Question

How can testing the assumption of different variances enable us to address the impact of one variable on the other better than just assuming the one variance?

Answer 1

If we are comparing the mean difference between two or more sample means (a t-test or one-way ANOVA), we always check the assumption of homogeinity of variances i.e the variances of the groups are equal. This is done because if one of the groups has a significantly large variance as compared to the other group, this would lead to overshadowing of the differences in the mean and hence we will not be able to ascertain the true mean difference due to the same. Serious repurcussions in scientific reearch can occur and lead to incorrect conclusions. It affects the Type-I error rate and can lead to more number of false positives. It can lead to the null hypothesis being incorrectly rejected or an increase in the Type 1 error rate. Hence, the assumption of equal variances is done to check the same.