Considerations for the Equal Variance Assumption
The use of statistical tools does not follow some exact cookbook. By their very nature, there is always an element of error associated with these tools. The same is true about the assumption of equal variances. Since the Y variable for both the two-sample t-test and ANOVA is the same for all samples, it is not likely that the variances will differ greatly from one sample to another. On the other hand, since one of the goals of a good project is to reduce the variation in Y, extreme differences in variability should be studied to determine why they occurred. It is not uncommon to observe that the variance of Y increases as the mean of Y increases, a condition that can be easily remedied with a data transformation. So, when assessing the validity of the equal variances assumption, keep in mind the points outlined earlier:
1. Robustness when samples sizes are equal.
2. Alternative procedures.
3. Data transformations.
4. The effects of unequal variances.
5. Parametric tests vs non-parametric tests.
6. Changes in variation can be desirable.