Re: comparing one group against "total" mean

On Jul 11, 10:16 pm, datamat...@xxxxxxxxx wrote:
I am not sure I follow this thread. Does this assume balanced
designs? If most of the data comes from one group, which is the group
in question, then the overall mean is essentially the mean of said
group. So you'd expect to see no difference. But there could be
difference between this group and the other groups, it seems.

DM
If there are two groups -- which, rightly or wrongly, is how I read
the OP -- then either both groups have the same mean, in which case
both means equal the grand mean; or one group mean differs from the
other, in which case both means differ from the grand mean, in
opposite directions. That much is simple algebra.

If there are more than two groups, then the same argument holds, but
with the mean of group 2, say, being replaced by the mean of the means
of groups 2,...,K. However, if the mean of group 1 equals the mean of
the means of the other groups, then the mean of group 1 could (but
need not) equal each of the means of the other groups; and if the mean
of group 1 differs from the mean of the means of the other groups,
then the mean of group 1 must differ from the mean of at least one of
the other groups.

.

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