Dear Dennis,
thank you for your fast response. Perhaps I should have described the
experimental situation in more detail.
> This tells you that Subject is being treated as a random block
> factor, and that
> Conditions 1 and 2 are combinations of treatments applied to each
> subject. In
> other words, this describes a randomized block design, so ordering
> in time is
> not represented in this model. Moreover, within-subject correlation
> due to the
> supposed repeated measures is not represented, either.
In each subject we perform one recording for every possible
combination of values of
both factors Condition1 and Condition2. Ordering in time is
not an issue here, because we do not want to study longitudinal
changes in
time. On the other hand, as each combination of the 2 conditions was
applied
in each subject within an experimental session, I thought this must
be analysed
with a repeated-measures approach.
As an example, the following lines show the beginning of a typical
result file for
the first 2 subjects A and B
Nr Subject Condition1 Condition2 Result
1 A C1a C2a 5.0000
2 A C1a C2b 3.0000
3 A C1b C2a 3.0000
4 A C1b C2b 3.0000
5 A C1c C2a 1.0000
6 A C1c C2b 4.0000
7 B C1a C2a 5.0000
8 B C1a C2b 4.0000
9 B C1b C2a 3.0000
10 B C1b C2b 2.0000
11 B C1c C2a 2.0000
12 B C1c C2b 3.0000
...
If this is a randomized block design, which is the best way to
analyse the effect of the
two factors Condition1 and Condition2 on Result? How to do post-hoc
tests to see whether
there significant differences, e. g., between C1a and C1b for
Condition1?
> ano <- aov(d$wPatternPulseSNR~ d$Bedingung*d$Felder + Error(d$VPerson/
> (d$Bedingung*d$Felder), data=d))
>
> Something seems amiss here, too. Where is the time element
> represented?
> Where is the correlation structure on the supposed repeated
> measures? I also
> think that you should have Person/Bedingung:Felder as the within-
> subject error
> term instead....
As mentioned above, there is no specific time element, but the
repeated measures
of the same type of result (here wPatternPulseSNR) under different
experimental
conditions (here d$Bedingung*d$Felder) should contain the correlation
structure.
As far as I understood the nomenclature, "Bedingung:Felder" means a
different
situation (split-plot) from the situation described above.
> It's entirely possible that the 'significance' seen in the above
> tests is due to
> an incorrect choice of error term. If Bedingung and Felder are
> both applied
> within-subject, then the appropriate error term should be the
> average within-person
> variance.
>
> A repeated measures design is structured rather similarly to a
> split-plot, except
> that in a RM design the within-subject observations are correlated
> in time and
> therefore the correlation can vary as a function of time - e.g., AR
> (1), where the
> correlation between observations decreases exponentially with the
> time gap
> between them. (In contrast, observations at the split-plot level
> are usually assumed
> to be equi-correlated due to randomization of levels of treatments
> within subjects.)
> In your case, there is no 'whole-plot/between subject' treatment -
> everything is at
> the within-subject level.
...
>
> I don't think you have the right model if this is indeed a repeated
> measures
> design, but I'll let others weigh in on the subject. As alluded to
> above, your
> model doesn't seem to represent the time element or the correlation
> structure
> that one would expect in a repeated measures design. I'd worry about
> getting the model right before proceeding to the multiple comparisons.
>
Hm, being not an expert in statistics I thank you very much for
advice and I agree that
the right model is essential. Perhaps my clarification of the data
might help to
fix this aspect. "Everything is at the within-subject level" this
is exactly true.
Thanks again
Thomas
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