Ok, I've taken another look at the paper (Lindberg et al, New Trends in Gender....Psych Bull, 2010).
I asked whether the average VR of 1.07 they reported in their first study was significantly different from a VR of 1.00 (and could have asked this about their second study, where it was 1.09). This made me wonder how they were obtaining their average VR ratios. I looked at it for their second study, where they had four large data set studies, each reporting VRs for multiple years. Did they consider each VR a data point, and lump them all together in one big average? Or did they consider each study separately, and then average the averages? If the first, then eyeballing it suggests that their average VR of 1.09 would differ significantly from 1.00 over 56 separate VR data points. If they only used the average of each study (four of them), the number of entries would be too small for a meaningful answer. But it seemed to me that lumping all the individual data points together was improper, and that they should only consider one a(average) VR value per study. So which was it? What did they do? I tried to find out. For the one big average case (n= 56), I calculated the VR ratio from their data as 1.103. With the average of averages (n = 4) it came to 1.0975 . Neither is the 1.09 they reported but both are very close to it, and are very close to each other. [My understanding, together with a bit of algebra to make sure is that the overall average is not necessarily the same as the average of averages, but if I'm wrong, I'm going to look pretty silly here]. They did say they used the method of Katzman and Alliger (1992), whose title indicates it's a critique of methods of averaging variances, so perhaps they did neither of the above. But the real news, which escaped me last time, is that these values of VR, however obtained, are not really that much lower from those she cites as earlier published estimates. So it's really, more or less (a bit less) a replication of earlier claims of variability, not "nearly equal male and female variances" as she says in her abstract. As Jim Clark showed, this difference can mean a big deal at the extreme end of the tail. So it leaves unconvincing her conclusion that "these findings support the view that males and females perform similarly in mathematics" . Also, I'd like to amend this statement with which I ended my previous post: > > 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. > . I should add to that I can also readily believe that the good old boys at Harvard may well harbour a certain prejudice against hiring women. So, like Larry Summers, I hedge my bets. 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: arch...@jab.org. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=6274 or send a blank email to leave-6274-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
