Re: Testing the effects of multiple terms in a two- / three-way ANOVA

On Feb 27, 6:16 pm, Bruce Weaver <bwea...@xxxxxxxxxxxx> wrote:
madhu.balasubraman...@xxxxxxxxx wrote:
Hi:

Could someone clarrify me how to setup the Mean squares terms for
simultaneously testing the effects of multiple factors / terms in a
two- / three-way ANOVA? To be very specific, consider the model:
y_ijk = mu + alpha_i + beta_j + gamma_k + <alpha><beta>_ij +
<alpha><gamma>_ik + eps_ijk

If I want to simultaneously test the effects / significance of the
terms beta and <alpha><beta> in the model, how do I construct the
numerator term for an F-statistic? I wondering whether to use 1)
[SOS(<beta>) + SOS(<alpha><beta>)] / [DF(<beta>) + DF(<alpha><beta>)]
or 2) [SOS(<beta>) / DF(<beta>) + SOS(<alpha><beta>) /
DF(<alpha><beta>)], where SOS - sum of squares, DF - degrees of
freedom. It will be very useful if you can clarrify their differences
or their validity as well.

Thank you very much.

Madhu.

In ANOVA/regression, it is the sums of squares (and degrees of freedom)
that are partitioned. So use your first option.

--
Bruce Weaver
bwea...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx/wv/bwhomedir- Hide quoted text -

- Show quoted text -

Thanks very much for your reply. Thinking about it, option 2)
[SOS(<beta>) / DF(<beta>) + SOS(<alpha><beta>) / DF(<alpha><beta>)],
is not at all a mean, just sum of two means. By the way, what do you
mean by 'partitioned'.

.

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