# Understanding test for equal variances

## What is test for equal variances?

Use a test for equal variances to test the equality of variances between populations or factor levels. Many statistical procedures, such as analysis of variance (ANOVA) and regression, assume that although different samples can come from populations with different means, they have the same variance.

Because the susceptibility of different procedures to unequal variances varies greatly, so does the need to do a test for equal variances. For example, ANOVA inferences are only slightly affected by inequality of variance if the model contains only fixed factors and has equal or almost equal sample sizes. Alternatively, ANOVA models with random effects and/or unequal sample sizes could be substantially affected.

For example, you plan to do an ANOVA testing the length of time callers are put on hold where the main fixed factor is the calling center. You use the ANOVA general linear model (GLM) because you have unequal sample sizes. Because this unbalanced condition increases the susceptibility to unequal variances, you decide to test the assumption of equal variances. If the resulting p-value is greater than adequate choices of alpha, you fail to reject the null hypothesis of the variances being equal. You can feel confident that the assumption of equal variances is being met.

For tests for equal variances, the hypotheses are:
• H0: All variances are equal
• H1: Not all variances are equal

## Which test should I base my conclusion on?

By default, Minitab's Test for Equal Variances command displays results for Levene's method and the multiple comparisons method. For most continuous distributions, both methods give you a type I error rate that is close to your specified significance level (also known as alpha or α). The multiple comparisons method is usually more powerful. If the p-value for the multiple comparisons method is significant, then you can use the summary plot to identify specific populations that have standard deviations that are different from each other. You should base your conclusions on the results for the multiple comparisons method, unless the following are true:
• Your samples have less than 20 observations each.
• The distribution for one or more of the populations is extremely skewed or has heavy tails. Compared to the normal distribution, a distribution with heavy tails has more data at its lower and upper ends.

When you have small samples from very skewed, or heavy-tailed distributions, the type I error rate for the multiple comparisons method can be higher than α. Under these conditions, if Levene's method gives you a smaller p-value than the multiple comparisons method, then you should base your conclusions on Levene's method. Otherwise, you can base your conclusions on the multiple comparisons method, but remember that your type I error rate is likely to be greater than α.

## The F-test and Barltett's test

Instead of the multiple comparisons method and Levene's method, you can choose to display results for the test based on the normal distribution. If you have only 2 groups or factor levels, then Minitab performs the F-test. If you have 3 or more groups or factor levels, then Minitab performs Bartlett's test.

The F-test and Bartlett's test are accurate only for normally distributed data. Any departure from normality can cause these tests to yield inaccurate results. However, if the data conform to the normal distribution, then the F-test and Bartlett's test are typically more powerful than either the multiple comparisons method or Levene's method.

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