# 2-Sample Hypothesis Test

Use 2-sample hypothesis tests to compare two samples with each other.

To add output from a 2-sample hypothesis test, go to Add and complete a form.

## 2 proportions

Use a 2 proportions test to determine whether the population proportions of two groups differ. You can also calculate a range of values that is likely to include the difference between the population proportions.

For example, you can test whether the process proportion defective is the same before and after a change has been made to the process. To see an example, go to Minitab Help: Example of 2 Proportions.

### Data considerations

Your data must contain only two categories, such as pass/fail. For more details, go to Minitab Help: Data considerations for 2 Proportions.

## 2-sample t

Use a 2-sample t-test to determine whether the population means of two groups differ. You can also calculate a range of values that is likely to include the difference between the population means.

For example, you can test whether the process mean is the same before and after a change has been made to the process. To see an example, go to Minitab Help: Example of 2-Sample t.

### Data considerations

Your data must be continuous values for Y (output). The sample data should not be severely skewed, and each sample size should be greater than 15. For more details, go to Minitab Help: Data considerations for 2-Sample t.

## Mann-Whitney

Use a Mann-Whitney test to determine whether the population medians of two groups differ. You can also calculate a range of values that is likely to include the difference between the population medians.

This test is an alternative to the 2-sample t-test and is used when the data from the two samples are not reasonably normal.

For example, a consultant compares the payrolls of two companies to determine whether their median salaries differ. If the medians from the two companies are different, the consultant uses the confidence interval to determine whether the difference is practically significant. To see an example, go to Minitab Help: Example of Mann-Whitney.

### Data considerations

The populations of each sample must have the same shape and spread. The data do not need to be normally distributed. However, if you have more than 15 observations in each sample or your data are not severely skewed, use a 2-Sample t-test because the test has more power. For more details, go to Minitab Help: Data considerations for Mann-Whitney.

## Paired t

Use a paired t-test to determine whether the mean of the differences between two paired samples differs from 0 or a target value. You can also calculate a range of values that is likely to include the population mean of the differences.

The paired t-test is useful for analyzing the same set of items that were measured under two different conditions, differences in measurements made on the same subject before and after a treatment, or differences between two treatments given to the same subject.

For example, a physiologist wants to determine whether a particular fitness program has an effect on resting heart rate. The heart rates of 15 randomly selected people were measured prior the program and then measured again one year later. Therefore, the before and after measurements for each person are a pair of observations. To see an example, go to Minitab Help: Example of Paired t.

### Data considerations

Your data must be continuous values for Y (output). You should have a set of paired (dependent) observations, such as measurements made on the same item under different conditions. For more details, go to Minitab Help: Data considerations for Paired t.

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