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I'd like to compare, in a within subject design, the dispersion of two conditions. At first I thought about taking the standard deviation by individual and condition, and compute a paired $t$-test on these values comparing conditions.

However I'm not sure about the validity of this method, so I'd like to know which measure you would take at the individual level, and which test you would run on it at the group level.

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  • $\begingroup$ Why would you want to test for this if you could? $\endgroup$ Jul 20, 2014 at 14:14
  • $\begingroup$ Just to clarify - your desired test is for equality of variances (standard deviations) between two groups? $\endgroup$
    – jbowman
    Jul 20, 2014 at 15:20

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There is no such thing as heteroscedasticity / heterogeneity of variance in a two condition within-subjects experiment. In such a situation, what the within-subjects $t$-test actually does is convert each subject's two observed values into a single difference and run a one-sample $t$-test on those differences. There cannot be heteroscedasticity in a one-sample $t$-test, and there is no need to try to check for it to validate your assumptions.

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