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1.2.4: Geography and the Scientific Method

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• Michael E. Ritter
• University of Wisconsin-Stevens Point via The Physical Environment

The steps in geographic inquiry are embodied in the "scientific method". The  scientific method  consists of systematic observation, formulation, testing and revision of hypotheses. If a hypothesis withstands the scrutiny of repeated experimentation and review it may be elevated to a theory. Theories may undergo revision as new data and research methods are improved.

The scientific method includes:

• Observation
• Hypothesis Formulation
• Choose methods of analysis
• Data collection
• Analysis: Hypothesis testing
• Hypothesis acceptance or rejection
• Report results

Let's look at a very simple example of how you as a geographer could use the scientific method.

Observation. During a trip through the Cascade Range of Oregon you notice that the western slope tends to have more lush vegetation than the eastern slope and wonder why. Our experience tells us that vegetation requires moisture to live, and more lush vegetation is found where precipitation is abundant. Could it be that the western slopes are rainier than the eastern slopes given the spatial variation in vegetation?

Hypothesis formulation.  A  hypothesis  is referred to as "an educated guess". That is, upon recognizing a particular pattern displayed by earth phenomenon, the geographer offers a "guess" or explanation as to what caused it. Previous research serves as the foundation for constructing hypotheses. Given our initial observation and past experience we suggest that there is a relationship between slope orientation and precipitation.

A hypothesis is stated in a clear and concise way so that it can be tested through data collection and analysis.When constructing a hypothesis, scientists actually formulate two hypotheses related to their problem. The  null hypothesis  is a statement of no relationship. This is the hypothesis we will either reject or not reject. The null hypothesis (Ho) for our problem is:

H o : There is no relationship between slope orientation and precipitation.

The  alternative hypothesis  is a statement of relationship. The alternate hypothesis is:

H a : There is a relationship between slope orientation and precipitation.

Determine the methods  used to test our hypothesis is the next step. There are a variety of quantitative and qualitative methods to test our hypothesis. One could calculate the average precipitation for the western and eastern slopes and apply a difference of means test ( t-test ).

Data collection.  In order to test our hypothesis we must collect a sample of data. For most cases, a sample set of 30 will suffice.  Primary data  can be collected in the field and analyzed, or secondary data that has already been published can be used. Precipitation data is available from a variety of public and private sources.

Analysis: Testing the hypothesis.  A geographer often starts their analysis using some way to visualize the spatial pattern of precipitation. A map showing the geographic pattern of precipitation can be created if data from several places have been obtained. Or a graph of precipitation with the y-axis scaled for precipitation and x-axis for distance between locations along a  transect . Statistics describing the data are usually calculated. The mean or average of each data set (west side and east side of the mountains) are determined and finally the hypothesis is tested using the difference of means test.

Hypothesis Acceptance/Rejection (Explanation) . After testing our hypothesis we will either accept or reject our null hypothesis. In reality, we can't prove our hypothesis correct, we can only disprove it based on our analysis. That is, we reject the null hypothesis that there is no difference in precipitation based on the data that we have collected. If new data or better data collection techniques are available in the future, they may lead us to conclude that we cannot reject our null hypothesis. Hence it is hard to prove a hypothesis is correct as new information and understanding may present itself in the future.

Report Results. If we can accepted out hypothesis then we can report our results so others can scrutinize our work and test our hypothesis under different circumstances.If our null hypothesis is rejected we can turn to our alternative hypothesis or restate the null hypothesis in a different way. Thus, applying the scientific method can be an iterative process. If our work can be replicated many times under different circumstance the hypothesis can be elevated to a theory. A theory can be a hypothesis or group of hypotheses that has been validated through repeated experiments and coming to the same conclusion.

Assess your basic understanding of the preceding material by "Looking Back: The Discipline of Geography" or continue reading.

Intro to GIS and Spatial Analysis

Chapter 12 hypothesis testing, 12.1 irp/csr.

Figure 12.1: Could the distribution of Walmart stores in MA have been the result of a CSR/IRP process?

Popular spatial analysis techniques compare observed point patterns to ones generated by an independent random process (IRP) also called complete spatial randomness (CSR). CSR/IRP satisfy two conditions:

Any event has equal probability of occurring in any location, a 1st order effect .

The location of one event is independent of the location of another event, a 2nd order effect .

In the next section, you will learn how to test for complete spatial randomness. In later sections, you will also learn how to test for other non-CSR processes.

12.2 Testing for CSR with the ANN tool

12.2.1 arcgis’ average nearest neighbor tool.

ArcMap offers a tool (ANN) that tests whether or not the observed first order nearest neighbor is consistent with a distribution of points one would expect to observe if the underlying process was completely random (i.e. IRP). But as we will learn very shortly, ArcMap’s ANN tool has its limitations.

12.2.1.1 A first attempt

Figure 12.2: ArcGIS’ ANN tool. The size of the study area is not defined in this example.

ArcGIS’ average nearest neighbor (ANN) tool computes the 1 st nearest neighbor mean distance for all points. It also computes an expected mean distance (ANN expected ) under the assumption that the process that lead to the observed pattern is completely random.

ArcGIS’ ANN tool offers the option to specify the study surface area. If the area is not explicitly defined, ArcGIS will assume that the area is defined by the smallest area encompassing the points.

ArcGIS’ ANN analysis outputs the nearest neighbor ratio computed as:

\[ ANN_{ratio}=\dfrac{ANN}{ANN_{expected}} \]

Figure 12.3: ANN results indicating that the pattern is consistent with a random process. Note the size of the study area which defaults to the point layer extent.

If ANN ratio is 1, the pattern results from a random process. If it’s greater than 1, it’s dispersed. If it’s less than 1, it’s clustered. In essence, ArcGIS is comparing the observed ANN value to ANN expected one would compute if a complete spatial randomness (CSR) process was at play.

ArcGIS’ tool also generates a p-value (telling us how confident we should be that our observed ANN value is consistent with a perfectly random process) along with a bell shaped curve in the output graphics window. The curve serves as an infographic that tells us if our point distribution is from a random process (CSR), or is more clustered/dispersed than one would expect under CSR.

For example, if we were to run the Massachusetts Walmart point location layer through ArcGIS’ ANN tool, an ANN expected value of 12,249 m would be computed along with an ANN ratio of 1.085. The software would also indicate that the observed distribution is consistent with a CSR process (p-value of 0.28).

But is it prudent to let the software define the study area for us? How does it know that the area we are interested in is the state of Massachusetts since this layer is not part of any input parameters?

12.2.1.2 A second attempt

Figure 12.4: ArcGIS’ ANN tool. The size of the study is defined in this example.

Here, we explicitly tell ArcGIS that the study area (Massachusetts) covers 21,089,917,382 m² (note that this is the MA shapefile’s surface area and not necessarily representative of MA’s actual surface area). ArcGIS’ ANN tool now returns a different output with a completely different conclusion. This time, the analysis suggests that the points are strongly dispersed across the state of Massachusetts and the very small p-value (p = 0.006) tells us that there is less than a 0.6% chance that a CSR process could have generated our observed point pattern. (Note that the p-value displayed by ArcMap is for a two-sided test).

Figure 12.5: ArcGIS’ ANN tool output. Note the different output result with the study area size defined. The output indicates that the points are more dispersed than expected under IRP.

So how does ArcGIS estimate the ANN expected value under CSR? It does so by taking the inverse of the square root of the number of points divided by the area, and multiplying this quotient by 0.5.

\[ ANN_{Expected}=\dfrac{0.5}{\sqrt{n/A}} \]

In other words, the expected ANN value under a CSR process is solely dependent on the number of points and the study extent’s surface area.

Do you see a problem here? Could different shapes encompassing the same point pattern have the same surface area? If so, shouldn’t the shape of our study area be a parameter in our ANN analysis? Unfortunately, ArcGIS’ ANN tool cannot take into account the shape of the study area. An alternative work flow is outlined in the next section.

12.2.2 A better approach: a Monte Carlo test

The Monte Carlo technique involves three steps:

First, we postulate a process–our null hypothesis, \(Ho\) . For example, we hypothesize that the distribution of Walmart stores is consistent with a completely random process (CSR).

Next, we simulate many realizations of our postulated process and compute a statistic (e.g. ANN) for each realization.

Finally, we compare our observed data to the patterns generated by our simulated processes and assess (via a measure of probability) if our pattern is a likely realization of the hypothesized process.

