in my view, planned contrasts can be very important. i actually do
teach them in an ANOVA course, but my sense is that this is not
typical.
if we have, say, a 1x4 ANOVA, the between groups df is 3. this means
that there are three independent contrasts one could define that will
partition the sums of squares between groups. this concept can lead
to trend analyses - given an appropriate independent variable - where
we could get the sums of squares for a linear, quadratic or cubic
component.
if i had a 1x4 and was only interested in whether group 1 was
different from the mean of the other three groups, i could plan that
contrast, get its sums of squares and test it using my within groups
mean square. in this case, i would never do the overall F test, since
i am not "interested" in all the other contrasts that are imbedded in
the test of the null hypothesis.
from linear combinations, plus some constraints, the sums of squares
of a contrast (equal n per group) is:
n*(value of the contrast)**2/(sum of squared weights assigned to
each group).
so if we want to compare group 1 against the mean of groups 2,3 and 4:
the weights are 1 (group 1) and -1/3 (for each of groups 2,3 and
4). the weights must sum to 0.
use these weights with the sample means to get the value of the
contrast, plug in the value of n and the sum of the squared weights,
1.33 in this case, and you are done. you can test that this is 0 in
the population using F with 1 and error degrees of freedom. you will
notice that if the mean of group 1 is the same as the mean of the
other three group means, the value of the contrast is 0 as is its sums
of squares. also since the contrast has 1 degree of freedom, the sums
of squares and the mean square are the same.
hope this helps.
[EMAIL PROTECTED] (wuzzy) wrote in message
news:<[EMAIL PROTECTED]>...
> Has anyone come across an intro on planned contrasts.
> I suppose a background in algebra is required to teach vector-space
> contrasts. I've also seen multiple regression taught in terms of
> vector-space and matrix algebra. Are contrasts considered important
> to teach for experimental design,
> any recommended texts? eg., the argument could be made that omnibus
> tests are sufficient.
> Usually I don't see the term "planned contrast" in non-statistical
> literature, maybe I just haven't been aware of it.
> -wuzzy
.
.
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