hypothesis testing in business analytics

A Beginner’s Guide to Hypothesis Testing in Business Analytics

December 5, 2023
Analytics , Statistics

Hypothesis testing is a statistical method used to make decisions about a population based on a sample. It helps business analysts draw conclusions about business metrics and make data-driven decisions. This beginner’s guide will provide an introduction to hypothesis testing and how it is applied in business analytics.

What is a Hypothesis?

A hypothesis is an assumption about a population parameter. It is a tentative statement that proposes a possible relationship between two or more variables.

In statistical terms, a hypothesis is an assertion or conjecture about one or more populations. For example, a business hypothesis could be –

“Our social media advertising results in an increase in sales.”

“Customer ratings of our product have decreased this month compared to last month.”

A hypothesis can be:

Null hypothesis (H0) – a statement that there is no difference or no effect.
Alternative hypothesis (H1) – a claim about the population that is contradictory to H0.

Hypothesis testing evaluates two mutually exclusive statements (H0 and H1) to determine which statement is best supported by the sample data.

Why Hypothesis Testing is Important in Business

Hypothesis testing allows business analysts to make statistical inferences about a business problem. It is an objective data-driven approach to:

Evaluate business metrics against a target value. For example – is the current customer satisfaction score significantly lower than our target of 85%?
Compare business metrics across time periods or categories. For example – has website conversion rate increased this month compared to last month?
Quantify the impact of business initiatives. For example – did the email marketing campaign result in a significant increase in sales?

Some key benefits of hypothesis testing in business analytics:

Supports data-driven decision making with statistical evidence.
Helps save costs by making decisions backed by data insights.
Enables measurement of success for business initiatives like marketing campaigns, new product launches etc.
Provides a structured framework for business metric analysis.
Reduces the influence of individual biases in decision making.

By incorporating hypothesis testing in data analysis, businesses can make sound decisions that are supported by statistical evidence.

Steps in Hypothesis Testing

Hypothesis testing involves the following five steps:

1. State the Hypotheses

This involves stating the null and alternate hypotheses. The hypotheses are stated in a way that they are mutually exclusive – if one is true, the other must be false.

Null hypothesis (H0) – represents the status quo, states that there is no effect or no difference.

Alternative hypothesis (H1) – states that there is an effect or a difference.

For example –

H0: The average customer rating this month is the same as last month.

H1: The average customer rating this month is lower than last month.

2. Choose the Significance Level

The significance level (α) is the probability of rejecting H0 when it is actually true. It is the maximum risk we are willing to take in making an incorrect decision.

Typical values are 0.10, 0.05 or 0.01. A lower α indicates lower risk tolerance. For example α = 0.05 indicates only a 5% risk of concluding there is a difference when actually there is none.

3. Select the Sample and Collect Data

The sample should be representative of the population. Data is collected relevant to the hypotheses – for example, customer ratings this month and last month.

4. Analyze the Sample Data

An appropriate statistical test is applied to analyze the sample data. Common tests used are t-tests, z-tests, ANOVA, chi-square etc. The test provides a test statistic that can be compared against critical values to determine statistical significance.

5. Make a Decision

If the test statistic falls in the rejection region, we reject H0 in favor of H1. Otherwise, we fail to reject H0 and conclude there is not enough evidence against it.

The key question is – “Is the sample data unlikely, assuming H0 is true?” If yes, we reject H0.

Types of Hypothesis Tests

There are two main types of hypothesis tests:

1. Parametric Tests

These tests make assumptions about the shape or parameters of the population distribution.

Some examples are:

Z-test – Tests a population mean when population standard deviation is known.
T-test – Tests a population mean when standard deviation is unknown.
F-test – Compares variances from two normal populations.
ANOVA – Compares means of two or more populations.

Parametric tests are more powerful as they make use of the distribution characteristics. But the assumptions need to hold true for valid results.

2. Non-parametric Tests

These tests make no assumptions about the exact distribution of the population. They are based on either ranks or frequencies.

Chi-square test – Tests if two categorical variables are related.
Mann-Whitney U test – Compares medians from two independent groups.
Wilcoxon signed-rank test – Compares paired observations or repeated measurements.
Kruskal Wallis test – Compares medians from two or more groups.

Non-parametric tests are distribution-free but less powerful than parametric tests. They can be used when assumptions of parametric tests are violated.

The choice of statistical test depends on the hypotheses, data type and other factors.

One-tailed and Two-tailed Hypothesis Tests

Hypothesis tests can be one-tailed or two-tailed:

One-tailed test – When H1 specifies a direction. For example: H0: μ = 10 H1: μ > 10 (or μ < 10)
Two-tailed test – When H1 simply states ≠, not a specific direction. For example: H0: μ = 10 H1: μ ≠ 10

One-tailed tests have greater power to detect an effect in the specified direction. But we need prior knowledge on the direction of effect for using them.

Two-tailed tests do not assume any direction and are more conservative. They are used when we have no clear prior expectation on the directionality.

Interpreting Hypothesis Test Results

Hypothesis testing results can be interpreted based on:

p-value – Probability of obtaining sample results if H0 is true. Small p-value (< α) indicates significant evidence against H0.
Confidence intervals – Range of likely values for the population parameter. If it does not contain the H0 value, we reject H0.
Test statistic – Standardized value computed from sample data. Compared against critical values to determine statistical significance.
Effect size – Quantifies the magnitude or size of effect. Important for interpreting practical significance.

Hypothesis testing indicates whether an effect exists or not. Measures like effect size and confidence intervals provide additional insights on the observed effect.

Common Errors in Hypothesis Testing

Some common errors to watch out for:

Having unclear, ambiguous hypotheses.
Choosing an inappropriate significance level α.
Using the wrong statistical test for data analysis.
Interpreting a non-significant result as proof of no effect. Absence of evidence is not evidence of absence.
Concluding practical significance from statistical significance. Small p-values don’t always imply practical business impact.
Multiple testing without adjustment leading to elevated Type I errors.
Stopping data collection prematurely when a significant result is obtained.
Overlooking effect sizes, confidence intervals while focusing solely on p-values.

Proper application of hypothesis testing methodology minimizes such errors and improves decision making.

Real-world Example of Hypothesis Testing

Let’s take an example of using hypothesis testing in business analytics:

A retailer wants to test if launching a new ecommerce website has resulted in increased online sales.

The retailer gathers weekly sales data before and after the website launch:

H0: Launching the new website did not increase the average weekly online sales

H1: Launching the new website increased the average weekly online sales

Significance level is chosen as 0.05. Appropriate parametric / non-parametric test is selected based on data. Test results show that the p-value is 0.01, which is less than 0.05.

Therefore, we reject the null hypothesis and conclude that the new website launch has resulted in significantly increased online sales at the 5% significance level.

The analyst also computes a 95% confidence interval for the difference in sales before and after website launch. The retailer uses these insights to make data-backed decisions on marketing budget allocation between traditional and digital channels.

Hypothesis testing provides a formal process for making statistical decisions using sample data. It helps assess business metrics against benchmarks, quantify impact of initiatives and compare performance across time periods or segments. By embedding hypothesis testing in analytics, businesses can derive actionable insights for data-driven decision making.

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Hypothesis Testing in Business: Examples

hypothesis testing for business - examples

Are you a product manager or data scientist looking for ways to identify and use most appropriate hypothesis testing for understanding business problems and creating solutions for data-driven decision making? Hypothesis testing is a powerful statistical technique that can help you understand problems during exploratory data analysis (EDA) and identify most appropriate hypotheses / analytical solution. In this blog, we will discuss hypothesis testing with examples from business. We’ll also give you tips on how to use it effectively in your own problem-solving journey. With this knowledge, you’ll be able to confidently create hypotheses, run experiments, and analyze the results to derive meaningful conclusions. So let’s get started!

Before going any further, you may want to check out my detailed blog on hypothesis testing – Hypothesis testing steps & examples .

The picture below represents the key steps you can take to identify appropriate hypothesis tests related to your business problem you are trying to solve.

Table of Contents

Business Objective / Problem Analysis to Asking Key Questions

Here are the steps which you can use to come up with hypothesis tests related to your business problems. You can then use data to perform hypothesis tests and arrive at different conclusions or inferences.

Setting / Identifying business objective : First & foremost, you need to have a business objective which you want to achieve. For example, achieve an increase of 10% revenue in the year ahead.
Identifying key business divisions / units and products & services : Second step is to identify key departments / divisions and related products & services which can help achieve the business objective. For current example, sales can be increased by increase in sales of products and services. For service based companies, it can be increase in sales of existing services and one or more new services. For products based companies, it could be increase in sales of different products.
Identify key personas / stakeholders : For each business division / department, identify key personas or stakeholders who could be accountable for contributing to achievement of business objective. For current example, it could personas / stakeholders who would own the increase in sales of products and / or services.
Are the sales of product A, B and C different?
Are the sales of product A, B and C similar across all the regions, countries, states, etc.?
Are there differences between products and competitors’ products vis-a-vis sales?
Are there any differences between customer queries / complaints across different products (A, B, C)?
Are there any differences between product usage patterns across different products, and for each product?
Are there differences between marketing initiatives run for different products?
Are there differences between teams working on different products?

Hypothesis formulation

Once the questions have been asked / raised, you can create hypotheses from these questions in order to arrive at the answers based on data analysis and create strategy / action plan. Lets take a look at one of the question and how you can formulate hypothesis and perform hypothesis testing. We will also talk about data and analytics aspects.

In order to create strategy around increasing sales revenue, it is very important to understand how has been the sales of different products in past and whether the sales have been different for us to dig deeper into the reasons and create some action plan?

The status quo becomes null hypothesis ([latex]H_0[/latex]. In our current analysis, the status quo is that there is no difference between the sales revenue of different products and that each product is doing equally good and selling well with the customers.

[latex]H_0[/latex]: There is no difference between sales revenue of different products.

The new knowledge for which the null hypothesis can be thrown away can be called as alternate hypothesis, [latex]H_a[/latex]. In current example, the new knowledge or alternate hypothesis is that there is a significant difference between the sales revenue of different products.

[latex]H_a[/latex]: There is a significant difference between sales revenue of different products.

Identifying Test Statistics for Hypothesis Testing

Once the hypothesis has been formulated, the next step is to identify the test statistics which can be used to perform the hypothesis test.

We can perform one-way Anova test to check whether there is a difference between sales based on the product. One-way ANOVA test requires calculation of F-statistics . The factor is product and levels are product A, B and C. Read my blog post on one-way ANOVA test to learn about different aspect of this test. One-Way ANOVA Test: Concepts, Formula & Examples

Apart from Hypothesis test and statistics, one can also set the level of significance based on which one can reject the null hypothesis or otherwise. Generally, it is chosen as 0.05.