Following our working example, we randomly re-position the location of our Walmart points 1000 times (or as many times computationally practical) following a completely random process–our hypothesized process, \(Ho\) –while making sure to keep the points confined to the study extent (the state of Massachusetts).

Figure 12.6: Three different outcomes from simulated patterns following a CSR point process. These maps help answer the question how would Walmart stores be distributed if their locations were not influenced by the location of other stores and by any local factors (such as population density, population income, road locations, etc…)

For each realization of our process, we compute an ANN value. Each simulated pattern results in a different ANN expected value. We plot all ANN expected values using a histogram (this is our \(Ho\) sample distribution), then compare our observed ANN value of 13,294 m to this distribution.

Figure 12.7: Histogram of simulated ANN values (from 1000 simulations). This is the sample distribution of the null hypothesis, ANN expected (under CSR). The red line shows our observed (Walmart) ANN value. About 32% of the simulated values are greater (more extreme) than our observed ANN value.

Note that by using the same study region (the state of Massachusetts) in the simulations we take care of problems like study area boundary and shape issues since each simulated point pattern is confined to the exact same study area each and every time.

12.2.2.1 Extracting a \(p\) -value from a Monte Carlo test

The p-value can be computed from a Monte Carlo test. The procedure is quite simple. It consists of counting the number of simulated test statistic values more extreme than the one observed. If we are interested in knowing the probability of having simulated values more extreme than ours , we identify the side of the distribution of simulated values closest to our observed statistic, count the number of simulated values more extreme than the observed statistic then compute \(p\) as follows:

\[ \dfrac{N_{extreme}+1}{N+1} \]

where N extreme is the number of simulated values more extreme than our observed statistic and N is the total number of simulations. Note that this is for a one-sided test.

A practical and more generalized form of the equation looks like this:

\[ \dfrac{min(N_{greater}+1 , N + 1 - N_{greater})}{N+1} \]

where \(min(N_{greater}+1 , N + 1 - N_{greater})\) is the smallest of the two values \(N_{greater}+1\) and \(N + 1 - N_{greater}\) , and \(N_{greater}\) is the number of simulated values greater than the observed value. It’s best to implement this form of the equation in a scripting program thus avoiding the need to visually seek the side of the distribution closest to our observed statistic.

For example, if we ran 1000 simulations in our ANN analysis and found that 319 of those were more extreme (on the right side of the simulated ANN distribution) than our observed ANN value, our p-value would be (319 + 1) / (1000 + 1) or p = 0.32 . This is interpreted as “there is a 32% probability that we would be wrong in rejecting the null hypothesis H o .” This suggests that we would be remiss in rejecting the null hypothesis that a CSR process could have generated our observed Walmart point distribution. But this is not to say that the Walmart stores were in fact placed across the state of Massachusetts randomly (it’s doubtful that Walmart executives make such an important decision purely by chance), all we are saying is that a CSR process could have been one of many processes that generated the observed point pattern.

If a two-sided test is desired, then the equation for the \(p\) value takes on the following form:

\[ 2 \times \dfrac{min(N_{greater}+1 , N + 1 - N_{greater})}{N+1} \]

where we are simply multiplying the one-sided p-value by two.

12.3 Alternatives to CSR/IRP

Figure 12.8: Walmart store distribution shown on top of a population density layer. Could population density distribution explain the distribution of Walmart stores?

The assumption of CSR is a good starting point, but it’s often unrealistic. Most real-world processes exhibit 1 st and/or 2 nd order effects. We therefore may need to correct for a non-stationary underlying process. We can simulate the placement of Walmart stores using the population density layer as our inhomogeneous point process. We can test this hypothesis by generating random points that follow the population density distribution.

Figure 12.9: Examples of two randomly generated point patterns using population density as the underlying process.

Note that even though we are not referring to a CSR/IRP point process, we are still treating this as a random point process since the points are randomly located following the underlying population density distribution. Using the same Monte Carlo (MC) techniques used with IRP/CSR processes, we can simulate thousands of point patterns (following the population density) and compare our observed ANN value to those computed from our MC simulations.

Figure 12.10: Histogram showing the distribution of ANN values one would expect to get if population density distribution were to influence the placement of Walmart stores.

In this example, our observed ANN value falls far to the right of our simulated ANN values indicating that our points are more dispersed than would be expected had population density distribution been the sole driving process. The percentage of simulated values more extreme than our observed value is 0% (i.e. a p-value \(\backsimeq\) 0.0).

Another plausible hypothesis is that median household income could have been the sole factor in deciding where to place the Walmart stores.

Figure 12.11: Walmart store distribution shown on top of a median income distribution layer.

Running an MC simulation using median income distribution as the underlying density layer yields an ANN distribution where about 16% of the simulated values are more extreme than our observed ANN value (i.e. p-value = 0.16):

Figure 12.12: Histogram showing the distribution of ANN values one would expect to get if income distribution were to influence the placement of Walmart stores.

Note that we now have two competing hypotheses: a CSR/IRP process and median income distribution process. Both cannot be rejected. This serves as a reminder that a hypothesis test cannot tell us if a particular process is the process involved in the generation of our observed point pattern; instead, it tells us that the hypothesis is one of many plausible processes.

It’s important to remember that the ANN tool is a distance based approach to point pattern analysis. Even though we are randomly generating points following some underlying probability distribution map we are still concerning ourselves with the repulsive / attractive forces that might dictate the placement of Walmarts relative to one another–i.e. we are not addressing the question “can some underlying process explain the X and Y placement of the stores” (addressed in section 12.5 ). Instead, we are controlling for the 1 st order effect defined by population density and income distributons.

12.4 Monte Carlo test with K and L functions

MC techniques are not unique to average nearest neighbor analysis. In fact, they can be implemented with many other statistical measures as with the K and L functions. However, unlike the ANN analysis, the K and L functions consist of multiple test statistics (one for each distance \(r\) ). This results in not one but \(r\) number of simulated distributions. Typically, these distributions are presented as envelopes superimposed on the estimated \(K\) or \(L\) functions. However, since we cannot easily display the full distribution at each \(r\) interval, we usually limit the envelope to a pre-defined acceptance interval. For example, if we choose a two-sided significance level of 0.05, then we eliminate the smallest and largest 2.5% of the simulated K values computed for for each \(r\) intervals (hence the reason you might sometimes see such envelopes referred to as pointwise envelopes). This tends to generate a saw-tooth like envelope.

Figure 12.13: Simulation results for the IRP/CSR hypothesized process. The gray envelope in the plot covers the 95% significance level. If the observed L lies outside of this envelope at distance \(r\) , then there is less than a 5% chance that our observed point pattern resulted from the simulated process at that distance.

The interpretation of these plots is straight forward: if \(\hat K\) or \(\hat L\) lies outside of the envelope at some distance \(r\) , then this suggests that the point pattern may not be consistent with \(H_o\) (the hypothesized process) at distance \(r\) at the significance level defined for that envelope (0.05 in this example).

One important assumption underlying the K and L functions is that the process is uniform across the region. If there is reason to believe this not to be the case, then the K function analysis needs to be controlled for inhomogeneity in the process. For example, we might hypothesize that population density dictates the density distribution of the Walmart stores across the region. We therefore run an MC test by randomly re-assigning Walmart point locations using the population distribution map as the underlying point density distribution (in other words, we expect the MC simulation to locate a greater proportion of the points where population density is the greatest).

Figure 12.14: Simulation results for an inhomogeneous hypothesized process. When controlled for population density, the significance test suggests that the inter-distance of Walmarts is more dispersed than expected under the null up to a distance of 30 km.

It may be tempting to scan across the plot looking for distances \(r\) for which deviation from the null is significant for a given significance value then report these findings as such. For example, given the results in the last figure, we might not be justified in stating that the patterns between \(r\) distances of 5 and 30 are more dispersed than expected at the 5% significance level but at a higher significance level instead. This problem is referred to as the multiple comparison problem –details of which are not covered here.

12.5 Testing for a covariate effect

The last two sections covered distance based approaches to point pattern analysis. In this section, we explore hypothesis testing on a density based approach to point pattern analysis: The Poisson point process model.

Any Poisson point process model can be fit to an observed point pattern, but just because we can fit a model does not imply that the model does a good job in explaining the observed pattern. To test how well a model can explain the observed point pattern, we need to compare it to a base model (such as one where we assume that the points are randomly distributed across the study area–i.e. IRP). The latter is defined as the null hypothesis and the former is defined as the alternate hypothesis.

