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Topic: Need help understanding Homogeneity of Variance please
Replies: 3   Last Post: Oct 31, 2006 10:25 PM

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Richard Ulrich

Posts: 2,940
Registered: 12/13/04
Re: Need help understanding Homogeneity of Variance please
Posted: Oct 31, 2006 9:57 PM
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On 30 Oct 2006 21:26:03 -0800, "Reef Fish"
<> wrote:

> Richard Ulrich wrote:

> > On 30 Oct 2006 06:50:28 -0800, "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,

> > 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.

RU> >
> > 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]

RF >
> 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.

It is true that some violations are unmistakable.

I think it is untrue that this makes them inevitably more
serious. For larger N in all cells, the 2x2 phi has a test that
becomes increasingly identical to the test on the Pearson.
If the result is the test, what result is "wrong"?

On the other hand, for larger N and small associations, the
assumption of independence -- which may be hard to determine --
becomes increasingly important.

> 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,

- I'd judge, in the situation *above*, that definite non-normality
can be definitely not-serious. So there is often leeway.

> 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.

? What is the big difference? Formal reliance on the "right test"?

> >
> > 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.

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

RF >
> Or a different assumption may be appropriate, or both.

I'm not sure what the "both" should mean.

RU> >
> > 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.

RF >
> 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?

If you think that Logistic Regression might fit better than Normal
(Probit), you can test both ways. Same result? - no big problem.

Does an optional, debatable transformation give a different result?
If there is no difference, you can report that while reporting the
detailed result on either metric -- Showing that "It makes no
difference" is a way of finessing an overly-conservative demand
for "non-parametric" tests, in my experience.

When there *is* a different result for different analyses, then you
know that the assumptions *do* matter in a way -- and to an extent --
that needs to be explained.

> -- Reef Fish Bob.

RU > >
> > 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.
> >

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