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I have two dependent samples of data. Each sample contains N = 800 values (data points) and stem from the same human subjects, that is, sample one is the pre-experimental and sample two the post-experimental group of the same 800 subjects.

Aim: I am not interested in comparing the two groups’ mean for statistical significance, but their variance or, more generally, the distribution in sample one vs. sample two.

Question: I assume that a the Levene test (in case the samples are approximately normally distributed) or the Brown-Forsythe test (in case the samples lack normality) would be the right choice.

I am not interested in checking the data for parametric test assumptions (such as homogeneity of variance) because I would like to apply a t-Test later, but because I am interested in potentially different variances between both samples.

Are there better tests for my aim, or are the two suggested tests just fine in my case?

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    $\begingroup$ One classical example is the Pitman-Morgan test. Rand Wilcox discusses this test in this paper and proposes a robust alternative. $\endgroup$
    – COOLSerdash
    Commented Jul 19, 2023 at 18:33
  • $\begingroup$ Interesting, I never heard about the Pitman-Morgen test. I will check this one out. Thanks! $\endgroup$
    – Philipp
    Commented Jul 19, 2023 at 19:43

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