For example, we may want to assess if the Poisson point process model that pits the placement of Walmarts as a function of population distribution (the alternate hypothesis) does a better job than the null model that assumes homogeneous intensity (i.e. a Walmart has no preference as to where it is to be placed). This requires that we first derive estimates for both models.

A Poisson point process model (of the the Walmart point pattern) implemented in a statistical software such as R produces the following output for the null model:

and the following output for the alternate model.

Thus, the null model (homogeneous intensity) takes on the form:

\[ \lambda(i) = e^{-19.96} \]

and the alternate model takes on the form:

\[ \lambda(i) = e^{-20.1 + 1.04^{-4}population} \]

The models are then compared using the likelihood ratio test which produces the following output:

The value under the heading PR(>Chi) is the p-value which gives us the probability we would be wrong in rejecting the null. Here p=0.039 suggests that there is an 3.9% chance that we would be remiss to reject the base model in favor of the alternate model–put another way, the alternate model may be an improvement over the null.

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Hypothesis testing in Statistics Geography

Table of Contents

1. Introduction :

Hypothesis testing is a statistical tool. We use it in making statistical decisions by using different experimental data. Ronald Fisher, Karl Pearson, Jerzy Neyman, and E. Pearson are the famous personalities who introduce Hypothesis testing in their statistical analysis. It is basically an assumption that we make about the population parameter. A hypothesis is an intellectual or educated guess about something in the world around us. Each and every hypothesis should be testable, either by experiment or observation. For example, we can say- “Arsenic album will work better for preventing COVID-19 if it is used in a recommended dose”. So, today we will be learning more about Hypothesis testing in Statistics Geography .

2. Syntax of hypothesis statement:

When we go to propose a hypothesis, we remember the form or syntax of the hypothesis.

The syntax is:

It will be:  If > Subject (I/we/you/someone) > do any action (independent variable) > then > will happen (result) > statement dependent variable.

 a. If we (use the Arsenic album in a recommended dose) then (COVID-19 can be prevented).

 b. If I (increase the amount of water to a plant) then (it will increase in size).

 c. If Amal (gives exams at noon instead of 7 am) then (his test scores will improve).

 d. If you (look in the equatorial region) then (you will find more new species).

 e. If Government (extended lockdown twice per week) then (COVID-19 positive rate will decrease).

A good hypothesis statement should:

• According to the University of California, a hypothesis statement includes an “if” and “then” statement.
• Include both the independent and dependent variables in a hypothesis statement.
• The hypothesis statement will be testable by experiment, survey, or other scientifically sound technique.
• For engineering or programming projects hypothesis statements have design criteria.
• The hypothesis statement will be based on information in prior research. It may be yours or someone else’s.

3. Terminology and concepts:

I) null hypothesis: .

A null hypothesis is a statistical hypothesis in which there are no significant differences exist between the set of variables.

The null hypothesis is always an accepted fact. It is the original or default statement that is tested. We can reject a null hypothesis, but it cannot accept just on the basis of a single test.

Simple examples of null hypotheses which are true. They are:

• Everest is the highest peak in the world.
• Excluding Pluto, there are 8 planets in our solar system.
• Taking alcohol can increase our risk of liver problems.
• Generally, in a null hypothesis it is the observation. It is due to a chance factor. 
• We express the null hypothesis by; H 0  or H a  (H-zero or H-a): μ 1  = μ 2 , which shows that there is no difference between the two population means.

ii)  Alternative hypothesis: 

The alternative hypothesis is a statement in which some statistical significance between two measured or tested phenomena or observations.

It is contradictory to the null hypothesis; the alternative hypothesis shows that observations indeed are the result of a real effect. We represent it by H 1  (H-one) or H a  (H-a).

The acceptance of the alternative hypothesis depends upon the rejection of the null hypothesis. Generally until and unless the null hypothesis is rejected, an alternative hypothesis cannot be accepted.

iii) Level of significance:  

It refers to the degree of significance in which we accept or reject the null hypothesis.  100% accuracy is not possible for accepting or rejecting a hypothesis, so we, therefore, select a level of significance, and that is usually 5%.

iv) Error: 

Generally, in most cases, we consider two types of errors in hypothesis testing.

Type I error: 

When we reject the null hypothesis, though that hypothesis was true, then a type I error is found.   It is denoted by alpha ( α ).  In hypothesis testing, the normal probability curve that shows the critical region is called the alpha region.

Figure1. Different regions in Normal Probability Curve

Type II errors:  

We accept the null hypothesis when it is false. It is a type II error. It is denoted by beta ( β) .  In Hypothesis testing, the normal probability curve that shows the acceptance region is called the beta region.

Figure 2. Errors in Hypothesis

v) Power: 

We generally consider the probability of correctly accepting the null hypothesis.  1-beta is the power of the analysis in hypothesis testing.

vi) One-tailed test: 

When we see, the given statistical hypothesis is one value like H 0 : μ 1  = μ 2 . it is the one-tailed test.

vii) Two-tailed test: 

When we see, the given statistics hypothesis assumes a less than (<) or greater (>) than value, it is called the two-tailed test.

viii) P-value: 

In hypothesis testing, P-value is the calculated probability of the null hypothesis (H 0  )is true. In a statistical hypothesis, we perform a set of mathematical/statistical calculations to estimate the probability of what we are observing, given the H 0  is really true.

If the P-value is lower than the predefined significant level (alpha significant level), then we reject the null hypothesis (H 0 ) in favor of the alternative hypothesis (H 1 ) because there is sufficient evidence to prove the null hypothesis (H 0 ) is wrong. (P-value will discuss elaborately in the T-Test Video lecture)

4.  Area of acceptance & Rejection of Null Hypothesis:

Figure 3. Area of acceptance & rejection of Null Hypothesis.

5. Hypothesis testing in Statistics:

• In statistics, it is a way for us to test the results of a survey or experiment to see if we have meaningful results. We basically test whether our results are valid by figuring out the odds, or our results have happened by chance. If our results may have happened by chance, the experiment would not be repeatable.
•  At first, we have to identify our  null hypothesis . Then it will be easier. All of us should need to do:
• Figure out our null hypothesis,
• State our null hypothesis,
• Choose what kind of test we need to perform,
• We support or reject the null hypothesis.

6. Examples of Hypothesis testing in Statistics:

A research scholar thinks that, if COVID-19 positive patients take vapor to inhale twice a day (instead of 4 times), their recovery period will be longer. An average recovery time for COVID-19 positive patients is 3.5 weeks.

                The hypothesis statement in this question is that the researcher believes the average recovery time is more than 3.5 weeks. In mathematical terms – H1: μ > 3.5

                Now, the researcher will need to state the null hypothesis. The null hypothesis was, “if the vapor inhales time decrease, then the recovery period will be longer for COVID-19 positive patients”.

                If the researcher is wrong after the sufficient experiment and test then the null hypothesis is rejected and the alternative hypothesis is accepted.

                From the above example, if the researcher is wrong then the recovery time is less than or equal to 3.5 weeks. In the mathematical expression, that is:  H 0  : μ ≤ 3.5 , Error  Type II  takes place here.

                So, here we should reject the null hypothesis and accept the alternative hypothesis.

• Mathematical expression for decisions making:

Figure 4.  Mathematical expression for decisions making

7. Comparison of two Hypothesis:

Figure 5. Comparison of two Hypothesis

8. Conclusion:

There are two outcomes of a statistical test.

First- A null hypothesis is rejected and an alternative hypothesis is accepted.

Second- The null hypothesis is accepted, on the basis of the evidence.

Figure 6. Conclusion table for acceptance & rejection.

Video on Hypothesis testing in Statistics:

Here is my video on hypothesis testing, you can watch it for a better understanding and concept.

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9. Homework Assignments for Hypothesis testing in Statistics

H Q1. What is Hypothesis Testing? Explain the different types of hypotheses.  

HQ2. Discuss the acceptance and rejection area of the null hypothesis with a diagram.

HQ3. Figure out a null hypothesis for an example and explain its acceptance or rejection.

Advanced short answer questions (AQ)  (Answer expected on the comment box of this article) •

AQ1. What will be the name, if one value in the given statistical hypothesis is like H 0 : μ 1  = μ 2 ?

AQ2. Write an example of a good hypothesis statement.

AQ3. A null hypothesis is true yet we reject it. What type of error it is ?

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LAB 5: Hypothesis Testing

Where are we going, hypothesis testing, decision rule, selecting the appropriate test.

