[From Bruce Abbott (971204.0945 EST)]
Rick Marken (971203.2215) --
Bruce Abbott (971202.1045 EST)
If all the people are affected differently, then whatever average
effect is shown by the group-based method will be weak and certainly >
not the sort of thing that shows sufficient regularity (under the
conditions studied) to be worth additional effort. It is quite easy
to see which case you have if you are using the right kind of
group-based design (repeated measures).
I have already set up a spreadsheet, using a repeated measures
design, showing that this is not true.
Oh god, not again.
Each person in the group
was affected differently by the IV (the people were S-R devices
like those assumed by this methodology), some linearly, some
non-linearly (and often non-monotonicly) and some not at all.
But the result is a highly significant group effect that
"resembles" the effect seen for some subjects. I'd show you
the results but, as Bill said, it's probably better if you try
to do it yourself.
I have already stated that the average trend across individuals need not
resemble _any_ of the trends within individuals. (See Murray Sidman's
_Tactics of Scientific Research_, 1960.) But if you will look at your
spreadsheet data, you will find that they include the trend data for each
individual, which you can check for consistency against the group means.
You forget that there is no way for the person
doing the group research to know that this is a case that "works"
(where the group results reflect the results for each individual)
except by examining each individual case -- in which case the
"group" approach is moot; the researcher is studying subjects
on an individual basis.
A repeated measures design is an individual subject design replicated as
many times as there are subjects. Nothing precludes the investigator from
examining the data for each individual separately, and large differences in
the trends of individual subjects would show up as a large error term within
the ANOVA, as well as big standard errors around at least some of the