Gather Data

Once the hypothesis test and statistics gets chosen, next step is to gather data. You can identify the system which holds the sales data and then gather the data from that system for last 1 year.

Perform Hypothesis Testing

Once the data is gathered, you can use Excel tool or any other statistical packages in Python / R and perform hypothesis testing by doing the following:

Calculating the value of test statistics
Calculate P-value
Comparing the P-value with level of significance
Reject the null hypothesis or otherwise

In conclusion, hypothesis testing is an essential tool for businesses to make data-driven decisions. It involves identifying a problem or question, formulating a hypothesis, identifying the appropriate test statistics, gathering data, and performing hypothesis testing. By following these steps, businesses can gain valuable insights into their operations, identify areas of improvement, and make informed decisions. It is important to note that hypothesis testing is not a one-time process but rather a continuous effort that businesses must undertake to stay ahead of the competition. Examples of hypothesis testing in business can range from identifying the effectiveness of a new marketing campaign to determining the impact of changes in pricing strategies. By analyzing data and performing hypothesis testing, businesses can determine the significance of these changes and make informed decisions that will improve their bottom line.

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Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a or H 1 ).
Collect data in a way designed to test the hypothesis.
Perform an appropriate statistical test .
Decide whether to reject or fail to reject your null hypothesis.
Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

an estimate of the difference in average height between the two groups.
a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

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The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

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

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

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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Hypothesis Testing: A Step-by-Step Guide With Easy Examples

Introduction

When we hear the word ‘hypothesis,’ the first thing that comes to our mind is a kind of theory. Assuming and explaining theories is a fundamental part of Business Analytics. In the past few years, the field of Business Analytics has proliferated and made several advancements. As the number of people interested in its statistical applications in business has increased, the concept of hypothesis testing has grabbed everyone’s attention.

Let us find out more about testing of hypothesis and the different steps through which you can write a hypothesis.

What is Hypothesis?

A hypothesis’s general definition says, “Hypothesis is an assumption made based on some evidence.” It is a theory you propose about what will happen in the future based on current circumstances. Proposing a hypothesis is the first and most important step of any research or investigation as it decides the future path of the research/investigation and can lead it to a faithful and acceptable answer.

Key Points of a Hypothesis

The assumptions made while proposing the theory should be precise and based on proper evidence.
The hypothesis should target a specific topic only and should have the scope to conduct various experiments for proving the assumptions.
The sources used for developing a hypothesis must be based on scientific theories, common patterns that affect the thought process of the people, and observations made in past research programs on the same topic.

Types of Hypotheses With Examples

There are multiple types of hypotheses which are described below.

1. Simple Hypothesis

As the name suggests, a simple hypothesis is pretty simple to work on. It just deals with a single independent variable and one dependent variable. While proving a simple hypothesis, you just have to confirm that these two variables are linked.

Example: If you eat more vegetables, you will be safe from heart disease. Here eating vegetables is an independent variable and staying safe from heart disease is a dependent variable.

2. Complex Hypothesis

Unlike a simple hypothesis, a complex hypothesis deals with multiple dependent and independent variables in the assumption simultaneously. The involvement of multiple variables makes the hypothesis more accurate and more difficult to prove simultaneously.

Example: Age, diet, and weight affect the chances of diseases like diabetes or blood pressure. Age, diet, and weight are independent variables, and diabetes and blood pressure are dependent variables.

3. Null Hypothesis

The null hypothesis is the opposite of the simple hypothesis. Where a simple hypothesis tries to establish a link between the dependent and the independent variables, the Null hypothesis tries to prove that there’s no link between the given variables. Simply put, it tries to prove a statement opposite to the proposed hypothesis. It is represented as H0.

Example: Age and daily routine affect the chances of heart disease. In a Null hypothesis, you will try to prove that there is no relation between the given factors, i.e., age, weight, and heart disease.

4. Alternative Hypothesis

An alternative hypothesis tries to disapprove the assumptions or statements proposed in a null hypothesis. Generally, alternative and null hypotheses are used together. An alternative hypothesis is represented as HA.

It is to be noted that H0 ≠ H A. The alternate hypothesis further branches into two categories:

Directional Hypothesis: The result obtained through this type of alternative hypothesis is either negative or positive. It is represented by adding ‘>’ or ‘<‘ along with the HA symbol.
Non-Directional Hypothesis: This type of hypothesis only clarifies the dependency of the dependent variables on the independent variable. It does not state anything about the result being positive or negative.

Example:

Age and daily routine affect the chances of heart disease. In an Alternative Hypothesis, you will try to prove that age and daily routine affect heart disease chances.

If you prove the result is positive or negative, i.e., age and daily routine do or do not affect the chances of heart disease, it is a directional hypothesis
If you only prove that the chances of heart disease depend on variables like age and daily routine, it is a non-directional hypothesis.

5. Logical Hypothesis

Logical hypotheses cannot be proved with the help of scientific evidence. The assumptions made in a logical hypothesis are based on some logical explanation that backs up our assumptions. Logical hypotheses are mostly used in philosophy, and as the assumptions made are often too complex or simply unrealistic, they are untestable, and we have to rely on logical explanations.

Example:

Dinosaurs are related to the reptile family as both have scales. As the dinosaurs are extinct, we cannot test the given hypothesis and rely on our logical explanation on, not the experimental data.

6. Empirical Hypothesis

It is the complete opposite of the Logical Hypothesis. The assumptions made in an Empirical Hypothesis are based on empirical data and proved through scientific testing and analysis.

It is divided into two parts, namely theoretical and empirical. Both methods of research rely on testing that can be verified through experimental data. So, unlike logical hypotheses, an empirical hypothesis can be and will be tested.

Vegetables grow faster in cold climates as compared to warm and humid climates. The assumption stated here can be thoroughly tested through scientific methods.

7. Statistical Hypothesis

Statistical Hypothesis makes use of large statistical datasets to obtain results that consider larger populations. This type of hypothesis is used when we have to take into consideration all the possible cases present in the assumptions made in the hypothesis. It makes use of datasets or samples so that conclusions can be drawn from the broader dataset. For this, you may conduct tests for sufficient samples and obtain results with high accuracy that would remain stable across all the datasets.

Men in the U.S.A. are taller than men in India. It is simply impossible to measure the height of all the men present in India and the U.S.A., but by conducting the test on sufficient samples, you can obtain results with high accuracy that would remain constant over different samples.

What Makes a Good Hypothesis?

Before developing a good hypothesis, you must consider a few points.

Do the assumptions made in the hypothesis consist of dependent or independent variables?
Can you conduct safety tests for your assumptions in the hypothesis?
Are there any other alternative assumptions present that you can take into consideration?

Characteristics of a Good Hypothesis –

1. Candid Language

Make use of simple language in your hypothesis instead of being vague. Try to focus on the given topic through your assumptions; it should be simple yet justifiable. The use of candid language makes the hypothesis more understandable and reachable to the common people.

2. Cause and Effect

Understand the assumptions made in the hypothesis. For example, the cause of the assumption, the effect of the assumption being accepted or rejected, etc. Try to back up your assumptions with the help of proper scientific data and explanations.

3. The Independent and Dependent Variables

Before starting to write a hypothesis, figure out the number of dependent and independent variables in the hypothesis. This will help you make proper assumptions to establish a link between these variables or to prove that these variables are not interlinked. It will also help you to prepare a mind map for your hypothesis.

4. Accurate Results

One of the most important characteristics of a good hypothesis is the accuracy of the results. Hypotheses are generally used to predict the future based on current scenarios. This can help to figure out the problems that may arise in the future and find solutions accordingly.

5. Adherence to Ethics

Sticking to ethics while working on any research project is very important. You get an idea about the research structure through the generally followed ethics beforehand. It helps to guide the research project or hypothesis in a fruitful direction.

6. Testable Predictions

The conditions used in the hypothesis research project should be easily testable. This helps to make the results of the hypothesis more accurate and reliable. Before starting the research on the assumptions in the hypothesis, you should be aware of all the different ways that can be used to make the hypothesis applicable to modern testing methodologies.

How to Write a Hypothesis?

Well, there are many ways to write a hypothesis; here are the six most efficient and important steps that will help you craft a strong hypothesis:

Step 1: Ask a Question

The first and most important step of writing a hypothesis is deciding upon the questions or assumptions you will implement in your research. A hypothesis can’t be based on random questions or general thoughts. The questions you decide must be approachable and testable as it forms the foundation of your project.

Step 2: Carry out Preliminary Research

Once you have decided on the questions and assumptions to be included in your hypothesis, you should start your preliminary research on the same. For that, you should start reading older research papers on the topic, go through the web, collect the data, prepare the dataset for the experiments, etc.

Step 3: Define Your Variables

After conducting the preliminary research, you need to define the number of variables present in your assumption and classify them into dependent and independent variables. It will help you to conduct further research and establish a link between them or prove that there is no link between them.

Step-4: Collect Data to Support Your Hypothesis

After classifying the variables and conducting the basic preliminary research, you need to start collecting evidence and data that will help you support your hypothesis. This data will help you test your assumptions and infer statistical results about your interesting dataset.

Step-5: Perform Statistical Tests

The data you have collected from the above step can be used to perform different statistical tests. The type of tests you perform depends on the data you collect. All the different tests are based on in-group variance and between-group variance. Depending on the variance, your statistical test will reflect a high or low p-value.

After performing the tests, you should prepare a draft for writing down your hypothesis.

Step-6: Present It in an If-Then Form

Now that everything has been done, it is time to write down your hypothesis. Considering your draft, you should write down the hypothesis accordingly and ensure that it satisfies all the conditions like simple and to-the-point language, accurate results, relevant evidence and data sources, etc. The final hypothesis should be well-framed and address the topic clearly.

Conclusion

Research and hypothesis testing are an important part of the Business Analytics field. To write a good hypothesis or research, you need to conduct a good amount of research. Since you know about the different types of hypotheses and how to write a good hypothesis, writing a good and strong hypothesis by yourself is now much easier! If you want to pursue a career in the field of Business Analytics, you can check out the Integrated Program In Business Analytics by UNext Jigsaw. We hope now you understand “ what is hypothesis testing ?” and hypothesis testing steps in detail.

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Statistics for Business Analytics 101: Hypothesis Testing

Introduction

In statistics, a hypothesis is an assumption we make about a population parameter such as any quantity or measurement about this population that is fixed and that we can use it as a value to a distribution variable. Typical examples of parameters are the mean and the variance .

You might be wondering what this stuff has to do with you as an engineer, a salesman, a marketer or a customer support specialist. The truth is that these statistical tools are just a different approach to practices that you are already following in your work. Let’s see some examples.