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• Knowledge Base
• Choosing the Right Statistical Test | Types & Examples

Choosing the Right Statistical Test | Types & Examples

Published on January 28, 2020 by Rebecca Bevans . Revised on June 22, 2023.

Statistical tests are used in hypothesis testing . They can be used to:

• determine whether a predictor variable has a statistically significant relationship with an outcome variable.
• estimate the difference between two or more groups.

Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.

If you already know what types of variables you’re dealing with, you can use the flowchart to choose the right statistical test for your data.

Statistical tests flowchart

Table of contents

What does a statistical test do, when to perform a statistical test, choosing a parametric test: regression, comparison, or correlation, choosing a nonparametric test, flowchart: choosing a statistical test, other interesting articles, frequently asked questions about statistical tests.

Statistical tests work by calculating a test statistic – a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship.

It then calculates a p value (probability value). The p -value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true.

If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables.

If the value of the test statistic is less extreme than the one calculated from the null hypothesis, then you can infer no statistically significant relationship between the predictor and outcome variables.

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You can perform statistical tests on data that have been collected in a statistically valid manner – either through an experiment , or through observations made using probability sampling methods .

For a statistical test to be valid , your sample size needs to be large enough to approximate the true distribution of the population being studied.

To determine which statistical test to use, you need to know:

• whether your data meets certain assumptions.
• the types of variables that you’re dealing with.

Statistical assumptions

Statistical tests make some common assumptions about the data they are testing:

• Independence of observations (a.k.a. no autocorrelation): The observations/variables you include in your test are not related (for example, multiple measurements of a single test subject are not independent, while measurements of multiple different test subjects are independent).
• Homogeneity of variance : the variance within each group being compared is similar among all groups. If one group has much more variation than others, it will limit the test’s effectiveness.
• Normality of data : the data follows a normal distribution (a.k.a. a bell curve). This assumption applies only to quantitative data .

If your data do not meet the assumptions of normality or homogeneity of variance, you may be able to perform a nonparametric statistical test , which allows you to make comparisons without any assumptions about the data distribution.

If your data do not meet the assumption of independence of observations, you may be able to use a test that accounts for structure in your data (repeated-measures tests or tests that include blocking variables).

Types of variables

The types of variables you have usually determine what type of statistical test you can use.

Quantitative variables represent amounts of things (e.g. the number of trees in a forest). Types of quantitative variables include:

• Continuous (aka ratio variables): represent measures and can usually be divided into units smaller than one (e.g. 0.75 grams).
• Discrete (aka integer variables): represent counts and usually can’t be divided into units smaller than one (e.g. 1 tree).

Categorical variables represent groupings of things (e.g. the different tree species in a forest). Types of categorical variables include:

• Ordinal : represent data with an order (e.g. rankings).
• Nominal : represent group names (e.g. brands or species names).
• Binary : represent data with a yes/no or 1/0 outcome (e.g. win or lose).

Choose the test that fits the types of predictor and outcome variables you have collected (if you are doing an experiment , these are the independent and dependent variables ). Consult the tables below to see which test best matches your variables.

Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests.

The most common types of parametric test include regression tests, comparison tests, and correlation tests.

Regression tests

Regression tests look for cause-and-effect relationships . They can be used to estimate the effect of one or more continuous variables on another variable.

Comparison tests

Comparison tests look for differences among group means . They can be used to test the effect of a categorical variable on the mean value of some other characteristic.

T-tests are used when comparing the means of precisely two groups (e.g., the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g., the average heights of children, teenagers, and adults).

Correlation tests

Correlation tests check whether variables are related without hypothesizing a cause-and-effect relationship.

These can be used to test whether two variables you want to use in (for example) a multiple regression test are autocorrelated.

Non-parametric tests don’t make as many assumptions about the data, and are useful when one or more of the common statistical assumptions are violated. However, the inferences they make aren’t as strong as with parametric tests.

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This flowchart helps you choose among parametric tests. For nonparametric alternatives, check the table above.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient
• Null hypothesis

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Statistical tests commonly assume that:

• the data are normally distributed
• the groups that are being compared have similar variance
• the data are independent

If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.

A test statistic is a number calculated by a  statistical test . It describes how far your observed data is from the  null hypothesis  of no relationship between  variables or no difference among sample groups.

The test statistic tells you how different two or more groups are from the overall population mean , or how different a linear slope is from the slope predicted by a null hypothesis . Different test statistics are used in different statistical tests.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

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Research in Geography and Geography Education: The Roles of Theory and Thought

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Butt, G. (2020). Research in Geography and Geography Education: The Roles of Theory and Thought. In: Geography Education Research in the UK: Retrospect and Prospect. International Perspectives on Geographical Education. Springer, Cham. https://doi.org/10.1007/978-3-030-25954-9_8

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The Debate About Geography and Institutions

Geographical and institutional factors in the economic development of lodz, the effect of geography and institutions on economic development: the case of lodz.

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Joanna Dzionek-Kozlowska , Kamil Kowalski , Rafal Matera; The Effect of Geography and Institutions on Economic Development: The Case of Lodz. The Journal of Interdisciplinary History 2018; 48 (4): 523–538. doi: https://doi.org/10.1162/JINH_a_01198

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Economic development in the Polish city of Lodz was a function of both geography and institutions. Neither geographical nor institutional factors, if taken separately, was a sufficient condition for long-term development. Although the economic achievements of Lodz depended on environmental factors throughout the entire period before World War I, dynamic progress there had to await the establishment of a beneficial institutional background—a change from wool to cotton production, the abolition of a custom’s border, and the construction of a railway system—in the nineteenth century.

One of the longest, most heated, and still unsettled debates in economics is about pinpointing the factors responsible for economic development. What are the main factors that cause some areas to prosper whereas others do not? Two distinct approaches have emerged from this debate—the geography hypothesis that holds natural resources accountable for economic performance and the institutions hypothesis that credits socio-economic conditions as the major determinants of economic progress.

Using Lodz, one of the largest cities in Poland as a case study, this research note demonstrates that progress is a function of a combination of geographical and institutional factors. The history of Lodz provides an excellent opportunity to identify the extent to which these two types of factors serve as incentives for, or hindrances to, economic development. We focus on the period from the 1820s to World War I, during which the foundations of the city’s later economic performance were laid. 1

What explains the city’s economic stagnation for the four first centuries of its existence and its subsequent rapid growth, the pace of which, expressed in terms of population growth, was the fastest in nineteenth-century Europe? We want additionally to investigate why Lodz, rather than other towns in its vicinity, became the center of the textile industry. Our exploration enables us to suggest that neither geographical nor institutional factors, if taken separately, is a sufficient condition for long-term development, regardless of how favorable it may be. Even though we can identify a stronger influence of one factor over the other in specific moments of the city’s history, both factors need to work in unison to bring about long-term economic success.

The complexities of identifying the causes of economic progress have resulted in an overwhelming diversity of theories, which are difficult to encapsulate into a rigid classification. It seems, however, that at the most basic level, the existing theories range from highlighting the role of environmental components—the geography hypothesis—to highlighting human factors—the institutions hypothesis.

The crux of the geography hypothesis is the positive relationship between access to natural resources and economic performance. The availability of certain environmental components is considered a prerequisite for economic development, whereas the lack of them is claimed to hinder or even preclude progress. The two types of resources usually indicated are endowments—the elements vital to agriculture (a favorable climate, access to water, fertility of the soil, and a diversity of flora and fauna)—and energy sources such as coal, iron, and hydrocarbons. 2

According to the institutions hypothesis, however, the major factors behind economic development belong to the social environment, permitting opportunities to improve knowledge about how to use the resources at hand. Natural resources may be a gift, but the understanding, skills, and abilities to deploy them adequately are not. The answer to the question of which elements count as economic resources depends on people’s awareness of the methods available to benefit from them. The key task is to describe a social environment that enables people to do so. Hence, the indirect determinants of economic progress are the systems of rules, legal norms, values, customs, and/or beliefs that provide a framework for development. The contemporary economic literature refers to these “rules of the game in a society or, more formally, all the humanly devised constraints that shape human interaction” as institutions . 3

One of the strongest arguments in the twenty-first century regarding the influences on development comes from the work of Daron Acemoglu and James A. Robinson, especially Why Nations Fail: The Origins of Power, Prosperity, and Poverty (Chicago, 2012). Their model is placed squarely at the institutional end of the spectrum of theories. In their view, economic success takes place within a political order based on inclusive institutions that permit new social groups to engage in economic activity. Acemoglu and Robinson acknowledge that geographical factors may have been important, especially during the agricultural age, but they deny that the absence of these factors can explain either the contemporary inequalities or the long-term economic stagnation that besets certain nations. 4

Given the difficulty of untangling the complex mysteries of long-term economic development, it is hardly surprising that single-factor explanations are so rare. Nevertheless, as the theory of Acemoglu and Robinson illustrates, certain components tend to be advanced as leading sources of economic success, often setting the institutional and geographical hypotheses in opposition and embroiling economists in debates about the supremacy of one side or the other. The questions apply to cities, towns, and regions as much as they do to nations: Why do some municipal economies succeed and others fail? Can the economic prosperity and poverty of cities be the consequence solely of specific geographical patterns, or is it only a result of establishing effective economic institutions and eliminating destructive ones? Contrary to approaches that tend toward a monocausal explanation, this research note contends that long-term economic development needs both a favorable geographical and a favorable institutional context.

