Importance of homogenity of variance

[thrillhouse86]

Hey all,

When performing parametric statistical tests (especially t tests and ANOVA), why is the homogenity of variance important ?

I mean why do these tests care if the samples have significantly different variance ? Is it because the methods used to determine the test statistics require the same variances, or to interpret the results of these test statistics you need to assume the same variance for samples ?

Regards,
Thrillhouse

 

[statdad]

The formulas for the estimates, margins of error, and distributions of estimates and test statistics are based on the homogeneity of variances. Think about the two-sample mean problem, when we assume normality but different variances. The t-statistic is still used, with an awkward formula for df, but that's just an empirical approximation. things are more involved for more than two samples (ANOVA setting). same idea for regression.

 

[thrillhouse86]

Thanks Statdad