R: st: R: anova account for the same individuals

["Carlo Lazzaro" <carlo.lazzaro@tiscalinet.it>]

Dear David,
thanks a lot for your clear explanations.
I am not familiar with - xtmixed - (now I see why you recommend this approach) , so it did not spring to my mind as a solution for Liling's problem.
I suggested replacing group with a categorical variable (say, 0 for male and 1 for female) with MANOVA because the code:
......................................................................................................
manova rate*=group 

returns: 
error matrix not positive definite
insufficient residual degrees of freedom for this multivariate model
r(506);
......................................................................................................

whereas it works after the abovementioned replacement.

Best regards,
Carlo
-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di David Hoaglin
Inviato: giovedì 21 novembre 2013 13:41
A: statalist@hsphsun2.harvard.edu
Oggetto: Re: st: R: anova account for the same individuals

Dear Carlo,

The analysis needs to take into account that each ad is rated by the same people.  A one-way ANOVA does not do that, because it accounts for only one of the two factors.

Suppose Liling had 2 ads instead of 8.  Then we could compare the scores for the ads by using a paired t-test.  That is, a one-sample t-test on the within-person differences, (Score on Ad 2) - (Score on Ad 1).  The idea is to remove variation among persons from the comparison of the ads.

In the data that you constructed, I interpret "group did not reach statistical significance" as meaning that the effects of the 54 levels of group did not differ significantly from zero. Those effects, however, are averages over the 8 levels of number.  The effects of number are averages over the 54 levels of group, so the (additive) effect of group has been removed from them; but the standard errors for those effects need to reflect the fact that they come from repeated measures.  One approach to repeated measures views the analysis as MANOVA.  I don't understand why it would be necessary to introduce an additional categorical variable, which might be a factor or a covariate, depending on the design.  It should be possible to analyze the date by using -xtmixed- with a random intercept for group.

David Hoaglin

On Thu, Nov 21, 2013 at 2:54 AM, Carlo Lazzaro <carlo.lazzaro@tiscalinet.it> wrote:
> Dear David,
> Thanks for your remark. I see your point.
> Does it hold even though the IV group does not reach statistical significance in two-way ANOVA (as it occurred in my fictitious code)?
> I would also consider MANOVA for Liling's example, provided that the IV group can be divided (say) in two categorical variables (eg, male and female).
>
> Kind regards,
> Carlo
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