Testing for changes in variance following an intervention

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?

• Welcome to our site! We are trying to build a repository of statistical questions and answers that will be read for many years to come, so there's no need to put "good evening" at the start or "thanks in advance" at the end. I have given your text a brief copyedit, please feel free to revert any changes you disagree with – Silverfish Aug 13 '16 at 19:14

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.