Marketing : What number of e-mail do we need to send before someone signs-up for the product?
Product : How long the onboarding process takes for a new sign-up?
Sales : How long it takes for a lead to turn into a paying customer?
Customer support : How long it takes from the moment a new ticket is created until the first response?

All the above questions can be easily translate into “statistical” hypotheses or questions.

What is the mean number of e-mails that we need to send before someone signs up to our product? We can define the population here as the recipients of our drip campaigns.
What is the mean time between the first login of a user and the any other event on the product? The population here is our customers of course.
What is the mean time that it takes for a new lead to become a paying customer? The population here is the leads that we have in our CRM system.
What is the mean first response time to new tickets? Where the population in this case is the tickets we have created so far.

It is actually quite easy to do the translation between the everyday problems that anyone in a business seeks answers for, regardless the position, and the language of statistics. In statistics what we can do is to test our assumptions or hypotheses that we made for measurements like the ones we described earlier. For example,

The mean number of e-mails required to turn a lead into a customer is five.

The above assumption, or its negation, is a valid hypothesis that we can use statistical tools to investigate. The way to do that is by using a statistical technique that is called Hypothesis Testing .

To be more precise, the goal of hypothesis testing, is to determine if there’s enough evidence in a given data set to conclude that the assumption we made stands for the whole population. So, although for the above assumption with the e-mails there will be cases where a smaller or a larger number of e-mails is required, by doing such a test we can be confident that the assumption we made is likely to hold for the whole population.

Hypothesis Testing

So, can we be confident that overall it will take our company around 5 e-mails to convert a new lead into a customer? To answer this question using statistical tools we need to follow the next four steps:

State the hypothesis . As an example we did this earlier with the number of e-mails.
Formulate an analysis plan .
Analyze the data we have available .
Interpret the results .

For the formulation of the analysis plan the steps involved are:

Select a significance level. This a value between 0 and 1 but a common number that is used is 0.05
Select a test method which involves a test statistic and a sampling distribution. During the analysis of the available data, the test statistic is calculated and together with it we calculate a P-value

A P-value is the probability of observing a sample statistic as extreme as the test statistic, assuming that the hypothesis we made is true .

Finally we interpret the results by comparing the p-value with the selected significance level . Usually when the p-value is less than the significance level the hypothesis is rejected.

ADD_THIS_TEXT

In a summary and without the technical details, what we are doing with hypothesis testing is the following,

Make an initial assumption
Collect data
Based on the data decide where the assumptions stands true or not

This is more or less something that everyone does as part of her job regardless the tools used, here we just use a more formal and scientific way of doing it.

Using such a statistical methodology doesn’t guarantee that we can actually have an answer to our questions. More precisely there are errors that can occur during the process.

Type I error. When we reject the hypothesis but it is actually true. The probability of committing such an error is called the significance level .
Type II error. When we do not reject the hypothesis while we should. The probability of not committing a type II error is called the power of the test.

We can control type I errors by adjusting accordingly the significance level and there are tools to perform power analysis to decide if the data we have contain enough evidence to perform these tests. Power analysis is a very powerful tool and we’ll discuss it in another post more thoroughly.

We barely scratched the surface of the tools that statistics offer but hopefully this post is a good starting point to investigate further how these tools can be used for the problems that any professional has to deal with. There are many details that someone has to address to make these tools to work properly and we’ll go through these in future posts.

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What is Hypothesis Testing? Types and Methods

Soumyaa Rawat
Jul 23, 2021

Hypothesis Testing

Hypothesis testing is the act of testing a hypothesis or a supposition in relation to a statistical parameter. Analysts implement hypothesis testing in order to test if a hypothesis is plausible or not.

In data science and statistics , hypothesis testing is an important step as it involves the verification of an assumption that could help develop a statistical parameter. For instance, a researcher establishes a hypothesis assuming that the average of all odd numbers is an even number.

In order to find the plausibility of this hypothesis, the researcher will have to test the hypothesis using hypothesis testing methods. Unlike a hypothesis that is ‘supposed’ to stand true on the basis of little or no evidence, hypothesis testing is required to have plausible evidence in order to establish that a statistical hypothesis is true.

Perhaps this is where statistics play an important role. A number of components are involved in this process. But before understanding the process involved in hypothesis testing in research methodology, we shall first understand the types of hypotheses that are involved in the process. Let us get started!

Types of Hypotheses

In data sampling, different types of hypothesis are involved in finding whether the tested samples test positive for a hypothesis or not. In this segment, we shall discover the different types of hypotheses and understand the role they play in hypothesis testing.

Alternative Hypothesis

Alternative Hypothesis (H1) or the research hypothesis states that there is a relationship between two variables (where one variable affects the other). The alternative hypothesis is the main driving force for hypothesis testing.

It implies that the two variables are related to each other and the relationship that exists between them is not due to chance or coincidence.

When the process of hypothesis testing is carried out, the alternative hypothesis is the main subject of the testing process. The analyst intends to test the alternative hypothesis and verifies its plausibility.

Null Hypothesis

The Null Hypothesis (H0) aims to nullify the alternative hypothesis by implying that there exists no relation between two variables in statistics. It states that the effect of one variable on the other is solely due to chance and no empirical cause lies behind it.

The null hypothesis is established alongside the alternative hypothesis and is recognized as important as the latter. In hypothesis testing, the null hypothesis has a major role to play as it influences the testing against the alternative hypothesis.

(Must read: What is ANOVA test? )

Non-Directional Hypothesis

The Non-directional hypothesis states that the relation between two variables has no direction.

Simply put, it asserts that there exists a relation between two variables, but does not recognize the direction of effect, whether variable A affects variable B or vice versa.

Directional Hypothesis

The Directional hypothesis, on the other hand, asserts the direction of effect of the relationship that exists between two variables.

Herein, the hypothesis clearly states that variable A affects variable B, or vice versa.

Statistical Hypothesis

A statistical hypothesis is a hypothesis that can be verified to be plausible on the basis of statistics.

By using data sampling and statistical knowledge, one can determine the plausibility of a statistical hypothesis and find out if it stands true or not.

(Related blog: z-test vs t-test )

Performing Hypothesis Testing

Now that we have understood the types of hypotheses and the role they play in hypothesis testing, let us now move on to understand the process in a better manner.

In hypothesis testing, a researcher is first required to establish two hypotheses - alternative hypothesis and null hypothesis in order to begin with the procedure.

To establish these two hypotheses, one is required to study data samples, find a plausible pattern among the samples, and pen down a statistical hypothesis that they wish to test.

A random population of samples can be drawn, to begin with hypothesis testing. Among the two hypotheses, alternative and null, only one can be verified to be true. Perhaps the presence of both hypotheses is required to make the process successful.

At the end of the hypothesis testing procedure, either of the hypotheses will be rejected and the other one will be supported. Even though one of the two hypotheses turns out to be true, no hypothesis can ever be verified 100%.

(Read also: Types of data sampling techniques )

Therefore, a hypothesis can only be supported based on the statistical samples and verified data. Here is a step-by-step guide for hypothesis testing.

Establish the hypotheses

First things first, one is required to establish two hypotheses - alternative and null, that will set the foundation for hypothesis testing.

These hypotheses initiate the testing process that involves the researcher working on data samples in order to either support the alternative hypothesis or the null hypothesis.

Generate a testing plan

Once the hypotheses have been formulated, it is now time to generate a testing plan. A testing plan or an analysis plan involves the accumulation of data samples, determining which statistic is to be considered and laying out the sample size.

All these factors are very important while one is working on hypothesis testing.

Analyze data samples

As soon as a testing plan is ready, it is time to move on to the analysis part. Analysis of data samples involves configuring statistical values of samples, drawing them together, and deriving a pattern out of these samples.

While analyzing the data samples, a researcher needs to determine a set of things -

Significance Level - The level of significance in hypothesis testing indicates if a statistical result could have significance if the null hypothesis stands to be true.

Testing Method - The testing method involves a type of sampling-distribution and a test statistic that leads to hypothesis testing. There are a number of testing methods that can assist in the analysis of data samples.

Test statistic - Test statistic is a numerical summary of a data set that can be used to perform hypothesis testing.

P-value - The P-value interpretation is the probability of finding a sample statistic to be as extreme as the test statistic, indicating the plausibility of the null hypothesis.

Infer the results

The analysis of data samples leads to the inference of results that establishes whether the alternative hypothesis stands true or not. When the P-value is less than the significance level, the null hypothesis is rejected and the alternative hypothesis turns out to be plausible.

Methods of Hypothesis Testing

As we have already looked into different aspects of hypothesis testing, we shall now look into the different methods of hypothesis testing. All in all, there are 2 most common types of hypothesis testing methods. They are as follows -

Frequentist Hypothesis Testing

The frequentist hypothesis or the traditional approach to hypothesis testing is a hypothesis testing method that aims on making assumptions by considering current data.

The supposed truths and assumptions are based on the current data and a set of 2 hypotheses are formulated. A very popular subtype of the frequentist approach is the Null Hypothesis Significance Testing (NHST).

The NHST approach (involving the null and alternative hypothesis) has been one of the most sought-after methods of hypothesis testing in the field of statistics ever since its inception in the mid-1950s.

Bayesian Hypothesis Testing

A much unconventional and modern method of hypothesis testing, the Bayesian Hypothesis Testing claims to test a particular hypothesis in accordance with the past data samples, known as prior probability, and current data that lead to the plausibility of a hypothesis.

The result obtained indicates the posterior probability of the hypothesis. In this method, the researcher relies on ‘prior probability and posterior probability’ to conduct hypothesis testing on hand.

On the basis of this prior probability, the Bayesian approach tests a hypothesis to be true or false. The Bayes factor, a major component of this method, indicates the likelihood ratio among the null hypothesis and the alternative hypothesis.

The Bayes factor is the indicator of the plausibility of either of the two hypotheses that are established for hypothesis testing.

(Also read - Introduction to Bayesian Statistics )

To conclude, hypothesis testing, a way to verify the plausibility of a supposed assumption can be done through different methods - the Bayesian approach or the Frequentist approach.

Although the Bayesian approach relies on the prior probability of data samples, the frequentist approach assumes without a probability. A number of elements involved in hypothesis testing are - significance level, p-level, test statistic, and method of hypothesis testing.

(Also read: Introduction to probability distributions )

A significant way to determine whether a hypothesis stands true or not is to verify the data samples and identify the plausible hypothesis among the null hypothesis and alternative hypothesis.

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3 Statistical Analysis Methods You Can Use to Make Business Decisions

Business professionals using statistical analysis methods

15 Dec 2021

Data is a driving force in business. More information is being collected than ever before, which professionals continually seek to leverage for success. Across all business functions, it’s essential to have analytical skills to interpret data and put it to use.

