Hi
On 30 Jan 2004, JJ Diamond wrote:
> it seems to me that it's a repeated measure as the exact same people
> are responding to more than one condition. one can certainly break up
> the 3 degrees of freedom for "treatments" into the contrasts with one
> DF for each. but how does one break up the subjects X treatment
> interaction (DF=21) into separate error terms?
One way to think of this (and actually do it if so inclined) is
to compute scores for each subject for each effect using the
appropriate contrast coefficients. To illustrate, use the
following coefficients to compute three scores (A, B, AB) for
each subject, with A = -1*A1B1 + -1*A1B2 + +1*A2B1 + +1*A2B2, and
so on.
A1B1 A1B2 A2B1 A2B2
A -1 -1 +1 +1
B -1 +1 -1 +1
AxB +1 -1 -1 +1
Each of these new scores has a mean and a variance associated
with it. One can test whether each mean differs from 0 using the
respective variance. You can do either a t-test or an equivalent
F test for a single mean. These tests are equivalent to the ANOVA
effects for A, B, and A*B. Note for example, that each test will
have df = 8-1 = 7 in the denominator (and 1 in the numerator if
you choose the F-test approach).
If you want to fully reproduce the ANOVA, then you would need to
use normalized coefficients. To illustrate,
A -1/sqr(4) -1/sqr(4) +1/sqr(4) +1/sqr(4)
where 4 = -1^2 + -1^2 + +1^2 + +1^2
Using normalized coeffients allows you to directly obtain
SSeffect and SSerror for each of the effects.
Best wishes
Jim
============================================================================
James M. Clark (204) 786-9757
Department of Psychology (204) 774-4134 Fax
University of Winnipeg 4L05D
Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED]
CANADA http://www.uwinnipeg.ca/~clark
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