Re: Need help understanding Homogeneity of Variance please


Richard Ulrich wrote:
On 30 Oct 2006 06:50:28 -0800, "Reef Fish"
<large_nassua_grouper@xxxxxxxxx> 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,
RF >
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.

I would prefer to say, "the method *may* be all wrong," and I think
that RF expresses that more relaxed idea in his closing comments,
where some violations are more serious than others ....
[snip, some detail]

BUt those are TWO DIFFERENT sets of statements.

In the above, it means If the ASSUMPTION(s) are NOT valid, then
the statistical results based on the method WILL be all wrong.
There is no "may be" about it. If you have two binary variables
X and Y and you test its correlation with the test statistic T for
the Pearson correlation coefficient (which would be phi for the
two binary variables), the result WILL be wrong because the
assumption is violated 100%, without question.

In the situation below, it's about the VALIDATION of the assumption.
If Normality is required of a variable, and it is not known 100% to be
nonnormal, then there is leeway in deciding what is a serious
violation and what is not, because in that case (unlike the case it
does not require any thinking to know that the (0,1) variable is
NOT normal) the DATA can never prove with 100% certainty
whether it came from a Normal population or not.

There is a BIG difference in the above two situations.

RF >
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.


A apparent violation of assumptions gives you a *warning* that
some other method might be more appropriate.

Or a different assumption may be appropriate, or both.

The violation gives you the immediate problem that the
p-values may be wrong, in the sense that a "more appropriate"
analysis would give something rather different. If you have a
choice of two analyses, the easy cross-check is to see if they differ.

And how do you conclude (if they differ) in your "cross-check"
what is correct and what isn't? And what do you mean by
cross-check?

-- Reef Fish Bob.


The "neat" solution to "failed assumptions" occurs when one solution
fixes all the apparent violations -- such as, when one transformation
provides linearity, homogeneity of variance, normality (of the
variable, or especially, of the residuals), and an "interval" scale of
measurement. - Otherwise, you might have to invent a new
analysis, or trying to weigh the importance of different violations.



--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html

.

Relevant Pages

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