Statistical analysis is the basis for many business analytics approaches. Gaining a firm understanding of different statistical analysis methods is one of the first steps to unlocking the power of business analytics. With this knowledge, you can make sense of data, project future outcomes, and make more informed decisions.

Related: Examples of Business Analytics in Action

Below are three helpful statistical analysis methods that lead to better business decisions.

Access your free e-book today.

Statistical Analysis Methods for Business

1. hypothesis testing.

Hypothesis testing is a statistical method used to substantiate a claim about a population. This is done by formulating and testing two hypotheses: the null hypothesis and the alternative hypothesis.

Related: A Beginner’s Guide to Hypothesis Testing in Business

The null hypothesis (denoted by H₀) is a statement about the issue at hand, generally based on historical data and conventional wisdom. A hypothesis test always starts by assuming the null hypothesis is true and then testing to see if it can be nullified.

The alternative hypothesis (denoted by H₁) represents the theory or assumption being tested and is the opposite of the null hypothesis. If the data effectively nullifies the null hypothesis, then the alternative hypothesis can be substantiated.

In business, hypothesis testing is an effective means of assessing theories and assumptions before acting on them. For managers, leaders, and those looking to become more data-driven, this method of statistical analysis is a helpful decision-making tool. Putting this practice into action can lead to better foresight and positive outcomes when planning a business’s future.

For example, you might conduct a hypothesis test to substantiate that if your company launches a new product line, sales and revenue will increase as a result. Since this initiative would be expensive, your company might launch the product in a small test market and use the data it collects to justify rolling it out on a larger scale.

Hypothesis testing is a complex yet highly valuable statistical method for business. If you want to learn about hypothesis testing in more detail, taking an online statistics or business analytics course can be worthwhile.

2. Single Variable Linear Regression

Linear regression analysis is used for two main purposes: to identify and evaluate the relationship between two variables and forecast a variable based on its relationship to another one.

In single variable linear regression analysis, the relationship between a dependent variable and an independent variable is evaluated by identifying the line of best fit.

To find the line of best fit, use the following equation:

Single Variable Linear Regression Formula

Here, ŷ represents the expected value of the dependent variable for a given value of X, which represents the independent variable. α is equal to the Y-intercept, or the point at which the regression line crosses the Y-axis, when X is equal to zero. β is the slope that equals the average change of the dependent variable (Y) as the independent variable (X) increases by one. Finally, ε is the error term that equals Y – ŷ, or the difference between the actual value of the dependent variable and its expected value.

Using this method, you can forecast a defined variable based on known data.

Consider the relationship between advertising spend and revenue, for example. A business can use historical data relating the advertising dollars spent to the amount of revenue generated for various campaigns or time periods. Using a single variable linear regression analysis, it can use that information to find the line of best fit and subsequently use the slope to forecast revenue for future campaigns.

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3. Multiple Regression

Whereas single variable linear regression analysis studies the relationship between two variables—a dependent variable and an independent variable— multiple regression analysis investigates the relationship between a dependent variable and multiple independent variables.

Forecasting with multiple regression analysis is similar to using single variable linear regression. However, instead of entering only one value for an independent variable, a value is input for each independent variable. Using the same notation as the single variable linear regression equation, the following equation applies to multiple regression:

In business, multiple regression analysis is helpful for predicting the outcomes of complicated scenarios. For example, think back to the relationship between advertising spend and revenue. Instead of looking at total advertising expenditures, you can use multiple regression analysis to evaluate how different types of campaigns, such as television, radio, and social media ads, impact revenue.

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Developing Your Analytical Skills

An analytical mindset is essential to business success. After all, data is one of the most valuable resources in today’s world, and knowing how to leverage it can lead to better decision-making and outcomes.

Related: How to Improve Your Analytical Skills

Depending on your current knowledge of statistics and business analytics and long-term goals, there are many options you can pursue to develop your skills. Taking an online course dedicated to honing and applying analytical skills in a professional setting is a great way to get started.

Do you want to leverage the power of data within your organization? Explore our eight-week online course Business Analytics —one of three courses comprising our Credential of Readiness (CORe) program —to learn how to use data analysis to solve business problems.

About the Author

Statistics for Business Analytics

12.2 hypothesis testing.

Another way to look at the uncertainty of parameters is to test a statistical hypothesis. As it was discussed in Section 7 , I personally think that hypothesis testing is a less useful instrument for these purposes than the confidence interval and that it might be misleading in some circumstances. Nonetheless, it has its merits and can be helpful if an analyst knows what they are doing. In order to test the hypothesis, we need to follow the procedure, described in Section 7 .

12.2.1 Regression parameters

The classical hypotheses for the parameters are formulated in the following way: \[\begin{equation} \begin{aligned} \mathrm{H}_0: \beta_i = 0 \\ \mathrm{H}_1: \beta_i \neq 0 \end{aligned} . \tag{12.3} \end{equation}\] This formulation of hypotheses comes from the idea that we want to check if the effect estimated by the regression is indeed there (i.e. statistically significantly different from zero). Note however, that as in any other hypothesis testing, if you fail to reject the null hypothesis, this only means that you do not know, we do not have enough evidence to conclude anything. This does not mean that there is no effect and that the respective variable can be removed from the model. In case of simple linear regression, the null and alternative hypothesis can be represented graphically as shown in Figure 12.4 .

Figure 12.4: Graphical presentation of null and alternative hypothesis in regression context

The graph on the left in Figure 12.4 demonstrates how the true model could look if the null hypothesis was true - it would be just a straight line, parallel to x-axis. The graph on the right demonstrates the alternative situation, when the parameter is not equal to zero. We do not know the true model, and hypothesis testing does not tell us, whether the hypothesis is true or false, but if we have enough evidence to reject H $_0$ , then we might conclude that we see an effect of one variable on another in the data. Note, as discussed in Section 7 , the null hypothesis is always wrong, and it will inevitably be rejected with the increase of sample size.

Given the discussion in the previous subsection, we know that the parameters of regression model will follow normal distribution, as long as all assumptions are satisfied (including those for CLT ). We also know that because the standard errors of parameters are estimated, we need to use Student’s distribution, which takes the uncertainty about the variance into account. Based on this, we can say that the following statistics will follow t with $n-k$ degrees of freedom: \[\begin{equation} \frac{b_i - 0}{s_{b_i}} \sim t(n-k) . \tag{12.4} \end{equation}\] After calculating the value and comparing it with the critical t-value on the selected significance level or directly comparing p-value based on (12.4) with the significance level, we can make conclusions about the hypothesis.

The context of regression provides a great example, why we never accept hypothesis and why in the case of “Fail to reject H $_0$ ”, we should not remove a variable (unless we have more fundamental reasons for doing that). Consider an example, where the estimated parameter $b_1=0.5$ , and its standard error is $s_{b_1}=1$ , we estimated a simple linear regression on a sample of 30 observations, and we want to test, whether the parameter in the population is zero (i.e. hypothesis (12.3) ) on 1% significance level. Inserting the values in formula (12.4) , we get: \[\begin{equation*} \frac{|0.5 - 0|}{1} = 0.5, \end{equation*}\] with the critical value for two-tailed test of $t_{0.01}(30-2)\approx 2.76$ . Comparing t-value with the critical one, we would conclude that we fail to reject H $_0$ and thus the parameter is not statistically different from zero. But what would happen if we check another hypothesis: \[\begin{equation*} \begin{aligned} \mathrm{H}_0: \beta_1 = 1 \\ \mathrm{H}_1: \beta_1 \neq 1 \end{aligned} . \end{equation*}\] The procedure is the same, the calculated t-value is: \[\begin{equation*} \frac{|0.5 - 1|}{1} = 0.5, \end{equation*}\] which leads to exactly the same conclusion as before: on 1% significance level, we fail to reject the new H $_0$ , so the value is not distinguishable from 1. So, which of the two is correct? The correct answer is “we do not know”. The non-rejection region just tells us that uncertainty about the parameter is so high that it also include the value of interest (0 in case of the classical regression analysis). If we constructed the confidence interval for this problem, we would not have such confusion, as we would conclude that on 1% significance level the true parameter lies in the region $(-2.26, 3.26)$ and can be any of these numbers.

In R, if you want to test the hypothesis for parameters, I would recommend using lm() function for regression:

This output tells us that when we consider the parameter for the variable speed, we reject the standard H $_0$ on the pre-selected 1% significance level (comparing the level with p-value in the last column of the output). Note that we should first select the significance level and only then conduct the test, otherwise we would be bending reality for our needs.

12.2.2 Regression line

Finally, in regression context, we can test another hypothesis, which becomes useful, when a lot of parameters of the model are very close to zero and seem to be insignificant on the selected level: \[\begin{equation} \begin{aligned} \mathrm{H}_0: \beta_1 = \beta_2 = \dots = \beta_{k-1} = 0 \\ \mathrm{H}_1: \beta_1 \neq 0 \vee \beta_2 \neq 0 \vee \dots \vee \beta_{k-1} \neq 0 \end{aligned} , \tag{12.5} \end{equation}\] which translates into normal language as “H $_0$ : all parameters (except for intercept) are equal to zero; H $_1$ : at least one parameter is not equal to zero”. This hypothesis is only needed, when you have a model with many statistically insignificant variables and want to see if the model explains anything. This is done using F-test, which can be calculated based on sums of squares: \[\begin{equation*} F = \frac{ SSR / (k-1)}{SSE / (n-k)} \sim F(k-1, n-k) , \end{equation*}\] where the sums of squares are divided by their degrees of freedom. The test is conducted in the similar manner as any other test (see Section 7 ): after choosing the significance level, we can either calculate the critical value of F for the specified degrees of freedom, or compare it with the p-value from the test to make a conclusion about the null hypothesis.

This hypothesis is not very useful, when the parameter are significant and coefficient of determination is high. It only becomes useful in difficult situations of poor fit. The test on its own does not tell if the model is adequate or not. And the F value and related p-value is not comparable with respective values of other models. Graphically, this test checks, whether in the true model the slope of the straight line on the plot of actuals vs fitted is different from zero. An example with the same stopping distance model is provided in Figure 12.5 .

Figure 12.5: Graphical presentation of F test for regression model.

What the test is tries to get insight about, is whether in the true model the blue line coincides with the red line (i.e. the slope is equal to zero, which is only possible, when all parameters are zero). If we have enough evidence to reject the null hypothesis, then this means that the slopes are different on the selected significance level.

Here is an example with the speed model discussed above with the significance level of 1%:

In the output above, the critical value is lower than the calculated, so we can reject the H $_0$ , which means that there is something in the model that explains the variability in the variable dist . Alternatively, we could focus on p-value. We see that the it is lower than the significance level of 1%, so we reject the H $_0$ and come to the same conclusion as above.

