Hi Henk,
Ok, back. Please, see below:
Am 26.02.14 08:02, schrieb H van Steenbergen:
> 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.
Should have been ok then, good!
>
> 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.
Yep. Sorry, I had added an extra row (actually, an extra column, as they
are transposed) to the F1 and F2. So, as I replied earlier today, the
correct F-tests should be:
F1:
1 0 0 0 0 0
0 1 0 0 0 0
F2:
0 0 0 1 0 0
0 0 0 0 1 0
> 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
Yep!
> 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
These look ok to me:
- If the MainA means group differences being all zero, yes, F1 is right.
If you'd like the overall mean, then it's the C3 that needs to be looked
at (and only C3).
- If the MainCOV means the overall effect of the covariate, yep, F2 is
good too. However, instead of an F-test, I'd just look at the C6, which
gives the direction.
- For the interaction, F3 is good too: it's going to test whether the
pairwise differences of the 3 possible interactions (Group1xCOV,
Group2xCOV, Group3xCOV) are all zero.
> 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)?
For simple designs that involve discrete regressors as this it's easy to
spot by visual inspection (in that example, EV3=EV4*EV2+EV5). When the
design is more complicated or with continuous regressors, things may not
be obvious, but the rank can be calculated in Matlab or Octave with the
function "rank".
Randomise doesn't complain about rank deficiency in either the matrix or
the contrast because it deals with it internally. However, it helps to
interpret the results later if all columns of the matrix and contrast
are unique when they are entered.
All the best,
Anderson
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