Thanks a lot, Anderson. If I understand your new factor-effect model correctly it is identical to the one I proposed for the group with three levels, except that I: a) already included a demeaned covariate; b) used a different order of EVs; and c) did not describe the additional t-tests in case one wants to get cell means.
Wrt to the t-tests and F-tests you described: the t-tests seems to get the cell means of the three levels groups and the three slopes (of the covariate) in these three groups. However, I am not sure about the F-test. When using the factor-effect approach you usually only includes K-1 contrasts for the F-test. I want to be explicit about this because other users may use the information posted here as well.
So with your model (COV still needs to be demeaned first, and columns 4 and 5 updated accordingly):
A2-Mn A3-Mn Mean A2-Mn*COV A3-Mn*COV COV
-1 -1 1 -0.6299 -0.6299 0.6299
-1 -1 1 -0.032 -0.032 0.032
-1 -1 1 -0.6147 -0.6147 0.6147
-1 -1 1 -0.3624 -0.3624 0.3624
1 0 1 0.0495 0 0.0495
1 0 1 0.4896 0 0.4896
1 0 1 0.1925 0 0.1925
1 0 1 0.1231 0 0.1231
1 0 1 0.2055 0 0.2055
0 1 1 0 0.1465 0.1465
0 1 1 0 0.1891 0.1891
0 1 1 0 0.0427 0.0427
0 1 1 0 0.6352 0.6352
would it not be better to use the following t-tests (I have renumbered your t-test into C7..C12)?
C1: 1 0 0 0 0 0
C2: 0 1 0 0 0 0
C3: 0 0 1 0 0 0
C4: 0 0 0 1 0 0
C5: 0 0 0 0 1 0
C6: 0 0 0 0 0 1
C7: -1 -1 1 0 0 0
C8: 1 0 1 0 0 0
C9: 0 1 1 0 0 0
C10: 0 0 0 -1 -1 1
C11: 0 0 0 1 0 1
C12: 0 0 0 0 1 1
and the following F-tests?
F1-MainA 1 1 0 0 0 0 0 0 0 0 0 0
F2-MainCOV 0 0 0 0 0 1 0 0 0 0 0 0
F3-AxCOV 0 0 0 1 1 0 0 0 0 0 0 0
In addition, you indicated that the original two-group model was rank deficient even though I was using the factor-effects approach. Given that randomise did not complain about rank-deficiency of the two-group x covariate model mentioned earlier, I was wondering whether there is an easy way to determine whether a model is rank deficient (e.g. in SPSS or matlab)?
Thanks for your help!
Best, Henk
|