🚀 go-pugleaf

Evan Cooch writes ...

>Suppose you want to do a simple analysis, say a single-classification
>anova. There are 5 levels of the classification variable. You do
>whatever homogeneity of variance/normality tests you subscribe to, and you
>find that the data is either/or heteroscedastic or non-normal.
>
>However, you also notice that no SINGLE transformation can be applied to
>all groups. I.E maybe x^2 works for data in one group, while log(x)
>works for another. Alternatively, the "best" Box-Cox transform differes
>among groups.
>
>Question: If you can't use the same transform for all your data, should
>          you transform at all?


A transformation is most importantly used to make the model additive in the
ANOVA.  In most cases, the homogeneity of variance assumption is met with
the same transformation.  If not, a nonparametric test can solve the
problem.  The designs for which a nonparametric test is available is
limit, however, so often another method must be used.  One such method is to
weight each group by an appropriate factor which is proportional to the
inverse of the group variance.  A better techique is a randomization test.
This test makes only the assumption that the data is from a random sample
and data are independent.  For more information see:

               Edgington (1987) Randomization Tests, 2nd Edition

I do not know of any software package that impliments this test without
involving programming.

Incidently, Fisher said "conclusions have no justification beyond the fact
that they agree with those which could have been arrived at by this
elementary method (randomization tests)." (Kempthorne, 1955)

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