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

Published on November 8, 2019 by Rebecca Bevans . Revised on December 7, 2022.

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.

## Table of contents

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- 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.

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

## Cite this Scribbr article

Bevans, R. (2022, December 07). Hypothesis Testing | A Step-by-Step Guide with Easy Examples. Scribbr. Retrieved March 13, 2023, from https://www.scribbr.com/statistics/hypothesis-testing/

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## Rebecca Bevans

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## Hypothesis tests

- • Hypothesis tests are used to assess whether a difference between two samples represents a real difference between the populations from which the samples were taken.
- • A null hypothesis of ‘no difference’ is taken as a starting point, and we calculate the probability that both sets of data came from the same population. This probability is expressed as a p -value.
- • When the null hypothesis is false, p- values tend to be small. When the null hypothesis is true, any p- value is equally likely.

## Learning objectives

By reading this article, you should be able to:

- • Explain why hypothesis testing is used.
- • Use a table to determine which hypothesis test should be used for a particular situation.
- • Interpret a p- value.

## Sampling error

where SD is the sample standard deviation, and n is the sample size.

We can interpret this as meaning ‘We are 95% confident that the actual mean is within this range.’

## Inference testing using a null hypothesis

- (i) Assume that both samples came from the same group. This is our ‘null hypothesis’.
- (ii) Calculate the probability that an experiment would give us these data, assuming that the null hypothesis is true. We express this probability as a p- value, a number between 0 and 1, where 0 is ‘impossible’ and 1 is ‘certain’.
- (iii) If the probability of the data is low, we reject the null hypothesis and conclude that there must be a difference between the two groups.

## Hypothesis testing in practice

## Categorical data: the χ 2 test

## Table 1

Summary of the results of the PROXI trial. Figures are numbers of patients.

## Continuous data: the t- test

## Table 2

## Controversies surrounding hypothesis testing

## Hypothesis testing: what next?

## Declaration of interest

The author declares that they have no conflict of interest.

Matrix codes: 1A03, 2A04, 3J03

## Supplementary material

The following is the Supplementary data to this article:

- Maths at uni
- Maths in Allied Health
- Maths for Business
- Maths for Education
- Maths for Humanities
- Maths for Nursing
- Maths for Psychology
- Measures of central tendency
- Measures of variability
- Probability and the normal distribution

## Hypothesis testing

## Basic concepts

## Probability value and types of errors

Effect size and statistical significance.

## Null and research hypotheses

To carry out statistical hypothesis testing, research and null hypothesis are employed:

H A: There is a relationship between intelligence and academic results.

H A: First year university students obtain higher grades after an intensive Statistics course.

H A; Males and females differ in their levels of stress.

H o : There is no relationship between intelligence and academic results.

H o : Males and females will not differ in their levels of stress.

- A critical value is the score the sample would need to decide against the null hypothesis.
- A probability value is used to assess the significance of the statistical test. If the null hypothesis is rejected, then the alternative to the null hypothesis is accepted.

- What if we observe a difference – but none exists in the population?
- What if we do not find a difference – but it does exist in the population?

These situations are known as Type I and Type II errors:

- Type I Error: is the type of error that involves the rejection of a null hypothesis that is actually true (i.e. a false positive).
- Type II Error: is the type of error that occurs when we do not reject a null hypothesis that is false (i.e. a false negative).

- A hypothesis that states that students who attend an intensive Statistics course will obtain higher grades than students who do not attend would be directional.
- A non-directional hypothesis states that there will be differences between students who attend do or don’t attend an intensive Statistics course, but we don’t know what group will get higher grades than the other. The hypothesis only states that they will obtain different grades.

## The hypothesis testing process

The hypothesis testing process can be divided into five steps:

- Restate the research question as research hypothesis and a null hypothesis about the populations.
- Determine the characteristics of the comparison distribution.
- Determine the cut off sample score on the comparison distribution at which the null hypothesis should be rejected.
- Determine your sample’s score on the comparison distribution.
- Decide whether to reject the null hypothesis.

This example illustrates how these five steps can be applied to text a hypothesis:

- Let’s say that you conduct an experiment to investigate whether students’ ability to memorise words improves after they have consumed caffeine.
- The experiment involves two groups of students: the first group consumes caffeine; the second group drinks water.
- Both groups complete a memory test.
- A randomly selected individual in the experimental condition (i.e. the group that consumes caffeine) has a score of 27 on the memory test. The scores of people in general on this memory measure are normally distributed with a mean of 19 and a standard deviation of 4.
- The researcher predicts an effect (differences in memory for these groups) but does not predict a particular direction of effect (i.e. which group will have higher scores on the memory test). Using the 5% significance level, what should you conclude?

Step 1 : There are two populations of interest.

Population 1: People who go through the experimental procedure (drink coffee).

Population 2: People who do not go through the experimental procedure (drink water).

- Research hypothesis: Population 1 will score differently from Population 2.
- Null hypothesis: There will be no difference between the two populations.

Step 2 : We know that the characteristics of the comparison distribution (student population) are:

You can find more examples here:

## Some commonly used statistical techniques

Correlation analysis, multiple regression.

## Chi-square test for independence

- The direction of the relationship: positive or negative- given by the sign of the correlation coefficient.
- The strength or magnitude of the relationship between the two variables- given by the correlation coefficient, which varies from 0 (no relationship between the variables) to 1 (perfect relationship between the variables).
- Direction of the relationship.

