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

[David Hoaglin <dchoaglin@gmail.com>]

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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