[Martin Taylor 971124 23:20]
Bill Powers (971124.0906 MST)]
You are actually arguing on my side and that of Richard Kennaway: there is
no way to determine the within-person relationship from the population
relationship. For persons with the same reference level, the relation
between reward and effort has a strongly negative slope; for the unsorted
data, the relation between reward and effort has a positive slope.
I've been arguing that it is true of this study, and would have been known
to be true of this study before the results were analyzed.
But _for that reason_ I am arguing that the study says nothing about
the results of other studies in which the group measure legitimately
does relate to the measures on individuals. For example, if one measures
the heights of a group of people and comes to the conclusion that
unknown mature individual X is probably not over 9ft tall, nor under
2 ft tall, one is justified in making that claim. Also in your study,
if you had actually measured the slope for the individuals, and averaged
those slopes to get your group measure, you would be jsutified in saying
something about the range of individual slopes from the group distribution.
My argument was about the _intrinsic_ impropriety of arguing from the
between subjects slope to the individual slopes. Your study shows its
_practical_ impropriety.
Martin
[From Bill Powers (971125.0819 MST)]
Martin Taylor 971124 23:20--
You are actually arguing on my side and that of Richard Kennaway: there is
no way to determine the within-person relationship from the population
relationship. For persons with the same reference level, the relation
between reward and effort has a strongly negative slope; for the unsorted
data, the relation between reward and effort has a positive slope.
I've been arguing that it is true of this study, and would have been known
to be true of this study before the results were analyzed.
How would it have been known to be true of this study when each individual
contributed only one point to the array? I should add that this is
generally the case for all large studies. Large studies are done under the
assumption that people are interchangable.
But _for that reason_ I am arguing that the study says nothing about
the results of other studies in which the group measure legitimately
does relate to the measures on individuals. For example, if one measures
the heights of a group of people and comes to the conclusion that
unknown mature individual X is probably not over 9ft tall, nor under
2 ft tall, one is justified in making that claim. Also in your study,
if you had actually measured the slope for the individuals, and averaged
those slopes to get your group measure, you would be jsutified in saying
something about the range of individual slopes from the group distribution.
But that is not an IV-DV study, which is what I was talking about. If the
slopes had been measured for each individual in the study I simulated, the
group study would have been unnecessary. Why would anyone want to know the
_group_ slope, except someone who deals only with groups? Why would anyone
want to know the _average_ height of a population, except someone who sells
or designs doors or basketball courts?
My argument was about the _intrinsic_ impropriety of arguing from the
between subjects slope to the individual slopes. Your study shows its
_practical_ impropriety.
OK, OK, you were right all along. Post hoc, anyway.
Best,
Bill P.