9.4 Full Hypothesis Test Examples

Tests on means, example 9.8.

Jeffrey, as an eight-year old, established a mean time of 16.43 seconds for swimming the 25-yard freestyle, with a standard deviation of 0.8 seconds . His dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster using goggles. Frank bought Jeffrey a new pair of expensive goggles and timed Jeffrey for 15 25-yard freestyle swims . For the 15 swims, Jeffrey's mean time was 16 seconds. Frank thought that the goggles helped Jeffrey to swim faster than the 16.43 seconds. Conduct a hypothesis test using a preset α = 0.05.

Set up the Hypothesis Test:

Since the problem is about a mean, this is a test of a single population mean .

Set the null and alternative hypothesis:

In this case there is an implied challenge or claim. This is that the goggles will reduce the swimming time. The effect of this is to set the hypothesis as a one-tailed test. The claim will always be in the alternative hypothesis because the burden of proof always lies with the alternative. Remember that the status quo must be defeated with a high degree of confidence, in this case 95 % confidence. The null and alternative hypotheses are thus:

H 0 : μ ≥ 16.43 H a : μ < 16.43

For Jeffrey to swim faster, his time will be less than 16.43 seconds. The "<" tells you this is left-tailed.

Determine the distribution needed:

Random variable: X ¯ X ¯ = the mean time to swim the 25-yard freestyle.

Distribution for the test statistic:

The sample size is less than 30 and we do not know the population standard deviation so this is a t-test. and the proper formula is: t c = X ¯ - μ 0 σ / n t c = X ¯ - μ 0 σ / n

μ 0 = 16.43 comes from H 0 and not the data. X ¯ X ¯ = 16. s = 0.8, and n = 15.

Our step 2, setting the level of significance, has already been determined by the problem, .05 for a 95 % significance level. It is worth thinking about the meaning of this choice. The Type I error is to conclude that Jeffrey swims the 25-yard freestyle, on average, in less than 16.43 seconds when, in fact, he actually swims the 25-yard freestyle, on average, in 16.43 seconds. (Reject the null hypothesis when the null hypothesis is true.) For this case the only concern with a Type I error would seem to be that Jeffery’s dad may fail to bet on his son’s victory because he does not have appropriate confidence in the effect of the goggles.

To find the critical value we need to select the appropriate test statistic. We have concluded that this is a t-test on the basis of the sample size and that we are interested in a population mean. We can now draw the graph of the t-distribution and mark the critical value. For this problem the degrees of freedom are n-1, or 14. Looking up 14 degrees of freedom at the 0.05 column of the t-table we find 1.761. This is the critical value and we can put this on our graph.

Step 3 is the calculation of the test statistic using the formula we have selected. We find that the calculated test statistic is 2.08, meaning that the sample mean is 2.08 standard deviations away from the hypothesized mean of 16.43.

Step 4 has us compare the test statistic and the critical value and mark these on the graph. We see that the test statistic is in the tail and thus we move to step 4 and reach a conclusion. The probability that an average time of 16 minutes could come from a distribution with a population mean of 16.43 minutes is too unlikely for us to accept the null hypothesis. We cannot accept the null.

Step 5 has us state our conclusions first formally and then less formally. A formal conclusion would be stated as: “With a 95% level of significance we cannot accept the null hypothesis that the swimming time with goggles comes from a distribution with a population mean time of 16.43 minutes.” Less formally, “With 95% significance we believe that the goggles improves swimming speed”

If we wished to use the p-value system of reaching a conclusion we would calculate the statistic and take the additional step to find the probability of being 2.08 standard deviations from the mean on a t-distribution. This value is .0187. Comparing this to the α-level of .05 we see that we cannot accept the null. The p-value has been put on the graph as the shaded area beyond -2.08 and it shows that it is smaller than the hatched area which is the alpha level of 0.05. Both methods reach the same conclusion that we cannot accept the null hypothesis.

The mean throwing distance of a football for Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20 throws. For the 20 throws, Marco’s mean distance was 45 yards. The coach thought the different grip helped Marco throw farther than 40 yards. Conduct a hypothesis test using a preset α = 0.05. Assume the throw distances for footballs are normal.

First, determine what type of test this is, set up the hypothesis test, find the p -value, sketch the graph, and state your conclusion.

Example 9.9

Jane has just begun her new job as on the sales force of a very competitive company. In a sample of 16 sales calls it was found that she closed the contract for an average value of 108 dollars with a standard deviation of 12 dollars. Test at 5% significance that the population mean is at least 100 dollars against the alternative that it is less than 100 dollars. Company policy requires that new members of the sales force must exceed an average of $100 per contract during the trial employment period. Can we conclude that Jane has met this requirement at the significance level of 95%?

H 0 : µ ≤ 100 H a : µ > 100 The null and alternative hypothesis are for the parameter µ because the number of dollars of the contracts is a continuous random variable. Also, this is a one-tailed test because the company has only an interested if the number of dollars per contact is below a particular number not "too high" a number. This can be thought of as making a claim that the requirement is being met and thus the claim is in the alternative hypothesis.
Test statistic: t c = x ¯ − µ 0 s n = 108 − 100 ( 12 16 ) = 2.67 t c = x ¯ − µ 0 s n = 108 − 100 ( 12 16 ) = 2.67
Critical value: t a = 1.753 t a = 1.753 with n-1 degrees of freedom= 15

The test statistic is a Student's t because the sample size is below 30; therefore, we cannot use the normal distribution. Comparing the calculated value of the test statistic and the critical value of t t ( t a ) ( t a ) at a 5% significance level, we see that the calculated value is in the tail of the distribution. Thus, we conclude that 108 dollars per contract is significantly larger than the hypothesized value of 100 and thus we cannot accept the null hypothesis. There is evidence that supports Jane's performance meets company standards.

It is believed that a stock price for a particular company will grow at a rate of $5 per week with a standard deviation of $1. An investor believes the stock won’t grow as quickly. The changes in stock price is recorded for ten weeks and are as follows: $4, $3, $2, $3, $1, $7, $2, $1, $1, $2. Perform a hypothesis test using a 5% level of significance. State the null and alternative hypotheses, state your conclusion, and identify the Type I errors.

Example 9.10

A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses salad dressings is working properly when 8 ounces are dispensed. Suppose that the average amount dispensed in a particular sample of 35 bottles is 7.91 ounces with a variance of 0.03 ounces squared, s 2 s 2 . Is there evidence that the machine should be stopped and production wait for repairs? The lost production from a shutdown is potentially so great that management feels that the level of significance in the analysis should be 99%.

Again we will follow the steps in our analysis of this problem.

STEP 1 : Set the Null and Alternative Hypothesis. The random variable is the quantity of fluid placed in the bottles. This is a continuous random variable and the parameter we are interested in is the mean. Our hypothesis therefore is about the mean. In this case we are concerned that the machine is not filling properly. From what we are told it does not matter if the machine is over-filling or under-filling, both seem to be an equally bad error. This tells us that this is a two-tailed test: if the machine is malfunctioning it will be shutdown regardless if it is from over-filling or under-filling. The null and alternative hypotheses are thus:

STEP 2 : Decide the level of significance and draw the graph showing the critical value.

This problem has already set the level of significance at 99%. The decision seems an appropriate one and shows the thought process when setting the significance level. Management wants to be very certain, as certain as probability will allow, that they are not shutting down a machine that is not in need of repair. To draw the distribution and the critical value, we need to know which distribution to use. Because this is a continuous random variable and we are interested in the mean, and the sample size is greater than 30, the appropriate distribution is the normal distribution and the relevant critical value is 2.575 from the normal table or the t-table at 0.005 column and infinite degrees of freedom. We draw the graph and mark these points.

STEP 3 : Calculate sample parameters and the test statistic. The sample parameters are provided, the sample mean is 7.91 and the sample variance is .03 and the sample size is 35. We need to note that the sample variance was provided not the sample standard deviation, which is what we need for the formula. Remembering that the standard deviation is simply the square root of the variance, we therefore know the sample standard deviation, s, is 0.173. With this information we calculate the test statistic as -3.07, and mark it on the graph.

STEP 4 : Compare test statistic and the critical values Now we compare the test statistic and the critical value by placing the test statistic on the graph. We see that the test statistic is in the tail, decidedly greater than the critical value of 2.575. We note that even the very small difference between the hypothesized value and the sample value is still a large number of standard deviations. The sample mean is only 0.08 ounces different from the required level of 8 ounces, but it is 3 plus standard deviations away and thus we cannot accept the null hypothesis.

STEP 5 : Reach a Conclusion

Three standard deviations of a test statistic will guarantee that the test will fail. The probability that anything is within three standard deviations is almost zero. Actually it is 0.0026 on the normal distribution, which is certainly almost zero in a practical sense. Our formal conclusion would be “ At a 99% level of significance we cannot accept the hypothesis that the sample mean came from a distribution with a mean of 8 ounces” Or less formally, and getting to the point, “At a 99% level of significance we conclude that the machine is under filling the bottles and is in need of repair”.

Hypothesis Test for Proportions

Just as there were confidence intervals for proportions, or more formally, the population parameter p of the binomial distribution, there is the ability to test hypotheses concerning p .

The population parameter for the binomial is p . The estimated value (point estimate) for p is p′ where p′ = x/n , x is the number of successes in the sample and n is the sample size.

When you perform a hypothesis test of a population proportion p , you take a simple random sample from the population. The conditions for a binomial distribution must be met, which are: there are a certain number n of independent trials meaning random sampling, the outcomes of any trial are binary, success or failure, and each trial has the same probability of a success p . The shape of the binomial distribution needs to be similar to the shape of the normal distribution. To ensure this, the quantities np′ and nq′ must both be greater than five ( np′ > 5 and nq′ > 5). In this case the binomial distribution of a sample (estimated) proportion can be approximated by the normal distribution with μ = np μ = np and σ = npq σ = npq . Remember that q = 1 – p q = 1 – p . There is no distribution that can correct for this small sample bias and thus if these conditions are not met we simply cannot test the hypothesis with the data available at that time. We met this condition when we first were estimating confidence intervals for p .

Again, we begin with the standardizing formula modified because this is the distribution of a binomial.

Substituting p 0 p 0 , the hypothesized value of p , we have:

This is the test statistic for testing hypothesized values of p , where the null and alternative hypotheses take one of the following forms:

The decision rule stated above applies here also: if the calculated value of Z c shows that the sample proportion is "too many" standard deviations from the hypothesized proportion, the null hypothesis cannot be accepted. The decision as to what is "too many" is pre-determined by the analyst depending on the level of significance required in the test.

