On 5 Nov 2010 at 22:45, Jim Clark wrote:
> Going just on Stephen's summary, some people just do not appear to understand
> the impact of tiny differences
> on extreme scores for very large numbers of people. The following SPSS
> program generates <snip>
> So even with the very modest values reported, it is possible to
get substantial gender imbalances. One would have to guess
that the percentage of the population with PhDs in mathematics
or theoretical physics would be tiny, that is a very select group,
and perhaps even smaller than my 100 out of 1,000,000
observations above. > >
This is a clever and very interesting analysis of Jim's. It
prompted me to take a look at the article itself, something I
really didn't want to do. As I anticipated, it was something less
than transparently clear, especially to a statistics-challenged
person such as myself.
Here's essentially all that the authors said about the variance
issue:
"Sixth, do males display greater variance in scores and, if so, by
how much? The overall VR in Study 1 was 1.07. That is, males
displayed a somewhat larger variance, but the VR was not far
from 1.0 or equal variances. In Study 2, the average VR was
1.09, again not far from 1.0. In addition, the NELS:88 data (see
Table 3) show several VRs that are
1.0, indicating that greater male variability is not ubiquitous. VRs
less than 1.0 have also been found in some national and
international data sets (Hyde et al., 2008; Hyde & Mertz, 2009). "
This seems strikingly non-quantitative to me ("somewhat larger
variance, but not far from 1.0"; "again, not far") in a paper which
claims to be quantitative in the extreme.
How far is "not far".? Perhaps I'm showing some of my
promised statistical ignorance, but couldn't they have tested
whether a VR of 1.07 was significantly different from a VR of
!.00 (i.e. equality)?
Second, if one looks at the VRs they reported in Study 2 for the
four (I think) major studies used in the analysis, one can see
that the VR ratios as a function of year of testing are all over the
map. In particular the VRs for the LSAY (Longitudinal Studies of
American Youth) give results for each of 6 years between 1987
and 1992 ranging from 1.14 to 1.34. These indicate a
substantial variance ratio by anyone's criterion. I'm not sure that
lumping this study with three others not showing such large
efffects is any way to resolve the issue, even if this is standard
meta-analysis technique. Why are the results of this study so
different?
Finally, if the authors are correct, and there is no difference in
variance in these newer studies, one might expect that the
future looks bright for these math whiz women to start showing
up at Harvard. I'd imagine it should have just about started
happening now. Unless of course, discrimination is the real
reason they haven't been there all along.
For what it's worth, the hypothesis that seems most likely to me
is the self-selection one. Women may just not find full
professorship at Harvard in mathematics one of the most
fulfilling things they can do with their lives. That, of course, and
innate ability at the very, very high end.
Stephen
--------------------------------------------
Stephen L. Black, Ph.D.
Professor of Psychology, Emeritus
Bishop's University
Sherbrooke, Quebec, Canada
e-mail: sblack at ubishops.ca
---------------------------------------------
---
You are currently subscribed to tips as: [email protected].
To unsubscribe click here:
http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=6262
or send a blank email to
leave-6262-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
