> > I have a very basic ANOVA question regarding transformed variable.
> >
> > Example: I have 6 different types of habitats and I have obtained 25
> > readings from each of the different type of habitats. After doing the
>ANOVA
> > procedure, I discovered that non-constant error variance is present.
> >
> > Thus, I would need to transform the readings with natural log to be able
>to
> > use the ANOVA procedure.
>
> - Well, "need to transform" is your conclusion, from some sort of
>evidence. Directly, the conclusion is that the test is not efficient
>since the error is not i.i.d. (identical and independently
>distributed). This also hints that the additive ANOVA model is not
>adequate.
Yes, you are right. The additive ANOVA model is not adequate since the
residual vs. fitted plot is not showing normality and the error variance is
non-constant. After the log transformation, the residual plots and error
variance are OK. I guess I just followed the guideline on what steps to take
if the data does not meet the ANOVA model adequacy checks. This is mentioned
in almost all the books I read but, none mentioned about the hypothesis
validity at all. That's why this question came about.
> >
> > Question: After transformation, does any of the hypothesis regarding the
> > original variable still holds, using the latest ANOVA procedure?
> >
> > If it still holds, may I know what is the rationale?
> >
>If there is no difference between groups, there's no difference.
>
>How different is it, to test the (a) in y=ax+b or log(y)= ax+b?
>
>Well, how much does it distort the scaling of y, to take the log? -
>that is how much the one test is a distortion of the other test.
>
>
> > If it does not hold, why then bother on transforming the readings
>variable
> > in the first place?
>
> - Hey, that was your idea.... presumably, to get a 'better test'.
>
>This happens when a transformation "fixes the ANOVA" but
>is hard to justify in simple, logical terms: we are faced with
>a good test of a somewhat-wrong hypothesis, or an inferior
>test of the right hypothesis.
>
>You have to listen to arguments for both sides. But you won't settle
>it until you learn (maybe) that one test works better in the long run,
>for similar instances, and consistent with larger samples.
Yes, would like to hear from both sides of the argument based on practical
experience. Any one out there had similar situation/problem?
Regards,
Beng Hai
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