priority to make these methodologies known to the scientific community, managers and administration, in order to prioritise conservation actions with the best available methods," say the authors.

"In the future, new methodologies must continue to be developed, as has been done in this study, as they are key to understanding how wild populations function, what measures need to be implemented to conserve them, and how to make these measures as efficient as possible. In the case of endangered species such as the Bonelli's eagle, knowing the rates of emigration and immigration is key to understanding the state of self-sustainability of a population, and thus implementing efficient conservation measures," concludes the team.

• Ecology Research
• Wild Animals
• Biodiversity
• Environmental Policy
• Population dynamics of fisheries
• Weather forecasting
• Wildlife gardening
• Data mining
• Scientific visualization
• Temperature record of the past 1000 years
• Scientific method
• IPCC Report on Climate Change - 2007

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Materials provided by University of Barcelona . Note: Content may be edited for style and length.

Journal Reference :

• Jaume A. Badia-Boher, Joan Real, Antonio Hernández-Matías. Assumptions about survival estimates and dispersal processes can have severe impacts on population viability assessments . Biological Conservation , 2024; 292: 110550 DOI: 10.1016/j.biocon.2024.110550

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