I have a simple within subject design: I measure my variable (time point A), then do an intervention and measure the same variable afterwards once again (time point B) - my subjects are of course the same. I suggest that the variance decreases due to the intervention - Var(A)>Var(B).

My problem is, that I struggle to find an appropriate procedure to test if the change is significant or not. I can´t use the Levene-test or the F-Test, because they can only be used for independent variables (right?).

So: Does anybody know a suitable test similar to the e.g. Levene-test for this kind of design? Or, can I simply use 2 confidence intervals?

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You want Pitman's test. Form two new variables: $S = A + B$ and $D = A - B$ to use your notation. The compute Pearson's correlation $r$ between them in the usual way. Then the test of $r = 0$ is the test that the variances are equal.


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