Tests of equal variance

Which test should I base my conclusions 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 1 error rate that is close to your specified significance level (also known as alpha or a). 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 1 error rate for the multiple comparisons method can be higher than a. 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 1 error rate is likely to be greater than a.

Calculations for Levene's method and the multiple comparisons method

The computational method for Levene's test is based on the Brown and Forsythe modification of Levene's procedure. This method considers the distances of the observations from their sample median rather than their sample mean. Using the sample median makes the test more robust for smaller samples.

The comparison intervals for the multiple comparisons method are calculated using algorithms similar to the multiple comparisons method for the means proposed by Hochberg et. al. (1982).

The F-test and Bartlett'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.

For addition references, and complete reference information, choose Help > Help and refer to "Tests of Equal Variance" in the Help index.