Introduction to Equal Variance Assumption

Use of Equal Variance Assumption with ANOVA

The equal variance assumption is important in statistics because it applies to two of the most widely used tools, the two-sample t-test, and Analysis of Variance (ANOVA). Both of these tools are used to test whether there are differences in population means, based upon the evidence present in samples of data taken from the respective populations. Please continue reading to learn more about the Equal Variance Assumption, or EVA.

Since this assumption plays a prominent role when utilizing these popular tools, it is often suggested that tests be run to check on the validity of this assumption. When doing so, one should always keep in mind the following points:

1. Robustness when samples sizes are equal
Both the two-sample t-test and ANOVA are very robust to the equal variance assumption when the sample sizes are equal, or nearly equal.

2. Alternative procedures
The two-sample t-test can be used either with or without the assumption of equal variances. In fact, the default method in Minitab does not assume equal variances.

3. Data transformations
If the variances of the samples are correlated with the size of the data (as Y increases, the variance of Y increases), it may be possible to use a log transformation (or the Box-Cox power transformation) to correct the problem.

4. The effects of unequal variances
In all cases, unequal variances affect the overall estimate of the error variance. This in turn affects the corresponding t or F statistics, which in turn affects the reported p-values. The p-value (probability of making a Type I error) is underestimated when the assumption of equal variances is violated. In other words, the true p-value is somewhat larger than the reported p-value.