[From Mike Acree (971209.0252 PST)]
I think the role of individual trends in the analysis is made clearest
in the regression approach, where the J occasions of measurement are
used to construct J-1 trends (e.g., orthogonal polynomials). Each such
trend then constitutes a separate DV; the scores are the values of
individual trends, and the error terms are the deviations from, say,
linearity, across individuals. (The traditional approach discussed so
far lumps all these trends together in a single (J-1)-df test.) The
point of the ANOVA is still, of course, to make a statement about the
_average_ trend, for each DV; and, as parties on both sides of the
exchange have pointed out, it is a common, but mistaken, inference from
average results to individual trends. Someone else, probably Abbott,
also observed that, in the absence of any other evidence, that average
was better than nothing, in the sense of long-run statistical
performance, if we had to predict an individual trend. That resort, of
course, merely substitutes an average at another level. On that point,
Ian Hacking pointed out in his _The Logic of Statistical Inference_
(1965) that the long-run average performance of a statistical test tells
us nothing about its credibility on each occasion of use. Churchill
Eisenhart also drove a wedge between the long-run average and the
individual case with his example, in 1947, of the price of Coke being
raised from 5 cents to 6 cents, when the machine was set to take only
nickels. If at random one in every six bottles was empty, then the
machine may still be said to be fair, in terms of the average price. . .
. (I fear the example loses its force with 1947 prices, but you can
imagine a dollar machine that doesn't make change.) On the other hand,
there are times when we appeal to averages, with exiguous justification.
Consider Peirce's example of being forced to choose between drawing from
a pack with 1 black and 25 red cards and one with 1 red and 25 black
ones, where a red card meant "eternal felicity" and a black one
"everlasting woe." In the nature of the risk, it couldn't be repeated,
so it is not altogether obvious how to justify our preference for the
first pack. (Some have thought Peirce's own resolution of this dilemma
a stretch. He thought we necessarily made implicit appeal to the whole
of humankind, and found therein support for the Biblical virtues of
faith, hope, and charity.)
In confess that taking up this repeated-measures,
individual-vs.-aggregate thread again feels pretty silly, especially
since it appeared ready to die a quiet death already. The process
seemed worth one further comment, though it is also becoming too
predictable to remain interesting for long. My own opinion of the value
of conventional psychological research, and of the use of statistics
within it, is so low that I would never have expected to be accused,
even implicitly, of "defending" it. But that's the way our
conversations work. Someone, usually Marken, makes a statement about
some non-PCT approach that is so extreme as to be misleading or false.
Since silence risks being construed as agreement, those of us trying to
control perceptions of ourselves as intelligent/critical/thoughtful are
obliged by that goal to attempt a clarifying response, which reliably
serves only to have us labeled as defenders of that particular
orthodoxy--and on it goes. No harm, I suppose, for those who enjoy it,
unless we care about creating the impression that we are just another
bunch of boys who like fighting better than anything else. But I think
Bill was once moved (in dialogue with Hans?) to declare that his future
silence should not be construed as acquiescence, and I'm feeling
inclined toward a similar declaration myself. I participated earlier in
a couple of extended threads, on the understandable but mistaken
assumption that PCTers generally agreed with Chapter 17 of B:CP, to
which I could appeal as a common ground; the issues didn't become less
interesting to me when I eventually found out that common ground
actually lay considerably deeper, but they were already too peripheral
to the interests of others on the Net. As only an occasional
participant anyway, it should be relatively easy for me to withdraw
without inducing funny attributions about my level of interest or
agreement. But I hope a similar frustration hasn't prompted others,
with more relevant expertise, to withdraw, or to withhold participation.
Mike