Lodz as a Small Rural Town (Fifteenth to Eighteenth Century)

The geographical effect on Lodz was subtle, linked to the city’s specific history. The development of Lodz did not proceed gradually and steadily but by sharp leaps and bounds in which both geography and politics played a role. Surrounded by forests, and not easily accessible, Lodz remained a small settlement on the periphery of the main Polish regions—Great Poland, Mazovia, and Little Poland—for many decades. In a sense, Lodz was born twice. The first birth was in 1423, when King Wladyslaw Jagiello granted the city its charter, and the Bishop of Wloclawek established the townspeople’s dues and duties. Since the city was far from the diocese, the bishops showed little enthusiasm for its growth. The second birth occurred in the 1820s, when the authorities of the Kingdom of Poland designated Lodz as a new industrial center. During this period, the city became part of various states—the Polish-Lithuanian Commonwealth until 1793, the Kingdom of Prussia from 1793 to 1807, the Duchy of Warsaw from 1807 to 1815, and the Kingdom of Poland from 1815 until World War I.

The city is situated in a region called the Lodz Upland in central Poland. Only one-fifth of the area was suitable for agriculture. The quality of the land was even worse during the pre-industrial era, when the high water levels turned it into an acidic swamp. The uneven terrain lacked drainage, liming, and fertilization. A combination of poor agricultural prospects and general inaccessibility discouraged the migration of new settlers and trade for almost four centuries. 5

Like many cities elsewhere in the world, those in Lodz’s vicinity evolved along rivers—both the larger rivers, such as the Warta and the Pilica, and the smaller ones, such as the Bzura, the Ner, and the Prosna—eventually becoming trade centers with urban populations. Lodz, however, was situated on a line of drainage basins near the watershed of the Vistula and the Odra rivers, the two biggest rivers in Poland. Even though nineteen rivulets and brooks that flowed into tributaries of these rivers cut through the town, their significance to Lodz’s development was minor since they were non-navigable.

Nor were the institutional system and policies throughout Poland from 1400 to 1700 conducive to urban development. The growing political role of the Polish nobility ( szlachta ) beginning in the fifteenth century culminated in an institutional order that diminished the political and economic standing of the other social classes. In 1496, the elite landowners made certain that villages would retain a competitive advantage over cities by preventing farm laborers from seeking work outside rural areas. The confinement of peasants to agriculture guaranteed an inexpensive, if not entirely free, workforce for the nobility. These policies weakened the domestic demand for agricultural production, as well as for the local crafts that were crucial to urbanization. Hence, Poland’s cities were significantly smaller in number and size than those in such Western European countries as the Netherlands and Britain where the conditions that encouraged cities to prosper were fostered.

During the fifteenth century, Lodz remained a small town that peaked at about 100 households and 30 craftsmen, including weavers, wheelers, ironsmiths, and shoemakers. In the seventeenth century, the town obtained permission to organize a market once a week. However, a series of wars with Russians, Tartars, Cossacks, Turks, and an especially damaging war with the Swedes, was an enormous setback for Lodz and other Polish cities. The aftermath of these conflicts was the eventual partition of Poland into Russian, Prussian, and Austrian territories in the late eighteenth century.

Two years before the collapse of the Polish state in 1793, Prussia annexed the Lodz region during the second partition of Poland. At that time, when Lodz had only 44 households and 200 inhabitants in the town, the Prussian authorities considered withdrawing its city rights and reverting it to village status. Although it retained its rights, a new administrative map removed it from the estates of the Bishop of Wloclawek. From 1796 to 1798, it devolved to the state authorities, along with all other former church estates. After the formation of the Kingdom of Poland, the property fell under the heading of so-called “government goods.”

Secularization and the easing of rules regarding ownership created foundations for Lodz to undergo an economic boost c. 1820. Between the years 1793 and 1808, the population doubled, due partly to an influx of Jewish migrants (from eleven in 1793 to fifty-eight in 1808). Another legacy of the fourteen-year Prussian rule was the emergence of German colonies around the city. The Prussian invaders made Lodz a trading center to revitalize economic activity in the region. The overarching policy of the Prussian authorities, however, aimed at the liquidation of industry in the Polish lands incorporated into the Prussian monarchy. The lands were to be converted into farmland to provide agricultural products for the western parts of the country. The area was also intended to serve as a market for industrial goods from Western Prussia. 6

The “Take-Off” Moment in the First Half of the Nineteenth Century

The economic development initiated by the Prussian regulations flourished in the new political order established at the end of the Napoleonic wars, after the Vienna Congress of 1815. The borders between the three partitioning countries shifted, and Lodz, which had earlier belonged to Prussia, became a part of the newly established Kingdom of Poland—a semi-autonomous state connected to the Russian Empire. These border shifts triggered not only political but also economic consequences, cutting traditional trade connections. As a result, the textile industry in Greater Poland and Silesia, both of which still belonged to Prussia, began to suffer. The producers there were isolated from their former customers. They could not compensate for decline in demand because of the highly competitive internal Prussian market. At that time, the textile industry in the Kingdom of Poland was not sufficiently developed to increase its capacity quickly enough to benefit from the unsatisfied demand in its market. The resultant opportunity to make profits, however, triggered a gradual influx of bankrupt weavers from Greater Poland and Silesia to the Kingdom of Poland. 7

The geographical location of Lodz turned out to be an advantage. The redrawing of the borders in 1815 turned many of the central Polish cities—Wloclawek, Kalisz, Sieradz, Wielun, and Czestochowa—into border cities. Lodz’s location in the center of the Kingdom of Poland, 100 km from the nearest border on the west, became a political safety net; in this turbulent era, investments along the borders carried high risk. Another stimulus for the creation of industrial centers in the Kingdom of Poland was related to changes in its tariff policy with Prussia, on the one hand, and with Russia, on the other. In 1822, following a brief liberal period, Russia returned to a protective customs policy vis-à-vis both the Kingdom of Poland and Prussia. Hence, the Kingdom of Poland’s industry gained protection from Prussian traders, but it was also separated from the Russian market. Yet, Ksawery Drucki-Lubecki, Polish Minister of the Treasury, was able to negotiate a favorable customs agreement with Russia in which the tariffs on textile products made in the Kingdom of Poland were lowered to 1 to 3 percent, whereas both Prussian and Austrian textiles were still claimed at 40 to 50 percent. This policy encouraged German textile craftsmen and entrepreneurs to settle in the Kingdom of Poland. 8

In these complicated circumstances, Lodz stumbled into another advantage over other cities in the region—its natural resources. It’s clay became a stimulant for economic development in the nineteenth century, when bricks were needed to build factories. Its non-navigable streams became the basis for producing energy in the production of woolen, linen, and cotton fabrics, all the more given that the water was soft and clean. The timber in its forests helped to meet the growing demand for housing construction. Thus, in the new phase of technological progress, Lodz’s previously insignificant resources became its economic calling cards. When taken together, these advantages set the stage for Lodz’s economic development. But they neither brought rapid progress to the city nor can account for the demographic explosion that occurred in subsequent decades. 9

The crucial institutional element responsible for the boom was the establishment of “industrial villages” in which the economic order was based on a set of highly inclusive institutions designed to invigorate industrialization in the Kingdom of Poland. When the influential representatives of the Kingdom’s authorities noticed the geographical potential of Lodz, they designated the city as an industrial village. 10

