Homoscedasticity is the property that the variances of a continuous variable is the same in different groups. I confess this is here more because it’s such a posh sounding word than because it’s terribly important! See variance if this is alien.
The only reason that homoscedasticity, and its complement, heteroscedasticity, matter is because many traditional statistical tests for differences of a continuous variable between groups, strictly tests of differences in the mean of the variable across the groups, assume homoscedasticity and can give misleading results, misleading p values, if the groups differ in their variances. For some tests, notably the t-test, there are simple corrections that handle heteroscedasticity, for some other tests things are less simple and it is actually moderately important if doing traditional inferential hypothesis testing that variances are checked and possible impact of differences considered. Perhaps fortunately, that approach is rightly losing its dominance in applied statistics and in the analysis of therapy data it is rarely the most helpful approach.
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