Example 9.11

The mortgage department of a large bank is interested in the nature of loans of first-time borrowers. This information will be used to tailor their marketing strategy. They believe that 50% of first-time borrowers take out smaller loans than other borrowers. They perform a hypothesis test to determine if the percentage is the same or different from 50% . They sample 100 first-time borrowers and find 53 of these loans are smaller that the other borrowers. For the hypothesis test, they choose a 5% level of significance.

STEP 1 : Set the null and alternative hypothesis.

H 0 : p = 0.50 H a : p ≠ 0.50

The words "is the same or different from" tell you this is a two-tailed test. The Type I and Type II errors are as follows: The Type I error is to conclude that the proportion of borrowers is different from 50% when, in fact, the proportion is actually 50%. (Reject the null hypothesis when the null hypothesis is true). The Type II error is there is not enough evidence to conclude that the proportion of first time borrowers differs from 50% when, in fact, the proportion does differ from 50%. (You fail to reject the null hypothesis when the null hypothesis is false.)

STEP 2 : Decide the level of significance and draw the graph showing the critical value

The level of significance has been set by the problem at the 95% level. Because this is two-tailed test one-half of the alpha value will be in the upper tail and one-half in the lower tail as shown on the graph. The critical value for the normal distribution at the 95% level of confidence is 1.96. This can easily be found on the student’s t-table at the very bottom at infinite degrees of freedom remembering that at infinity the t-distribution is the normal distribution. Of course the value can also be found on the normal table but you have go looking for one-half of 95 (0.475) inside the body of the table and then read out to the sides and top for the number of standard deviations.

STEP 3 : Calculate the sample parameters and critical value of the test statistic.

The test statistic is a normal distribution, Z, for testing proportions and is:

For this case, the sample of 100 found 53 first-time borrowers were different from other borrowers. The sample proportion, p′ = 53/100= 0.53 The test question, therefore, is : “Is 0.53 significantly different from .50?” Putting these values into the formula for the test statistic we find that 0.53 is only 0.60 standard deviations away from .50. This is barely off of the mean of the standard normal distribution of zero. There is virtually no difference from the sample proportion and the hypothesized proportion in terms of standard deviations.

STEP 4 : Compare the test statistic and the critical value.

The calculated value is well within the critical values of ± 1.96 standard deviations and thus we cannot reject the null hypothesis. To reject the null hypothesis we need significant evident of difference between the hypothesized value and the sample value. In this case the sample value is very nearly the same as the hypothesized value measured in terms of standard deviations.

STEP 5 : Reach a conclusion

The formal conclusion would be “At a 95% level of significance we cannot reject the null hypothesis that 50% of first-time borrowers have the same size loans as other borrowers”. Less formally we would say that “There is no evidence that one-half of first-time borrowers are significantly different in loan size from other borrowers”. Notice the length to which the conclusion goes to include all of the conditions that are attached to the conclusion. Statisticians for all the criticism they receive, are careful to be very specific even when this seems trivial. Statisticians cannot say more than they know and the data constrain the conclusion to be within the metes and bounds of the data.

Try It 9.11

A teacher believes that 85% of students in the class will want to go on a field trip to the local zoo. She performs a hypothesis test to determine if the percentage is the same or different from 85%. The teacher samples 50 students and 39 reply that they would want to go to the zoo. For the hypothesis test, use a 1% level of significance.

Example 9.12

Suppose a consumer group suspects that the proportion of households that have three or more cell phones is 30%. A cell phone company has reason to believe that the proportion is not 30%. Before they start a big advertising campaign, they conduct a hypothesis test. Their marketing people survey 150 households with the result that 43 of the households have three or more cell phones.

Here is an abbreviate version of the system to solve hypothesis tests applied to a test on a proportions.

Example 9.13

The National Institute of Standards and Technology provides exact data on conductivity properties of materials. Following are conductivity measurements for 11 randomly selected pieces of a particular type of glass.

1.11; 1.07; 1.11; 1.07; 1.12; 1.08; .98; .98 1.02; .95; .95 Is there convincing evidence that the average conductivity of this type of glass is greater than one? Use a significance level of 0.05.

Let’s follow a four-step process to answer this statistical question.

H 0 : μ ≤ 1
H a : μ > 1
Plan : We are testing a sample mean without a known population standard deviation with less than 30 observations. Therefore, we need to use a Student's-t distribution. Assume the underlying population is normal.
Do the calculations and draw the graph .
State the Conclusions : We cannot accept the null hypothesis. It is reasonable to state that the data supports the claim that the average conductivity level is greater than one.

Example 9.14

In a study of 420,019 cell phone users, 172 of the subjects developed brain cancer. Test the claim that cell phone users developed brain cancer at a greater rate than that for non-cell phone users (the rate of brain cancer for non-cell phone users is 0.0340%). Since this is a critical issue, use a 0.005 significance level. Explain why the significance level should be so low in terms of a Type I error.

H 0 : p ≤ 0.00034
H a : p > 0.00034

If we commit a Type I error, we are essentially accepting a false claim. Since the claim describes cancer-causing environments, we want to minimize the chances of incorrectly identifying causes of cancer.

We will be testing a sample proportion with x = 172 and n = 420,019. The sample is sufficiently large because we have np' = 420,019(0.00034) = 142.8, nq' = 420,019(0.99966) = 419,876.2, two independent outcomes, and a fixed probability of success p' = 0.00034. Thus we will be able to generalize our results to the population.

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Everything you need to know about the normal distribution, an in-depth explanation of cumulative distribution function, a complete guide to chi-square test, a complete guide on hypothesis testing in statistics, understanding the fundamentals of arithmetic and geometric progression, the definitive guide to understand spearman’s rank correlation, a comprehensive guide to understand mean squared error, all you need to know about the empirical rule in statistics, the complete guide to skewness and kurtosis, a holistic look at bernoulli distribution.

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Lesson 10 of 24 By Avijeet Biswal

A Complete Guide on Hypothesis Testing in Statistics

In today’s data-driven world , decisions are based on data all the time. Hypothesis plays a crucial role in that process, whether it may be making business decisions, in the health sector, academia, or in quality improvement. Without hypothesis & hypothesis tests, you risk drawing the wrong conclusions and making bad decisions. In this tutorial, you will look at Hypothesis Testing in Statistics.

What Is Hypothesis Testing in Statistics?

Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.

Let's discuss few examples of statistical hypothesis from real-life -

A teacher assumes that 60% of his college's students come from lower-middle-class families.
A doctor believes that 3D (Diet, Dose, and Discipline) is 90% effective for diabetic patients.

Now that you know about hypothesis testing, look at the two types of hypothesis testing in statistics.

Hypothesis Testing Formula

Z = ( x̅ – μ0 ) / (σ /√n)

Here, x̅ is the sample mean,
μ0 is the population mean,
σ is the standard deviation,
n is the sample size.

How Hypothesis Testing Works?

An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.

The null hypothesis is typically an equality hypothesis between population parameters; for example, a null hypothesis may claim that the population means return equals zero. The alternate hypothesis is essentially the inverse of the null hypothesis (e.g., the population means the return is not equal to zero). As a result, they are mutually exclusive, and only one can be correct. One of the two possibilities, however, will always be correct.

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Null Hypothesis and Alternate Hypothesis

The Null Hypothesis is the assumption that the event will not occur. A null hypothesis has no bearing on the study's outcome unless it is rejected.

H0 is the symbol for it, and it is pronounced H-naught.

The Alternate Hypothesis is the logical opposite of the null hypothesis. The acceptance of the alternative hypothesis follows the rejection of the null hypothesis. H1 is the symbol for it.

Let's understand this with an example.

A sanitizer manufacturer claims that its product kills 95 percent of germs on average.

To put this company's claim to the test, create a null and alternate hypothesis.

H0 (Null Hypothesis): Average = 95%.

Alternative Hypothesis (H1): The average is less than 95%.

Another straightforward example to understand this concept is determining whether or not a coin is fair and balanced. The null hypothesis states that the probability of a show of heads is equal to the likelihood of a show of tails. In contrast, the alternate theory states that the probability of a show of heads and tails would be very different.

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Hypothesis Testing Calculation With Examples

Let's consider a hypothesis test for the average height of women in the United States. Suppose our null hypothesis is that the average height is 5'4". We gather a sample of 100 women and determine that their average height is 5'5". The standard deviation of population is 2.

To calculate the z-score, we would use the following formula:

z = ( x̅ – μ0 ) / (σ /√n)

z = (5'5" - 5'4") / (2" / √100)

z = 0.5 / (0.045)

We will reject the null hypothesis as the z-score of 11.11 is very large and conclude that there is evidence to suggest that the average height of women in the US is greater than 5'4".

Steps of Hypothesis Testing

Step 1: specify your null and alternate hypotheses.

It is critical to rephrase your original research hypothesis (the prediction that you wish to study) as a null (Ho) and alternative (Ha) hypothesis so that you can test it quantitatively. Your first hypothesis, which predicts a link between variables, is generally your alternate hypothesis. The null hypothesis predicts no link between the variables of interest.

Step 2: Gather Data

For a statistical test to be legitimate, sampling and data collection must be done in a way that is meant to test your hypothesis. You cannot draw statistical conclusions about the population you are interested in if your data is not representative.

Step 3: Conduct a Statistical Test

Other statistical tests are available, but they all compare within-group variance (how to spread out the data inside a category) against between-group variance (how different the categories are from one another). If the between-group variation is big enough that there is little or no overlap between groups, your statistical test will display a low p-value to represent this. This suggests that the disparities between these groups are unlikely to have occurred by accident. Alternatively, if there is a large within-group variance and a low between-group variance, your statistical test will show a high p-value. Any difference you find across groups is most likely attributable to chance. The variety of variables and the level of measurement of your obtained data will influence your statistical test selection.

Step 4: Determine Rejection Of Your Null Hypothesis

Your statistical test results must determine whether your null hypothesis should be rejected or not. In most circumstances, you will base your judgment on the p-value provided by the statistical test. In most circumstances, your preset level of significance for rejecting the null hypothesis will be 0.05 - that is, when there is less than a 5% likelihood that these data would be seen if the null hypothesis were true. In other circumstances, researchers use a lower level of significance, such as 0.01 (1%). This reduces the possibility of wrongly rejecting the null hypothesis.

Step 5: Present Your Results

The findings of hypothesis testing will be discussed in the results and discussion portions of your research paper, dissertation, or thesis. You should include a concise overview of the data and a summary of the findings of your statistical test in the results section. You can talk about whether your results confirmed your initial hypothesis or not in the conversation. Rejecting or failing to reject the null hypothesis is a formal term used in hypothesis testing. This is likely a must for your statistics assignments.

Types of Hypothesis Testing

To determine whether a discovery or relationship is statistically significant, hypothesis testing uses a z-test. It usually checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more, can a z-test be applied.