In 1816, Jozef Zajaczek, the governor of the Kingdom, issued a policy statement entitled “Provisions for the Settlement of Useful Foreigners in the Country, such as Manufacturers, Craftsmen and Farmers.” It enabled new homesteaders to receive parcels of land along with low-interest loans and assistance in procuring the materials needed for building their houses. It also exempted new arrivals from paying some of the municipal taxes and to import goods and stock duty free. Equally important, it exempted settlers and their sons from army service and gave them the right to return to their home country. 11

In 1821, a new clothing settlement (the so-called New City) and, between 1824 and 1828, a cotton-linen settlement (with four colonies) were officially founded under the new spatial regulations. Watermills were built on both banks of the nearby Lodka and Jasien Rivers. Soon, the area saw the construction of a mangling mill, a fulling mill, a starching mill, and a bleaching mill, all needed for cotton-fabric production. Large volumes of clean water were necessary in all these devices. Thanks to the personal intercession of province authorities, numerous craftsmen and entrepreneurs, such as Krystian Wendisch and Ludwik Geyer, who opened mechanized cotton mills with steam engines and built the first steam mill in the Kingdom of Poland, established businesses in Lodz. In the same area, government factory settlements were also created in Dabie, Gostynin, Przedecz, and Zgierz. Two other towns near Lodz—Aleksandrow and Konstantynow—with private owners did not thrive because of their private ownership, which precluded government backing.

A change from wool to cotton production, inspired by the government’s counsel that cheaper cotton mills would be easier to sell, distinguished Lodz from other textile settlements in Mazowsze province (Zgierz, Tomaszow Mazowiecki, and Ozorkow). The environment of Lodz was also highly suitable to cotton production, especially given the swift currents of the Lodka and the Jasien Rivers, which powered the process. Not all towns were so fortunate. In Leczyca, for example, the stream of the Bzura was too weak to sustain a properly functioning hydraulic system and not as clean and mineral-free as that in Lodz.

In the early 1830s, Lodz produced slightly more than 3 percent of the wool textiles and more than 70 percent of the cotton textiles in the region. This volume served the city well in the local market, especially given the failure of the anti-Tsarist uprising in November 1830, which resulted in severe repression, including high tariffs on cloth exported to Russia. From that point forward, Polish commodities dispatched to Russia were subject to a 3 to 16 percent duty, while Russian exports were still under the 1822 liberal regulations. Moreover, Polish products could not be transported via Russia to far eastern markets (mainly China). These regulations severely wounded the woolen industry, which exported most of its production to eastern markets. The tsar’s liquidation of the Kingdom’s army, a major recipient of woolen textiles, was a further hardship. These measures resulted in the collapse of textile production in nearby Ozorkow, Zgierz, and Tomaszow Mazowiecki. Lodz emerged relatively unscathed, since its cheap cotton was sold mainly in the local markets of the Kingdom. 12

Institutional Factors Affecting the Development of Lodz Before World War I

The first wave of technical revolution in Lodz took place in the 1840s and 1850s. In a short time, manufacturing scaled up from workshop to factory production. The unprecedented investment in technology facilitated exceptional productivity. Within only a single decade, the number of Geyer’s local competitors grew to five large manufacturers—Traugott Grohman, Dawid Lande, Jakub Peters, Karol Moess, and the especially successful, Karol Scheibler, whose thirty mechanical looms combined cotton spinning and weaving in 1844. Scheibler’s greater production capacity not only captured the local market but also ventured into other markets, becoming a threat to the smaller producers.

Another acceleration in cotton production derived from the removal of the customs border with Russia in 1851 and from the tsar’s subsequent customs policies. The abolition of the customs barrier, combined with British reforms to permit the export of machinery, facilitated the industrial modernization of the entire Kingdom but especially of Lodz. Three years later, during the Crimean War, Lodz’s economy received an additional boost from an extension to eastern markets when several European countries established a blockade against Russia. A new Russian tariff policy in 1877 that required all customs duties to be paid in gold (the so-called “gold tariff”) also helped.

Germany responded with “retaliatory tariffs.” Manufacturers in Lodz who imported cotton yarn from Bremen and Hamburg were caught in the crossfire. The most important consequence of the tariff war between Russia and Germany, however, was the slowdown of Western European textiles imported to Russia. Lodz seized the opportunity to dominate the textile trade to Russia and the Far East during late nineteenth century, exporting around 70 to 80 percent of its textile products there.

Certain other factors (albeit not decisive ones) that stimulated the development of Lodz also deserve attention. In the 1850s and 1860s, the Bank of Poland increased its volume of credits to industrialists and merchants—those from Lodz among the biggest recipients. When the enfranchisement of the peasantry in 1864 increased the demand for affordable textiles, Lodz also benefited from the flood of cheap labor from the nearby villages. Between 1875 and 1895, nearly two-thirds of the people arriving to work in Lodz came from villages. As a result, the textile industry in the Kingdom of Poland became highly concentrated in Lodz. At the end of the 1870s, 95 percent of the textile plants were located in the Lodz district; they produced nearly 90 percent of the fabric in the Kingdom and provided 75 percent of the jobs. Three-quarters of Lodz’s employees were involved in manufacturing nine out of the ten textile products produced in the Kingdom. Scheibler and Israel Poznanski owned the largest factories. 13

Until the mid-1860s, the train station closest to Lodz was 30’km away. The prosperity of the city was strengthened considerably by a railway connection that linked the center of the city with Warsaw in 1865. Calisian Rail, launched in 1903, enabled a western connection with the rest of the Kingdom. The first electric railway line in the city was inaugurated in 1898, and tram connections between Lodz and neighboring areas began in 1907.

The speed of Lodz’s transformations can be illustrated demographically. Between 1830 and 1837, the population (permanent and temporary) doubled to 10,000, and again to 20,000 in 1846. By 1857, the number had doubled once more to 40,000. A brief period of stagnation followed until 1865, but the city rebounded in the last decade of the nineteenth century to 200,000 inhabitants. Some statistics indicate that the population exceeded 300,000 during the 1900s. By the outbreak of World War I, more than a half-million people lived in Lodz. Within less than a century, the population had grown a thousand-fold (see Figure 1 ). 14

The Population of Lodz 1793–1914 (in Thousands)

The Role of Minorities in the Development of Lodz

In the context of the institutional factors decisive for Lodz’s long-term growth in the nineteenth century, special mention should go to Lodz’s German and Jewish minorities. Jews were subject to fiscal persecution for many years in the Kingdom of Poland, forced to pay a recruitment tax, an alcoholic-beverage tax, a property-lease tax, a rental-agreement tax, a transportation tax (when traveling to Warsaw), and a kosher-meat tax, in addition to other local taxes. A policy enacted in the 1820s allowed cities to designate certain districts for Jewish populations. When Lodz imposed this regulation in 1825, only the affluent and the educated members of the Jewish community were exempt from it.

In 1859, the local authorities expanded Lodz’s Jewish quarter. In 1862, Tsar Alexander II’s decree conferring equal civil rights to all residents allowed members of the Jewish community to vote and to stand for elections to municipal and county government positions. As the Prussians had done a half-century earlier, the Russians opened its closed areas and granted everyone access to corporate trade and crafts. Subsequent laws also abolished the extra taxes and allowed Jewish people to enter new professions. Yet, even though the law changed, informal institutions were slow to respond. Certain traditional barriers to the economic development of the Jewish population remained. Administrative and civil-service positions were still off limits. Trade was restricted, as was access to the production and sale of alcoholic beverages outside Jewish settlements. Nevertheless, due to the legislative changes of the 1860s, tolerance toward the Jewish population gradually increased; interethnic cooperation and the erosion of stereotypes resulted in economic progress. 15

After the decree of 1862, Jewish entrepreneurs began to invest in the textile industry; Jewish capital eventually displaced German capital. At the beginning of the twentieth century, when the textile industry accounted for more than 90 percent of Lodz’s total production, Jewish businessmen owned 40 percent of the textile factories and Germans 25 percent. Jewish entrepreneurs owned 47 percent of the industry and German entrepreneurs 44 percent; other ethnic groups, including the Poles, held only 9 percent. The number of Jewish factories in the textile industry increased between 1869 and 1913 from around 40 to more than 200—from 13 percent of the total to 52 percent. During the same period, the production and employment of workers in Jewish plants increased from 16 percent to about 40 percent of Lodz’s total. 16

As the competition between the factory owners and financiers escalated, the incentives for lowering production costs caused the rivals to invest in the newest and most efficient machines, thus accelerating technological progress. Before the abolition of the discriminatory legislation, the Germans were the most active economic agents. When the playing field was more level, the Jewish contribution to technological change was as great or even greater than that of the Germans (not to mention the other ethnic groups). 17

This research note indicates that both geographical factors and institutional changes were highly influential during the early period of Lodz’s development. The first, long development phase featured institutions that were predominantly exclusive. Lodz’s environment was then insufficient to spur development. Not until the nineteenth century, with its accompanying administrative and legal changes, did natural resources and institutions begin to play positive roles.

