# Homogeneity of variance hypothesis test

A hypothesis test formally tests if the populations have equal variances.

Many statistical hypothesis tests and estimators of effect size assume that the variances of the populations are equal. This assumption allows the variances of each group to be pooled together to provide a better estimate of the population variance. A better estimate of the variance increases the statistical power of the test meaning you can use a smaller sample size to detect the same difference, or detect smaller differences and make sharper inferences with the same sample size.

The hypotheses to test depends on the number of samples:
• For two samples, the null hypothesis states that the ratio of the variances of the populations is equal to a hypothesized value (usually 1 indicating equality), against the alternative hypothesis that it is not equal to (or less than, or greater than) the hypothesized value.
• For more than two samples, the null hypothesis states that the variances of the populations are equal, against the alternative hypothesis that at least one population variance is different.

When the test p-value is small, you can reject the null hypothesis and conclude that the populations differ in variance.

Published 8-Jan-2017
Version 4.90