Marken's new spreadsheet

CSGnet Archive CSG1997
1

[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
individual means.

Regards,

Bruce

2

[From Bill Powers (971204.1335 MST)]

Bruce Abbott (971204.0945 EST)--

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.

Being a statistical non-guru, I have to ask what the "repeated measures"
design is. Is this the case where if you have 20 people in the sample, you
use 20 (0r more) different values of the IV, to get a 20x20 matrix? This,
of course, would combine individual measures (testing specimens) with group
measures (casting nets). If that's what you mean, I'm puzzled about the
purpose of the group measure. It seems to me that the way to proceed would
be to fit a model to each individual, and then see if there are any
commonalities in the parameters over the group.

It must be that in the applications of statistics that we see, there is
spectrum ranging from perfectly acceptable to completely unacceptable, in
terms of applicability to individual characteristics. I'm thinking of the
"second-hand smoke" studies, in which, surely, there could be no "repeated
measures" of the data concerning the hypothesis that second-hand smoke is
"found to be a contributing factor in deaths due to heart disease, lung
disease,etc.." Here we have a vaguely defined IV and a DV which is buried
among much more dramatic effects, and each individual in the study can be
evaluated only once. Furthermore, the risk, instead of being stated in
terms of actual chances of a given person's being affected, is given in
total numbers: 3000 PEOPLE PER YEAR DIE FROM SECOND-HAND SMOKE!" (Which, of
course, is not at all what the finding is). Don't studies like this tend
toward the unacceptable end?

There must be many similar situations where individuals can be measured
only once, or at most a few times (too few to fit any model to the data),
yet individual characteristics are deduced from population trends. My demo
with 4000 control systems was of that kind: each "person" yielded only one
point in the diagram, so there could be no question of finding the trend
for any individual.

Perhaps we could classify different applications of statistics to
individuals according to the degree to which individual data, and trends,
ever become known. In survey data, for example, it's clear that each person
is measured only once, so all survey data are suspect as a way of
characterizing individuals (the average voter is about 53% Democrat,
according to recent polls). At the other end of the spectrum,
psychophysical data are almost entirely about individuals repeatedly
measured, although I don't know what happens to those individual measures
once they're obtained (are those exponents averages over many individuals?).

I don't know what all the applications of statistics are, but perhaps some
netters who do know might be willing to cast an eye over the field to see
how various kinds of studies are spread over the spectrum. Might even be
worth a paper somewhere -- maybe Science, since Richard Kennaway is
breaking the ice there.

Best,

Bill P.

3

[From Tim Carey (971206.0725)]

Hi Bill,

Being a statistical non-guru, I have to ask what the "repeated measures"
design is.

One of the statistics texts I have provides what I believe to be a fairly
standard explanation of repeated measures (also referred to as within
subjects). The reference is: Keppel, G. (1991). Design and Analysis: A
researcher's handbook (3rd edition). New Jersey: Prentice-Hall.

p 19 "A popular design in the behavioral sciences is one in which each
subject serves in all the treatment conditions, rather than only in one.
This type of design is commonly referred to in psychology as a
repeated-measures design. The design is also known as the within-subjects
design because any differences in behavior observed among the treatment
conditions are based on the same set of subjetcs; that is, treatment
effects are represented by differences within the single group of subjects
serving in the experiment.
    A within-subjects design requires fewerr subjects and is more sensitive
than a corresponding completely randomized or between-subjects design.
Problems with the design center on relatively restrictive statistical
assumptions and the fact that subjects can change while they are receiving
the different treatment conditions."

I could go on, but I'm sure you get the general idea,

Cheers,

Tim