Environmental factors were necessary but not sufficient for the Lodz’s development. Equally important for the city’s industrial thrust was the 1820 decision to create a favorable institutional background and Rajmund Rembielinski’s support for the establishment of a clothier settlement, which constituted a decisive political and institutional action with significant economic consequences. The list of the vital institutional factors shaping the economic development of Lodz is presented in Table 1 . 18

Institutional Factors (Events and Decisions) Influencing Lodz’s Development

Both geography and institutions mattered in the economic development of Lodz. Throughout the entire period before World War I, the economic achievements of Lodz depended on geographical factors. The government’s decisions and the economic choices made by multi-ethnic entrepreneurs were strictly connected with the geography of the city and its access to natural resources. Yet, given the track record of poor development in the first phase of Lodz’s history, the environment was obviously an insufficient stimulus for the city’s growth. Only the establishment of a beneficial institutional background in the nineteenth century could create a geographical-institutional catalyst capable of sparking the dynamic progress of the city. Among the main advantages of Lodz over other towns were the diversification of its textile industry and the perfect timing of its switch into cotton production. Another wave in the development of the city took place at the beginning in the 1860s, when a small number of inclusive economic institutions appeared (especially the lifting of the restrictions against Jewish participation in the full economic life of the city).

Our case study may be regarded as a precursor to further research into the geographical or institutional factors in the economic growth of other cities. A meaningful foundation for future comparisons requires a focus on two kinds of study: (1) an analysis of the roots of development in cities with a path similar to that of Lodz and (2) an investigation of the reasons for a lack of development in places with abundant natural resources that were engines of economic growth elsewhere during the era of the Industrial Revolution.

Cities with paths possibly similar to that of Lodz are the industrial districts of Manchester in the United Kingdom, Lille and Roubaix in France, and Chemnitz and Eberfeld in Germany. A preliminary look at the histories of those cities reveals the presence of natural resources that were promising for the creation of a strong textile industry but not, at least initially, the institutional circumstances necessary to take advantage of them. Nonetheless, the “take off” moments in the history of these cities were indeed related to institutional changes. The eradication of British trade protectionism in the cotton industry between 1690 and 1813 eventually resulted in the technological progress requisite for Manchester’s economic prosperity. The key factor in Roubaix’s success was not its grant of a textile-manufacturing privilege in the fifteenth century but its acquisition of the same right as Lille to manufacture all of the textiles made in Britain during the second half of the eighteenth century. Similarly, in the nineteenth century, the German Custom Union (the Zollverein ) facilitated the economic growth of German cities in 1834 by affording them protection from foreign competition in the local markets through heavy tariffs and other prohibitions. 19

The question of why certain places failed to develop despite favorable geographical circumstances is much more intriguing. As numerous cases indicate, the major barriers to economic development seem to be institutional. For instance, Engerman and Sokoloff point out that the development of Latin American cities in the nineteenth century was suppressed by the institution of slavery. They support the hypothesis that good institutions can result in a more efficient use of existing resources enabling societies to overcome inferior geography. The history of African urban centers illustrates that access to natural resources did not always bring prosperity. Numerous areas abundant in coal and oil did not manage to reach their industrial potential. The first oil mines in Poland launched during the mid-nineteenth century did not drive development in the cities of Krosno, Jaslo, and Gorlice in the district of Galicia because the Habsburg Empire’s institutional arrangements were weaker than the Kingdom of Poland’s. 20

The debate between proponents of geographical and of institutional causation is reminiscent of Marshall’s famous metaphor, deployed in another context: “We might as reasonably dispute whether it is the upper or the under blade of a pair of scissors that cuts a piece of paper. . . . It is true that when one blade is held still, and the cutting is effected by moving the other, we may say with careless brevity that the cutting is done by the second; but the statement is not strictly accurate, and is to be excused only so long as it claims to be merely a popular and not a strictly scientific account of what happens.” In the case of Lodz, the institutional and geographical blades were equally necessary to initiate economic development. However, the blades are merely the instruments in the hands of people, who must learn to use them effectively. 21

Lodz means boat in the Polish language. The inhabitants of Lodz are sometimes called “boat people.”

Notable modern adherents to the geographical approach include Jeffrey Sachs, The End of Poverty: The Economic Possibilities for Our Time (New York, 2005); Paul Colinvaux, The Fates of Nations: A Biological Theory of History (New York, 1980); Jared Diamond, Guns, Germs and Steel: The Fates of Human Societies (New York, 1997); idem , Collapse: How Societies Choose to Fail or Succeed (New York, 2005). For studies of the economic consequences of environmental components and climate changes, see, inter alia , Michael McCormick et al., “Climate Change during and after the Roman Empire: Reconstructing the Past from Scientific and Historical Evidence,” Journal of Interdisciplinary History , XLIII (2012), 169–220; Hui-wen Koo, “Weather, Harvests, and Taxes: A Chinese Revolt in Colonial Taiwan,” ibid. , XLVI (2015), 39–59; Faisal H. Husain, “Changes in the Euphrates River: Ecology and Politics in a Rural Ottoman Periphery, 1687–1702,” ibid. , XLVII (2016), 1–25.

Douglass C. North, Institutions, Institutional Change and Economic Performance (New York, 1990), 3. The essence of technological progress may lie in finding ways to use the gifts of nature in a more efficient manner. Before the era of the Industrial Revolution, the economic significance of coal or oil was small; the situation began to change as methods to make those resources useful as fuel were created.

For a critique of certain elements of Acemoglu and Robinson’s approach, see Dzionek-Kozlowska and Matera, “Institutions without Culture: A Critique of Acemoglu and Robinson’s Theory of Economic Development,” Lodz Economic Working Papers , IX (Univ. of Lodz, 2016).

Stanisław Liszewski, The Origins and Stages of Development of Industrial Łódź and the Łódź Urban Region , in idem and Craig Young (eds.), A Comparative Study of Łódź and Manchester: Geographies of European Cities in Transition (Łódź, 1997), 12.

Wiesław Puś, Żydzi w Łodzi w latach zaborów 1793–1914 (Łódź, 2003), 11; Karol Bajer, Przemysł włókienniczy na ziemiach polskich od początku XIX w. do 1939 r. (Łódź, 1958), 38.

See Witold Kula, Kształtowanie się kapitalizmu w Polsce (Warszawa, 1955), 53–61; Peter Kriedte, Hans Medick, and Jurgen Schlumbohm, Industrialization before Industrialization (New York, 1981), 309.

Willian Easterly, The Tyranny of Experts: Economists, Dictators and the Forgotten Rights of the Poor (New York, 2013), classifies borders as a special kind of formal institution. As an example, he presents the “Aleppo disease” in development as the setting of barriers (political borders) between regions that used to thrive from interaction, making trade costly and time-consuming by severing regions from their natural trading partners. However, the border changes after 1815 had a positive influence on Lodz (231–233).

Hard water containing salts of magnesium and calcium caused problems at almost every stage of textile production, making it more difficult to scour, bleach, dye, print, and mercerize textiles. In economic terms, it meant an increase in the production costs. Anna Rynkowska, Początki rozwoju kapitalistycznego miasta Łodzi (1820–1864): Źródła (Warsaw, 1960).

The creation of industrial villages is the equivalent of the modern-day practice of establishing special economic zones. Sharaf Rehman and Dzionek-Kozlowska, “Tale of Two Cities: A Comparative Study of Relationship between Education and Economic Prosperity,” Lodz Economic Working Papers , III (Univ. of Lodz, 2016), 12.

Rynkowska, Działalność gospodarcza władz Królestwa Polskiego na terenie Łodzi przemysłowej w latach 1821–1831 (Łódź, 1951), 21. The policy provided for long-term (twelve-year) mortgage credits with semi-annual installments at only 5% per year. Bohdan Baranowski and Jan Fijałek, Łódź: Dzieje miasta (Warszawa–Łódź, 1988), 224; Gryzelda Missalowa, Studia nad powstaniem łódzkiego okręgu przemysłowego 1815–1870 (Łódź, 1964), I, 63, 76.

