Re: st: My ANOVA and regression results don't agree

[David Hoaglin <dchoaglin@gmail.com>]

Phil,

I agree with your focus on the difference between the dummy-variable
coding in the regressions and the decomposition in the ANOVA.  I don't
recall seeing in Jess's messages, however, that her data are balanced.

When the data are not balanced, the contributions of the factors
depend on the order in which they enter the ANOVA model, as generally
happens with predictors in regression models.  If Jess's are balanced,
she doesn't have to face that complication in relating the results of
the ANOVA to the corresponding regression results.

David Hoaglin


On Tue, Jan 7, 2014 at 6:54 AM, Phil Schumm <pschumm@uchicago.edu> wrote:
> On Jan 6, 2014, at 8:59 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
>> Doesn't the ANOVA of those systolic data have some features of regression, because of the imbalance (18 observations in 4 cells)?  In the Partial SS column, sum of the SS for drug, disease, and drug#disease is less than the SS for the model.
>
>
> David,
>
> I'm not sure I understand your question (sorry).  It's true that the example I gave was unbalanced, and that therefore the main effects are not orthogonal; moreover, interpreting them requires care.  That said, I interpreted the original question as having to do with the difference between so-called dummy variable coding and the deviations from the (balanced) grand mean.  The question of how to interpret the latter in the unbalanced case and/or in the presence of interaction is a separate issue, though certainly important.  Perhaps I should have commented on this too.
>
> If you see another issue that I am missing here, please let me know.
>
> Thanks,
>
> -- Phil

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