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## Quick reference

### Variance Tests

The variance of a data set is the standard deviation squared (σ2). The F Test and Bartlett’s test compare the variance between sample sets to determine if they are statistically different.

### When to use

Two or more sample sets of data are often compared to determine if they are statistically equivalent. The answer to that question can help to identify cause and effect relationships in performance differences and to demonstrate before/after changes in performance. In order to test for similar means, a test for similar variances must first be done.

### Instructions

Variance tests are normally coupled with a test of means to determine whether two or more samples are statistically different. There may be cases where the hypothesis test is limited to only the variance of the samples but that is rare. The variance, which is the standard deviation squared, is a measure of the width of the data distribution in the sample. Even though variances may not be equal, additional hypothesis tests for mean values are often used in Lean Six Sigma projects. However, the statistical algorithms for those tests will change depending upon whether the variances are equal or not. For that reason, the primary use of this test is to set up the next tests, either T Tests or ANOVA.

The F Test is used when comparing two samples. The Bartlett’s test is used when comparing two or more samples. Normally the F Test is used as a precursor for the T Tests. The Bartlett’s Test is used as a precursor for the ANOVA.

- Excel is able to perform the F Test but not the Bartlett’s Test.
- Data Analysis Menu > F Test Two Sample for Variance
- Enter the range of each of the sample data sets.
- The calculation will provide a P Value for a one-tail analysis; reverse the order of the range of cells that are entered into the F Test dialog panel to check both tails.

- Minitab is able to perform the F Test.
- Stat > Basic Statistics > 2 Variances
- Select the format of the data and select the columns
- Select the option button to check the box for normal data and enter the relationship (equal to, greater than, or less than)

- Minitab is able to perform the Bartlett’s Test.
- Stat > ANOVA > Test for Equal Variances
- Select the format of the data and select the columns
- Select the option button to check the box for normal data and enter the relationship (equal to, greater than, or less than)

### Hints & tips

- Make sure you select the correct relationship of variances: equal to, greater than, or less than. Excel will only check “greater than” but the order of data sets you enter will determine which tail the test is checking.
- The F Test and Bartlett’s Test are used with normal data. We will use a different test for non-normal data.

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