Wiesław Puś, “The Development of the City of Łódź (1820–1939),” in Antony Polonsky (ed.), Jews in Łódź 1820–1939 (New York, 2004), 5. Production of woolen fabrics in Lodz fell by 70% between 1828 and 1832 (Missalowa, Studia nad powstaniem , 173–174), but cotton production rose dramatically (a tenfold increase) between 1831 and 1835. See Kula, “Przemysł włókienniczy w Królestwie Polskim (1831–1865),” Kwartalnik Historyczny , IV/V (1956), 190.

Andrzej Jezierski and Stanisław Maciej Zawadzki, Dwa wieki przemysłu w Polsce: Zarys dziejów (Warsaw, 1966), 205; Piotr Franaszek, Poland , in Elise van Nederveen Meerkerk, Els Hiemstra-Kuperus, and Heerma van Voss (eds.), The Ashgate Companion to the History of Textile Workers, 1650–2000 (Aldershot, 2010), 403; Puś, Rozwój przemysłu w Królestwie Polskim: 1870–1914 (Łódź, 1997), 75.

Mieczysław Bandurka, Akta miasta Łodzi [1471] 1794–1914 [1918]; Przewodnik po zespole (Warsaw, 1980), 11; Ryszard Rosin, Łódź: Dzieje miasta (Warsaw, 1980), 196.

Puś, Żydzi w Łodzi , 20.

Stefan Pytlas, Łódzka burżuazja przemysłowa (Łódź, 1994), 43–52; idem , Skład narodowościowy przemysłowców łódzkich do 1914 r. , in Puś and Liszewski (eds.), Dzieje Żydów w Łodzi 1820–1944 (Łódź, 1991), 55–78; Puś, Żydzi w Łodzi , 82.

Richard Florida, The Rise of the Creative Class: And How It’s Transforming Work, Leisure, Community and Everyday Life (New York, 2012), 77; According to Puś, Żydzi w Łodzi , “Jewish industrialists, apart from entrepreneurs of German origin, played a decisive role in the development of the Lodz industry” (104).

Walt Rostow, The Stages of Economic Growth: A Non-Communist Manifesto (Cambridge, 1990), 4–16. The conclusions reached in this research note parallel those of Alan Beattie, who posits that cities and nations are shaped not only by economic and geographical forces but also by choices of policymakers and the spontaneous decisions of a shifting population. Beattie, False Economy: A Surprising Economic History of the World (New York, 2009), 43.

For Manchester, see Prasannan Parthasarathi, Why Europe Grew Rich and Asia Did Not: Global Economic Divergence, 1600–1850 (New York, 2011), 112.

Krzysztof Broński, Rozwój gospodarczy większych miast galicyjskich w okresie autonomii (Kraków, 2003).

Alfred Marshall, Principles of Economics (London, 1920), book V, chapter III, paragraph 27.

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Grade 12 Geography Hypothesis Examples based on South African Topics

Grade 12 Geography Hypothesis Examples based on South African Topics:

A hypothesis is a proposed explanation or assumption for a specific phenomenon, event, or observation that can be tested through scientific investigation. It is a key component of the scientific method, as it provides a basis for researchers to design experiments, collect data, and ultimately confirm or refute the hypothesis.

Table of Contents

Relevant terminologies related to a hypothesis:

• Null hypothesis (H0): A statement that suggests there is no significant relationship between the variables being studied or that the observed effect is due to chance alone. The null hypothesis is often tested against an alternative hypothesis.
• Alternative hypothesis (H1 or Ha): A statement that contradicts the null hypothesis, asserting that there is a significant relationship between the variables or that the observed effect is not due to chance alone.
• Dependent variable: The variable being studied or measured in an experiment, often considered the “outcome” or “response” variable. It is dependent on the independent variable(s).
• Independent variable: The variable that is manipulated or controlled by the researcher in an experiment to study its effect on the dependent variable.
• Control group: A group in an experiment that does not receive the treatment or manipulation of the independent variable. The control group serves as a baseline for comparison with the experimental group.
• Experimental group: A group in an experiment that receives the treatment or manipulation of the independent variable.
• Confounding variable: A variable that may influence the relationship between the independent and dependent variables, potentially leading to incorrect conclusions.
• Internal validity: The degree to which the results of a study can be attributed to the manipulation of the independent variable rather than the influence of confounding variables.
• External validity: The degree to which the results of a study can be generalized to other populations, settings, or conditions.
• Statistical significance: A measure of the likelihood that the observed relationship between variables is due to chance alone. A statistically significant result indicates that there is strong evidence to reject the null hypothesis in favor of the alternative hypothesis.
• P-value: A probability value used to determine the statistical significance of a result. A smaller p-value (typically less than 0.05) indicates stronger evidence against the null hypothesis.

Here are possible hypothesis examples based on South African geography topics:

• Hypothesis: The severity and frequency of droughts in South Africa will increase due to climate change.
• This hypothesis could be investigated by analyzing historical drought data and comparing it to climate projections for the region. Researchers could also look at the impacts of droughts on agriculture, water availability, and socio-economic factors in different parts of the country.
• Hypothesis: The development of renewable energy infrastructure in South Africa will reduce the country’s dependence on fossil fuels and lead to a reduction in greenhouse gas emissions.
• This hypothesis could be investigated by examining trends in energy production and consumption, as well as government policies and incentives related to renewable energy. Researchers could also analyze the environmental and economic impacts of transitioning to renewable energy sources in different parts of the country.
• Hypothesis: Urbanization in South Africa is contributing to increased air pollution levels and negative health impacts.
• This hypothesis could be investigated by measuring air pollution levels in different urban areas and comparing them to national and international standards. Researchers could also examine the health impacts of air pollution on different demographic groups and assess the effectiveness of existing policies and interventions aimed at reducing air pollution.
• Hypothesis: Mining activities in South Africa are causing significant environmental degradation and negative impacts on local communities.
• This hypothesis could be investigated by analyzing the environmental impacts of different mining practices, such as open pit mining and deep level mining, and assessing the effectiveness of regulatory frameworks in mitigating these impacts. Researchers could also investigate the social and economic impacts of mining on local communities, including displacement, loss of livelihoods, and health impacts.
• Hypothesis: Climate change is exacerbating water scarcity in South Africa, particularly in regions with high levels of population growth and agricultural activity.
• This hypothesis could be investigated by analyzing historical rainfall data and assessing the impacts of changing rainfall patterns on water availability in different regions. Researchers could also examine the effectiveness of water management strategies, such as water conservation measures and investments in infrastructure, in mitigating the impacts of water scarcity on agriculture, industry, and domestic use.
• Hypothesis: Tourism development in South Africa is leading to environmental degradation and cultural commodification in some areas.
• This hypothesis could be investigated by analyzing the impacts of tourism development on local ecosystems, including wildlife and biodiversity, and assessing the effectiveness of existing policies and regulations in protecting these areas. Researchers could also investigate the socio-cultural impacts of tourism on local communities, including changes in traditional ways of life and the commodification of cultural practices.
• Hypothesis: The use of non-renewable energy sources in South Africa is contributing to climate change and global warming.
• This hypothesis could be investigated by analyzing energy production and consumption trends in the country and comparing them to national and international targets for reducing greenhouse gas emissions. Researchers could also examine the environmental impacts of different energy sources, such as coal and natural gas, and assess the feasibility and effectiveness of transitioning to renewable energy sources.
• Hypothesis: Land use change in South Africa is leading to deforestation and biodiversity loss.
• This hypothesis could be investigated by analyzing the drivers of land use change, including agricultural expansion and urbanization, and assessing their impacts on forest cover and biodiversity. Researchers could also investigate the effectiveness of existing policies and regulations aimed at protecting forests and conserving biodiversity, and assess the potential for sustainable land use practices.
• Hypothesis: Coastal erosion in South Africa is increasing due to sea level rise and human activities.
• This hypothesis could be investigated by analyzing historical data on coastal erosion rates and assessing the impacts of sea level rise and human activities, such as coastal development and mining, on coastal ecosystems. Researchers could also investigate the effectiveness of existing coastal management strategies, including coastal protection measures and land use planning, in mitigating the impacts of coastal erosion.

These are just a few examples of possible geography hypotheses related to South Africa. Actual research would require detailed planning, data collection, and analysis.

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GEOGRAPHY GRADE 12 RESEARCH TASK 2018

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