A statistical test called a t-test is employed to compare the means of two groups. To determine whether two groups differ or if a procedure or treatment affects the population of interest, it is frequently used in hypothesis testing.

Chi-Square

You utilize a Chi-square test for hypothesis testing concerning whether your data is as predicted. To determine if the expected and observed results are well-fitted, the Chi-square test analyzes the differences between categorical variables from a random sample. The test's fundamental premise is that the observed values in your data should be compared to the predicted values that would be present if the null hypothesis were true.

Hypothesis Testing and Confidence Intervals

Both confidence intervals and hypothesis tests are inferential techniques that depend on approximating the sample distribution. Data from a sample is used to estimate a population parameter using confidence intervals. Data from a sample is used in hypothesis testing to examine a given hypothesis. We must have a postulated parameter to conduct hypothesis testing.

Bootstrap distributions and randomization distributions are created using comparable simulation techniques. The observed sample statistic is the focal point of a bootstrap distribution, whereas the null hypothesis value is the focal point of a randomization distribution.

A variety of feasible population parameter estimates are included in confidence ranges. In this lesson, we created just two-tailed confidence intervals. There is a direct connection between these two-tail confidence intervals and these two-tail hypothesis tests. The results of a two-tailed hypothesis test and two-tailed confidence intervals typically provide the same results. In other words, a hypothesis test at the 0.05 level will virtually always fail to reject the null hypothesis if the 95% confidence interval contains the predicted value. A hypothesis test at the 0.05 level will nearly certainly reject the null hypothesis if the 95% confidence interval does not include the hypothesized parameter.

Simple and Composite Hypothesis Testing

Depending on the population distribution, you can classify the statistical hypothesis into two types.

Simple Hypothesis: A simple hypothesis specifies an exact value for the parameter.

Composite Hypothesis: A composite hypothesis specifies a range of values.

A company is claiming that their average sales for this quarter are 1000 units. This is an example of a simple hypothesis.

Suppose the company claims that the sales are in the range of 900 to 1000 units. Then this is a case of a composite hypothesis.

One-Tailed and Two-Tailed Hypothesis Testing

The One-Tailed test, also called a directional test, considers a critical region of data that would result in the null hypothesis being rejected if the test sample falls into it, inevitably meaning the acceptance of the alternate hypothesis.

In a one-tailed test, the critical distribution area is one-sided, meaning the test sample is either greater or lesser than a specific value.

In two tails, the test sample is checked to be greater or less than a range of values in a Two-Tailed test, implying that the critical distribution area is two-sided.

If the sample falls within this range, the alternate hypothesis will be accepted, and the null hypothesis will be rejected.

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Right Tailed Hypothesis Testing

If the larger than (>) sign appears in your hypothesis statement, you are using a right-tailed test, also known as an upper test. Or, to put it another way, the disparity is to the right. For instance, you can contrast the battery life before and after a change in production. Your hypothesis statements can be the following if you want to know if the battery life is longer than the original (let's say 90 hours):

The null hypothesis is (H0 <= 90) or less change.
A possibility is that battery life has risen (H1) > 90.

The crucial point in this situation is that the alternate hypothesis (H1), not the null hypothesis, decides whether you get a right-tailed test.

Left Tailed Hypothesis Testing

Alternative hypotheses that assert the true value of a parameter is lower than the null hypothesis are tested with a left-tailed test; they are indicated by the asterisk "<".

Suppose H0: mean = 50 and H1: mean not equal to 50

According to the H1, the mean can be greater than or less than 50. This is an example of a Two-tailed test.

In a similar manner, if H0: mean >=50, then H1: mean <50

Here the mean is less than 50. It is called a One-tailed test.

Type 1 and Type 2 Error

A hypothesis test can result in two types of errors.

Type 1 Error: A Type-I error occurs when sample results reject the null hypothesis despite being true.

Type 2 Error: A Type-II error occurs when the null hypothesis is not rejected when it is false, unlike a Type-I error.

Suppose a teacher evaluates the examination paper to decide whether a student passes or fails.

H0: Student has passed

H1: Student has failed

Type I error will be the teacher failing the student [rejects H0] although the student scored the passing marks [H0 was true].

Type II error will be the case where the teacher passes the student [do not reject H0] although the student did not score the passing marks [H1 is true].

Level of Significance

The alpha value is a criterion for determining whether a test statistic is statistically significant. In a statistical test, Alpha represents an acceptable probability of a Type I error. Because alpha is a probability, it can be anywhere between 0 and 1. In practice, the most commonly used alpha values are 0.01, 0.05, and 0.1, which represent a 1%, 5%, and 10% chance of a Type I error, respectively (i.e. rejecting the null hypothesis when it is in fact correct).

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A p-value is a metric that expresses the likelihood that an observed difference could have occurred by chance. As the p-value decreases the statistical significance of the observed difference increases. If the p-value is too low, you reject the null hypothesis.

Here you have taken an example in which you are trying to test whether the new advertising campaign has increased the product's sales. The p-value is the likelihood that the null hypothesis, which states that there is no change in the sales due to the new advertising campaign, is true. If the p-value is .30, then there is a 30% chance that there is no increase or decrease in the product's sales. If the p-value is 0.03, then there is a 3% probability that there is no increase or decrease in the sales value due to the new advertising campaign. As you can see, the lower the p-value, the chances of the alternate hypothesis being true increases, which means that the new advertising campaign causes an increase or decrease in sales.

Why is Hypothesis Testing Important in Research Methodology?

Hypothesis testing is crucial in research methodology for several reasons:

Provides evidence-based conclusions: It allows researchers to make objective conclusions based on empirical data, providing evidence to support or refute their research hypotheses.
Supports decision-making: It helps make informed decisions, such as accepting or rejecting a new treatment, implementing policy changes, or adopting new practices.
Adds rigor and validity: It adds scientific rigor to research using statistical methods to analyze data, ensuring that conclusions are based on sound statistical evidence.
Contributes to the advancement of knowledge: By testing hypotheses, researchers contribute to the growth of knowledge in their respective fields by confirming existing theories or discovering new patterns and relationships.

Limitations of Hypothesis Testing

Hypothesis testing has some limitations that researchers should be aware of:

It cannot prove or establish the truth: Hypothesis testing provides evidence to support or reject a hypothesis, but it cannot confirm the absolute truth of the research question.
Results are sample-specific: Hypothesis testing is based on analyzing a sample from a population, and the conclusions drawn are specific to that particular sample.
Possible errors: During hypothesis testing, there is a chance of committing type I error (rejecting a true null hypothesis) or type II error (failing to reject a false null hypothesis).
Assumptions and requirements: Different tests have specific assumptions and requirements that must be met to accurately interpret results.

After reading this tutorial, you would have a much better understanding of hypothesis testing, one of the most important concepts in the field of Data Science . The majority of hypotheses are based on speculation about observed behavior, natural phenomena, or established theories.

If you are interested in statistics of data science and skills needed for such a career, you ought to explore Simplilearn’s Post Graduate Program in Data Science.

If you have any questions regarding this ‘Hypothesis Testing In Statistics’ tutorial, do share them in the comment section. Our subject matter expert will respond to your queries. Happy learning!

1. What is hypothesis testing in statistics with example?

Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population. It involves formulating two competing hypotheses, the null hypothesis (H0) and the alternative hypothesis (Ha), and then collecting data to assess the evidence. An example: testing if a new drug improves patient recovery (Ha) compared to the standard treatment (H0) based on collected patient data.

2. What is hypothesis testing and its types?

Hypothesis testing is a statistical method used to make inferences about a population based on sample data. It involves formulating two hypotheses: the null hypothesis (H0), which represents the default assumption, and the alternative hypothesis (Ha), which contradicts H0. The goal is to assess the evidence and determine whether there is enough statistical significance to reject the null hypothesis in favor of the alternative hypothesis.

Types of hypothesis testing:

One-sample test: Used to compare a sample to a known value or a hypothesized value.
Two-sample test: Compares two independent samples to assess if there is a significant difference between their means or distributions.
Paired-sample test: Compares two related samples, such as pre-test and post-test data, to evaluate changes within the same subjects over time or under different conditions.
Chi-square test: Used to analyze categorical data and determine if there is a significant association between variables.
ANOVA (Analysis of Variance): Compares means across multiple groups to check if there is a significant difference between them.

3. What are the steps of hypothesis testing?

The steps of hypothesis testing are as follows:

Formulate the hypotheses: State the null hypothesis (H0) and the alternative hypothesis (Ha) based on the research question.
Set the significance level: Determine the acceptable level of error (alpha) for making a decision.
Collect and analyze data: Gather and process the sample data.
Compute test statistic: Calculate the appropriate statistical test to assess the evidence.
Make a decision: Compare the test statistic with critical values or p-values and determine whether to reject H0 in favor of Ha or not.
Draw conclusions: Interpret the results and communicate the findings in the context of the research question.

4. What are the 2 types of hypothesis testing?

One-tailed (or one-sided) test: Tests for the significance of an effect in only one direction, either positive or negative.
Two-tailed (or two-sided) test: Tests for the significance of an effect in both directions, allowing for the possibility of a positive or negative effect.

The choice between one-tailed and two-tailed tests depends on the specific research question and the directionality of the expected effect.

5. What are the 3 major types of hypothesis?

The three major types of hypotheses are:

Null Hypothesis (H0): Represents the default assumption, stating that there is no significant effect or relationship in the data.
Alternative Hypothesis (Ha): Contradicts the null hypothesis and proposes a specific effect or relationship that researchers want to investigate.
Nondirectional Hypothesis: An alternative hypothesis that doesn't specify the direction of the effect, leaving it open for both positive and negative possibilities.

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Avijeet is a Senior Research Analyst at Simplilearn. Passionate about Data Analytics, Machine Learning, and Deep Learning, Avijeet is also interested in politics, cricket, and football.

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Who’s Joe?

“A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty until found effective.”

– Edward Teller, Nuclear Physicist

During my first brainstorming meeting on my first project at McKinsey, this very serious partner, who had a PhD in Physics, looked at me and said, “So, Joe, what are your main hypotheses.” I looked back at him, perplexed, and said, “Ummm, my what?” I was used to people simply asking, “what are your best ideas, opinions, thoughts, etc.” Over time, I began to understand the importance of hypotheses and how it plays an important role in McKinsey’s problem solving of separating ideas and opinions from facts.

What is a Hypothesis?

“Hypothesis” is probably one of the top 5 words used by McKinsey consultants. And, being hypothesis-driven was required to have any success at McKinsey. A hypothesis is an idea or theory, often based on limited data, which is typically the beginning of a thread of further investigation to prove, disprove or improve the hypothesis through facts and empirical data.

The first step in being hypothesis-driven is to focus on the highest potential ideas and theories of how to solve a problem or realize an opportunity.

