## About this lesson

## Exercise files

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Levene's Test & Mann-Whitney Test.xlsx10.6 KB Levene's Test & Mann-Whitney Test - Solution.docx

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## Quick reference

### Levene's Test & Mann-Whitney Test

Levene’s Test and Mann-Whitney Test are hypothesis tests used for testing two non-normal data samples. Levene’s Test checks the variance of the data sample and the Mann-Whitney Test checks the medians.

### When to use

These tests are used for non-normal data sets. They are appropriate for comparing the two sets to determine if there are statistically significant differences. This helps to identify root cause factors for problems and to demonstrate the impact of implemented solutions.

### Instructions

#### Levene’s Test

Levene’s Test is similar to the F Test or Bartlett’s Test that is used with normal data. The variance, or spread, of two sets of sample data are compared to determine if they are statistically different. The test can be set to check equality, greater than or less than relationships.

- Minitab:
- Stat > Basic Statistics > 2 Variances
- Select the columns with the data, the order matters if doing a greater than or less than relationship.
- Use the Option button to change the type of relationship to be tested – default is equal/not equal.
- Use the Option button to ensure that the normality box is not checked (checking the box will result in an F Test instead of Levene’s Test).

#### Mann-Whitney Test

The Mann-Whitney Test is similar to the Two-Sample T Test used with normal data. The primary difference is that Mann-Whitney uses the median value since it is the preferred measure for central tendency with non-normal data. The test can be to check for equal medians or to check whether one is greater than or less than the other.

- Minitab:
- Stat > Nonparametrics > Mann Whitney
- Select the format of the data
- Select the columns with the data
- Select the relationship to be tested (equals, greater than, less than)
- The results are shown in the Session Window. Minitab states the “the test is significant at .XXX” This is the P Value for the test.

### Hints & tips

- The Levene’s Test provides a box plot that makes the differences between the data samples very clear.
- Check your data for normality first. If normal, use the F Test and Two-Sample T Test, if non-normal, use these tests.
- A small number of data points has a tendency to result in variances and medians with large confidence intervals. This makes it more difficult to identify true differences.

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