Under what condition(s) do I need to test for homoscedasticity (i.e. using the Levene's test)? Is this only for repeated-measure designs or do I need to test for this in independent designs as well?
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$\begingroup$ This may be worth your time (at least read the abstract) $\endgroup$– Glen_bJan 1, 2014 at 2:07
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1$\begingroup$ This also. These links relate to t-tests, but the points carry over. Avoiding the question of hypothesis testing of assumptions for a moment, you rely on the assumption of constant variance when you compute standard errors, p-values or confidence/prediction intervals via the usual normal-theory procedures. $\endgroup$– Glen_bJan 1, 2014 at 2:13
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Generally, you should try to be conscious of the assumptions of any analysis you wish to perform. If homoscedasticity is among these assumptions, you should probably test it.
Homoscedasticity is not only an assumption in repeated measures designs. For example, linear regression assumes homoscedasticity, but does not necessarily entail repeated measures.