Re: Need help understanding Homogeneity of Variance please

Reef Fish wrote:
stats newbie wrote:
Hi, I was hoping someone would be able to explain the assumption of
homogeneity of variance. What is it and why should it be addressed?
What are the consequences of not having homogeneity of variance. I hope
I have posetd this in the correct group. Thanks,

That is a ASSUMPTION behind many different statistical methods.

In order for the results of each method to apply, one must make sure
that the ASSUMPTION(s) are valid, else the statistical results based
the method will be all wrong.

The homogeneity of variance is an assumption in these common
statistical methods:

Most regression methods that have i.i.d N(0, sigma^2) as the
assumption.
The errors all have the same variance.

The usual T-test of the equality of means of two independent
populations.
The variances of the populations are assumed to be the same,
though unknown. If that's violated, then the T-distribution
in
the test would not apply (an unsolved Behrens-Fisher problem).

The usual Tests of the equality of several population means (one
say ANOVA problems). The variances of the different
populaitons
are assumed the same, for the F test to apply.

There are many, many more assumptions like that.

That is WHY before one runs any particular statistical procesure, one
should VALIDATE that the underlying assumptions are not SERIOUSLY
violated. One can tolerate small deviations and that's the property
that is called "robustness" to certain types of violations.

-- Reef Fish Bob.



I'll just add that the independent groups t-test and between-Ss ANOVA are more robust to heterogeneity of variance when all of the sample sizes are equal. E.g., when all sample sizes are equal, one-way ANOVA is pretty robust provided the ratio of largest variance to smallest is no greater than 4 or 5. The more discrepant the sample sizes become, the more important it is to have homogeneous variances.

--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
.

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