The assumption of equal variances across treatment groups may cause serious problems if violated in one-way analysis of variance models. A common test for homogeneity of variances is Bartlett's test. This statistical test checks whether the variances from different groups (or samples) are equal.
Suppose that there are r treatment groups and we want to test
In this context, we assume that we have independently chosen random samples of size ni, i = 1, …, r from each of the r independent populations. Let be independently distributed with a normal distribution having mean μi and variance σ2i for each j = 1, …, ni and each i = 1, …, r. Let be the sample mean and S2i the sample variance of the sample taken ...
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