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## 7.3: The Research Hypothesis and the Null Hypothesis

Hypotheses are predictions of expected findings.

## The Research Hypothesis

- The name of the groups being compared. This is sometimes considered the IV.
- What was measured. This is the DV.
- Which group are we predicting will have the higher mean.

## Directional Research Hypothesis

- Symbol: \( \displaystyle \bar{X} > \mu \)
- (The mean of the sample is greater than than the mean of the population.)
- Symbol: \( \displaystyle \bar{X} < \mu \)
- (The mean of the sample is less than than mean of the population.)

Answer in Symbols: \( \displaystyle \bar{X} > \mu \)

## Non-Directional Research Hypothesis

Answer in Symbols: \( \displaystyle \bar{X} \neq \mu \)

## The Null Hypothesis

\[\mathrm{H}_{0}: \bar{X} = \mu \nonumber \]

In sum, the null hypothesis is always : There is no difference between the groups’ means OR There is no relationship between the variables .

- There is no mean difference between the sample and population.
- The mean of the sample is the same as the mean of a specific population.
- \(\mathrm{H}_{0}: \bar{X} = \mu \nonumber \)
- We expect our sample’s mean to be same as the population mean.

Answer in Symbols: \( \bar{X} = \mu \)

## Contributors and Attributions

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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

## What can proofreading do for your paper?

- 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 February 28, 2023, from https://www.scribbr.com/statistics/hypothesis-testing/

## Is this article helpful?

## Rebecca Bevans

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## AP®︎/College Statistics

## Examples of null and alternative hypotheses

- P-values and significance tests
- Comparing P-values to different significance levels
- Estimating a P-value from a simulation
- Using P-values to make conclusions

## Want to join the conversation?

## Video transcript

## 13.1 Understanding Null Hypothesis Testing

- Explain the purpose of null hypothesis testing, including the role of sampling error.
- Describe the basic logic of null hypothesis testing.
- Describe the role of relationship strength and sample size in determining statistical significance and make reasonable judgments about statistical significance based on these two factors.

## The Purpose of Null Hypothesis Testing

In fact, any statistical relationship in a sample can be interpreted in two ways:

- There is a relationship in the population, and the relationship in the sample reflects this.
- There is no relationship in the population, and the relationship in the sample reflects only sampling error.

## The Logic of Null Hypothesis Testing

- Assume for the moment that the null hypothesis is true. There is no relationship between the variables in the population.
- Determine how likely the sample relationship would be if the null hypothesis were true.
- If the sample relationship would be extremely unlikely, then reject the null hypothesis in favor of the alternative hypothesis. If it would not be extremely unlikely, then retain the null hypothesis .

## The Misunderstood p Value

“Null Hypothesis” retrieved from http://imgs.xkcd.com/comics/null_hypothesis.png (CC-BY-NC 2.5)

## Role of Sample Size and Relationship Strength

## Statistical Significance Versus Practical Significance

“Conditional Risk” retrieved from http://imgs.xkcd.com/comics/conditional_risk.png (CC-BY-NC 2.5)

## Key Takeaways

- Null hypothesis testing is a formal approach to deciding whether a statistical relationship in a sample reflects a real relationship in the population or is just due to chance.
- The logic of null hypothesis testing involves assuming that the null hypothesis is true, finding how likely the sample result would be if this assumption were correct, and then making a decision. If the sample result would be unlikely if the null hypothesis were true, then it is rejected in favor of the alternative hypothesis. If it would not be unlikely, then the null hypothesis is retained.
- The probability of obtaining the sample result if the null hypothesis were true (the p value) is based on two considerations: relationship strength and sample size. Reasonable judgments about whether a sample relationship is statistically significant can often be made by quickly considering these two factors.
- Statistical significance is not the same as relationship strength or importance. Even weak relationships can be statistically significant if the sample size is large enough. It is important to consider relationship strength and the practical significance of a result in addition to its statistical significance.
- Discussion: Imagine a study showing that people who eat more broccoli tend to be happier. Explain for someone who knows nothing about statistics why the researchers would conduct a null hypothesis test.
- The correlation between two variables is r = −.78 based on a sample size of 137.
- The mean score on a psychological characteristic for women is 25 ( SD = 5) and the mean score for men is 24 ( SD = 5). There were 12 women and 10 men in this study.
- In a memory experiment, the mean number of items recalled by the 40 participants in Condition A was 0.50 standard deviations greater than the mean number recalled by the 40 participants in Condition B.
- In another memory experiment, the mean scores for participants in Condition A and Condition B came out exactly the same!
- A student finds a correlation of r = .04 between the number of units the students in his research methods class are taking and the students’ level of stress.
- Cohen, J. (1994). The world is round: p < .05. American Psychologist, 49 , 997–1003. ↵
- Hyde, J. S. (2007). New directions in the study of gender similarities and differences. Current Directions in Psychological Science, 16 , 259–263. ↵

## IMAGES

## VIDEO

## COMMENTS

A research hypothesis is a mathematical way of stating a research question. A research hypothesis names the groups (we'll start with a sample and a population), what was measured, and which we think will have a higher mean. The last one gives the research hypothesis a direction.

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.

The null and alternative hypotheses are both statements about the population that you are studying. The null hypothesis is often stated as the assumption that there is no change, no difference between two groups, or no relationship between two variables.

One interpretation is called the null hypothesis (often symbolized H0 and read as “H-naught”). This is the idea that there is no relationship in the population and that the relationship in the sample reflects only sampling error. Informally, the null hypothesis is that the sample relationship “occurred by chance.”