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

On Mar 2, 12:12 pm, Bruce Weaver <bwea...@xxxxxxxxxxxx> wrote:
madhu.balasubraman...@xxxxxxxxx wrote:

- 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'.

I thought this terminology was pretty standard across disciplines.
Perhaps I can explain by example. Here is a partitioning diagram for
the sums of squares in a one-way ANOVA.

SS(Total)
/ \
/ \
/ \
SS(Between-groups) SS(Within-groups)

SS(Total) is partitioned into SS(Between-groups) and SS(Within-groups).
Or putting it another way,

SS(Total) = SS(Between-groups) + SS(Within-groups)

You could do a similar partitioning diagram for the total degrees of
freedom by substituting df for SS.

In a partitioning diagram for a (balanced) two-way ANOVA, I would change
"groups" to "cells", and then further partition SS(Between-cells) into
SS(A), SS(B), and SS(AxB).

--
Bruce Weaver
bwea...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx/wv/bwhomedir

Thank you so much for the explanation!

.