2. The strength or magnitude of the relationship

Example of multiple regression model

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## 6 Steps to Evaluate the Effectiveness of Statistical Hypothesis Testing

## What Is Research Hypothesis Testing?

## Types of Statistical Hypothesis Testing

## Source: https://www.youtube.com/c/365DataScience

1. there are two types of hypothesis in statistics, a. null hypothesis.

## b. Alternate Hypothesis

Hypothesis Testing Example: A sanitizer manufacturer company claims that its product kills 98% of germs on average. To put this company’s claim to test, create null and alternate hypothesis H0 (Null Hypothesis): Average = 98% H1/Ha (Alternate Hypothesis): The average is less than 98%

## 2. Depending on the population distribution, you can categorize the statistical hypothesis into two types.

A simple hypothesis specifies an exact value for the parameter.

## b. Composite Hypothesis

A composite hypothesis specifies a range of values.

Hypothesis Testing Example: A company claims to have achieved 1000 units as their average sales for this quarter. (Simple Hypothesis) The company claims to achieve the sales in the range of 900 to 100o units. (Composite Hypothesis).

## 3. Based on the type of statistical testing, the hypothesis in statistics is of two types.

## b. Two-Tailed

Statistical Hypothesis Testing Example: Suppose H0: mean = 100 and H1: mean is not equal to 100 According to the H1, the mean can be greater than or less than 100. (Two-Tailed test) Similarly, if H0: mean >= 100, then H1: mean < 100 Here the mean is less than 100. (One-Tailed test)

## Steps in Statistical Hypothesis Testing

Step 1: develop initial research hypothesis.

## Step 2: State the null and alternate hypothesis based on your research hypothesis

## Step 3: Perform sampling and collection of data for statistical testing

## Step 4: Perform statistical testing based on the type of data you collected

## Step 5: Based on the statistical outcome, reject or fail to reject your null hypothesis

## Step 6: Present your final results of hypothesis testing

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Hypothesis testing is as old as the scientific method and is at the heart of the research process.

## What is a Hypothesis?

Read: What is Empirical Research Study? [Examples & Method]

## What are the Types of Hypotheses?

- Drinking soda and other sugary drinks can cause obesity.
- Smoking cigarettes daily leads to lung cancer.

## 2. Complex Hypothesis

Examples of Complex Hypotheses

- Adults who do not smoke and drink are less likely to develop liver-related conditions.
- Global warming causes icebergs to melt which in turn causes major changes in weather patterns.

## 3. Null Hypothesis

- This is no significant change in a student’s performance if they drink coffee or tea before classes.
- There’s no significant change in the growth of a plant if one uses distilled water only or vitamin-rich water.

Read: Research Report: Definition, Types + [Writing Guide]

## 4. Alternative Hypothesis

Examples of Alternative Hypotheses

- Starting your day with a cup of tea instead of a cup of coffee can make you more alert in the morning.
- The growth of a plant improves significantly when it receives distilled water instead of vitamin-rich water.

## 5. Logical Hypothesis

Examples of Logical Hypothesis

- Waking up early helps you to have a more productive day.
- Beings from Mars would not be able to breathe the air in the atmosphere of the Earth.

## 6. Empirical Hypothesis

- People who eat more fish run faster than people who eat meat.
- Women taking vitamin E grow hair faster than those taking vitamin K.

## 7. Statistical Hypothesis

Examples of Statistical Hypothesis

- 45% of students in Louisiana have middle-income parents.
- 80% of the UK’s population gets a divorce because of irreconcilable differences.

## What is Hypothesis Testing?

Explore: Research Bias: Definition, Types + Examples

## How Hypothesis Testing Works

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## What Are The Stages of Hypothesis Testing?

- Determine the null hypothesis
- Specify the alternative hypothesis
- Set the significance level
- Calculate the test statistics and corresponding P-value
- Draw your conclusion
- Determine the Null Hypothesis

Explore: What is Data Interpretation? + [Types, Method & Tools]

## Applications of Hypothesis Testing in Research

## What is an Example of Hypothesis Testing?

Step 1: Using the value of the mean population IQ, we establish the null hypothesis as 100.

Step 2: State that the alternative hypothesis is greater than 100.

Step 3: State the alpha level as 0.05 or 5%

Step 5: Calculate the test statistics using this formula

In this case, 2.99 > 1.645 so we reject the null.

## Importance/Benefits of Hypothesis Testing

- Hypothesis testing provides a reliable framework for making any data decisions for your population of interest.
- It helps the researcher to successfully extrapolate data from the sample to the larger population.
- Hypothesis testing allows the researcher to determine whether the data from the sample is statistically significant.
- Hypothesis testing is one of the most important processes for measuring the validity and reliability of outcomes in any systematic investigation.
- It helps to provide links to the underlying theory and specific research questions.

## Criticism and Limitations of Hypothesis Testing

- The interpretation of a p-value for observation depends on the stopping rule and definition of multiple comparisons. This makes it difficult to calculate since the stopping rule is subject to numerous interpretations, plus “multiple comparisons” are unavoidably ambiguous.
- Conceptual issues often arise in hypothesis testing, especially if the researcher merges Fisher and Neyman-Pearson’s methods which are conceptually distinct.
- In an attempt to focus on the statistical significance of the data, the researcher might ignore the estimation and confirmation by repeated experiments.
- Hypothesis testing can trigger publication bias, especially when it requires statistical significance as a criterion for publication.
- When used to detect whether a difference exists between groups, hypothesis testing can trigger absurd assumptions that affect the reliability of your observation.

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