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?