On 24 Sep 2000 23:30:57 -0700, [EMAIL PROTECTED] (Beng Hai Chea)
wrote:
> 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.
>
> 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.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
