On 19 Jun 2000 18:01:28 -0700, [EMAIL PROTECTED] (D�nal Murtagh) wrote:
< ... >
> Firstly, thank you for your comments. Am I right in saying that the two
> (equivalent) options I have are:
These are not quite equivalent options since the first one really
stinks -- If you are considering drawing conclusions about causation,
you need *random assignment* and the two Groups of performance are the
furthest thing from random.
Let's see: the simple notion of regression-to-the-mean says that the
Best performers should fall back, the Worst performers should improve;
that's a weird main-effect, which should wreak havoc with interpreting
other effects.
Or: If the Pre is powerful enough to measure potential, then a
continued-growth model says that Best performers should improve more,
even given no treatments.
For simple change-scores (and ANOVA interactions) from dichotomous
groups, you assume that neither of those possibilities are true, if
you want to be able to interpret them.
The Regression model at least places the contrasts into the realm
of comparing the regression lines. Your fundamental knowledge
of what is happening will probably come from examining and comparing
the scatterplots, pre-post, for the two treatments. (Another thing to
note from the picture: Are there ceiling/basement effects on the
performance test?)
> 1. ANOVA
>
> Yijk = mew + Ai + Bj + ABij + Eijk
>
> Ai: a fixed factor representing the treatments (2 levels)
> Bj: a fixed factor representing prior perfromance (2 levels)
> ABij: an interaction between Ai and Bj
> Yijk: the score of the kth child who received treatment i and is from group j
> Eijk: random error
>
> I suspect that this model is inapporpriate, as the Eijk term will represent
> between subjects (children) variation, which is not usually included in the
> estimate of random error.
>
> 2. MLR
>
> Y = Bo + B1*X1 + B2*X2 + B3*X3 + E
>
> X1: prior performance (0 => weak, 1 => strong)
> X2: treatment (0 => treament A, 1 => treatment B)
> X3: treatment*prior performance
>
> I appreciate that prior performance is probably better considered as a
> continuum, rather than a dichotomy.
>
- Treating it as a continuum is better by a lot, even if you were
sure that the Performance scale
was close to the ANOVA-analytic ideal, a normal distribution.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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