Let’s go over an example of being hypothesis-driven.

Let’s say you own a website, and you brainstorm ten ideas to improve web traffic, but you don’t have the budget to execute all ten ideas. The first step in being hypothesis-driven is to prioritize the ten ideas based on how much impact you hypothesize they will create.

The second step in being hypothesis-driven is to apply the scientific method to your hypotheses by creating the fact base to prove or disprove your hypothesis, which then allows you to turn your hypothesis into fact and knowledge. Running with our example, you could prove or disprove your hypothesis on the ideas you think will drive the most impact by executing:

1. An analysis of previous research and the performance of the different ideas 2. A survey where customers rank order the ideas 3. An actual test of the ten ideas to create a fact base on click-through rates and cost

While there are many other ways to validate the hypothesis on your prioritization , I find most people do not take this critical step in validating a hypothesis. Instead, they apply bad logic to many important decisions . An idea pops into their head, and then somehow it just becomes a fact.

One of my favorite lousy logic moments was a CEO who stated,

“I’ve never heard our customers talk about price, so the price doesn’t matter with our products , and I’ve decided we’re going to raise prices.”

Luckily, his management team was able to do a survey to dig deeper into the hypothesis that customers weren’t price-sensitive. Well, of course, they were and through the survey, they built a fantastic fact base that proved and disproved many other important hypotheses.

Why is being hypothesis-driven so important?

Imagine if medicine never actually used the scientific method. We would probably still be living in a world of lobotomies and bleeding people. Many organizations are still stuck in the dark ages, having built a house of cards on opinions disguised as facts, because they don’t prove or disprove their hypotheses. Decisions made on top of decisions, made on top of opinions, steer organizations clear of reality and the facts necessary to objectively evolve their strategic understanding and knowledge. I’ve seen too many leadership teams led solely by gut and opinion. The problem with intuition and gut is if you don’t ever prove or disprove if your gut is right or wrong, you’re never going to improve your intuition. There is a reason why being hypothesis-driven is the cornerstone of problem solving at McKinsey and every other top strategy consulting firm.

How do you become hypothesis-driven?

Most people are idea-driven, and constantly have hypotheses on how the world works and what they or their organization should do to improve. Though, there is often a fatal flaw in that many people turn their hypotheses into false facts, without actually finding or creating the facts to prove or disprove their hypotheses. These people aren’t hypothesis-driven; they are gut-driven.

The conversation typically goes something like “doing this discount promotion will increase our profits” or “our customers need to have this feature” or “morale is in the toilet because we don’t pay well, so we need to increase pay.” These should all be hypotheses that need the appropriate fact base, but instead, they become false facts, often leading to unintended results and consequences. In each of these cases, to become hypothesis-driven necessitates a different framing.

• Instead of “doing this discount promotion will increase our profits,” a hypothesis-driven approach is to ask “what are the best marketing ideas to increase our profits?” and then conduct a marketing experiment to see which ideas increase profits the most.

• Instead of “our customers need to have this feature,” ask the question, “what features would our customers value most?” And, then conduct a simple survey having customers rank order the features based on value to them.

• Instead of “morale is in the toilet because we don’t pay well, so we need to increase pay,” conduct a survey asking, “what is the level of morale?” what are potential issues affecting morale?” and what are the best ideas to improve morale?”

Beyond, watching out for just following your gut, here are some of the other best practices in being hypothesis-driven:

Listen to Your Intuition

Your mind has taken the collision of your experiences and everything you’ve learned over the years to create your intuition, which are those ideas that pop into your head and those hunches that come from your gut. Your intuition is your wellspring of hypotheses. So listen to your intuition, build hypotheses from it, and then prove or disprove those hypotheses, which will, in turn, improve your intuition. Intuition without feedback will over time typically evolve into poor intuition, which leads to poor judgment, thinking, and decisions.

Constantly Be Curious

I’m always curious about cause and effect. At Sports Authority, I had a hypothesis that customers that received service and assistance as they shopped, were worth more than customers who didn’t receive assistance from an associate. We figured out how to prove or disprove this hypothesis by tying surveys to transactional data of customers, and we found the hypothesis was true, which led us to a broad initiative around improving service. The key is you have to be always curious about what you think does or will drive value, create hypotheses and then prove or disprove those hypotheses.

Validate Hypotheses

You need to validate and prove or disprove hypotheses. Don’t just chalk up an idea as fact. In most cases, you’re going to have to create a fact base utilizing logic, observation, testing (see the section on Experimentation ), surveys, and analysis.

Be a Learning Organization

The foundation of learning organizations is the testing of and learning from hypotheses. I remember my first strategy internship at Mercer Management Consulting when I spent a good part of the summer combing through the results, findings, and insights of thousands of experiments that a banking client had conducted. It was fascinating to see the vastness and depth of their collective knowledge base. And, in today’s world of knowledge portals, it is so easy to disseminate, learn from, and build upon the knowledge created by companies.

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A Beginner's Guide to Hypothesis Testing in Business
3. One-Sided vs. Two-Sided Testing. When it's time to test your hypothesis, it's important to leverage the correct testing method. The two most common hypothesis testing methods are one-sided and two-sided tests, or one-tailed and two-tailed tests, respectively. Typically, you'd leverage a one-sided test when you have a strong conviction ...
Hypothesis Testing in Business Analytics
There are four main steps in hypothesis testing in business analytics: Step 1: State the Null and Alternate Hypothesis. After the initial research hypothesis, it is essential to restate it as a null (Ho) hypothesis and an alternate (Ha) hypothesis so that it can be tested mathematically. Step 2: Collate Data.
A Beginner's Guide to Hypothesis Testing in Business Analytics
Hypothesis testing is a statistical method used to make decisions about a population based on a sample. It helps business analysts draw conclusions about business metrics and make data-driven decisions. This beginner's guide will provide an introduction to hypothesis testing and how it is applied in business analytics.
Hypothesis Testing in Business: Examples
Hypothesis testing is a powerful statistical technique that can help you understand problems during exploratory data analysis (EDA) and identify most appropriate hypotheses / analytical solution. In this blog, we will discuss hypothesis testing with examples from business. We'll also give you tips on how to use it effectively in your own ...
Hypothesis Testing
Present the findings in your results and discussion section. Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps. Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test.
Hypothesis Testing: A Step-by-Step Guide With Easy Examples
Assuming and explaining theories is a fundamental part of Business Analytics. In the past few years, the field of Business Analytics has proliferated and made several advancements. As the number of people interested in its statistical applications in business has increased, the concept of hypothesis testing has grabbed everyone's attention.
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Introduction. Hypothesis testing is the detective work of statistics, where evidence is scrutinized to determine the truth behind claims. From unraveling mysteries in science to guiding decisions in business, this method empowers researchers to make sense of data and draw reliable conclusions.
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1.Formulating the Null and Alternative Hypothesis: The first step in performing Hypothesis Testing is to describe the Null and Alternative Hypothesis in words. These Hypotheses are described using ...
Statistics for Business Analytics 101: Hypothesis Testing
In statistics what we can do is to test our assumptions or hypotheses that we made for measurements like the ones we described earlier. For example, The mean number of e-mails required to turn a lead into a customer is five. The above assumption, or its negation, is a valid hypothesis that we can use statistical tools to investigate. The way to ...
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An essential procedure to understand business and analytics is hypothesis testing. This short course, designed by Tufts University expert faculty, will teach the fundamentals of hypothesis testing of a population mean and a population proportion, using Excel and Python for calculations. You'll also discover the central limit theorem, which is ...
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4. Photo by Anna Nekrashevich from Pexels. Hypothesis testing is a common statistical tool used in research and data science to support the certainty of findings. The aim of testing is to answer how probable an apparent effect is detected by chance given a random data sample. This article provides a detailed explanation of the key concepts in ...
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Chapter 7. Hypothesis testing. Hypothesis testing arises naturally from the idea of confidence intervals discussed in Section 6.4: instead of constructing the interval and getting the idea about the uncertainty of the parameter, we could check, whether the sample agrees with our expectations or not. For example, we could test, whether the ...
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Hypothesis Testing. Hypothesis testing is the act of testing a hypothesis or a supposition in relation to a statistical parameter. Analysts implement hypothesis testing in order to test if a hypothesis is plausible or not. In data science and statistics, hypothesis testing is an important step as it involves the verification of an assumption ...
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12.2 Hypothesis testing. Another way to look at the uncertainty of parameters is to test a statistical hypothesis. As it was discussed in Section 7, I personally think that hypothesis testing is a less useful instrument for these purposes than the confidence interval and that it might be misleading in some circumstances.Nonetheless, it has its merits and can be helpful if an analyst knows what ...
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A teacher believes that 85% of students in the class will want to go on a field trip to the local zoo. She performs a hypothesis test to determine if the percentage is the same or different from 85%. The teacher samples 50 students and 39 reply that they would want to go to the zoo. For the hypothesis test, use a 1% level of significance.
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Running with our example, you could prove or disprove your hypothesis on the ideas you think will drive the most impact by executing: 1. An analysis of previous research and the performance of the different ideas 2. A survey where customers rank order the ideas 3. An actual test of the ten ideas to create a fact base on click-through rates and cost
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A Beginner’s Guide to Hypothesis Testing in Business Analytics

What is a Hypothesis?

Why Hypothesis Testing is Important in Business

Steps in Hypothesis Testing

1. State the Hypotheses

2. Choose the Significance Level

3. Select the Sample and Collect Data

4. Analyze the Sample Data

5. Make a Decision

Types of Hypothesis Tests

1. Parametric Tests

2. Non-parametric Tests

One-tailed and Two-tailed Hypothesis Tests

Interpreting Hypothesis Test Results

Common Errors in Hypothesis Testing

Real-world Example of Hypothesis Testing

Hypothesis Testing in Business: Examples

Business Objective / Problem Analysis to Asking Key Questions

Hypothesis formulation

Identifying Test Statistics for Hypothesis Testing

Gather Data

Perform Hypothesis Testing

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Hypothesis Testing: A Step-by-Step Guide With Easy Examples

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Statistics for Business Analytics 101: Hypothesis Testing

Introduction

Hypothesis Testing

What is Hypothesis Testing? Types and Methods

Hypothesis Testing

Types of Hypotheses

Alternative Hypothesis

Null Hypothesis

Non-Directional Hypothesis

Directional Hypothesis

Statistical Hypothesis

Performing Hypothesis Testing

Establish the hypotheses

Generate a testing plan

Analyze data samples

Infer the results

Methods of Hypothesis Testing

Frequentist Hypothesis Testing

Bayesian Hypothesis Testing

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Statistics for Business Analytics

12.2.1 Regression parameters

12.2.2 Regression line

9.4 Full Hypothesis Test Examples

Example 9.9