Hi 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 500,000 female scores from a population with mu = 0, and sigma = 1, and 500,000 male scores from a population with mu = .05, and sigma = 1.04 (square root of 1.08). These represent data consistent with Stephen's description below.
*simulation of 2010 Hyde result: d = .05, vratio = 1.08. input program. loop i = 1 to 1000000. compute gend = mod(i - 1,2) + 1. if gend = 1 v = rv.norm(.05,1.04). if gend = 2 v = rv.norm(.0,1.0). end case. end loop. end file. end input program. I then selected cases for various degrees of selectivity. Of the top 10,000 scores, 5973 (59.73%) were for males and 4027 (40.27%) for females. Of the top 5,000 scores, 3058 (61.2%) were males and 1942 (38.8%) were females. Of the top 1,000 scores 663 (66.3%) were males and 337 (33.7%) were females. Of the top 100 scores, 69 (69%) were male and 31 (31%) were female. 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. Another issue someone may know the answer to is how discriminating the tests are at the upper end of the distribution. That too would influence how one should interpret the reported differences. Take care Jim James M. Clark Professor of Psychology 204-786-9757 204-774-4134 Fax [email protected] >>> <[email protected]> 05-Nov-10 7:17:26 PM >>> What, you thought maybe I was gonna talk about politics? This is a psychology list! Dr. Summers was rash enough to speculate, while President of some obscure place called Havahd, about the finding that few women are to be found among the highest reaches of the hard sciences, such as in the Department of Mathematics at Harvard. One of his speculations was that there was more innate aptitude at the high end of the bell curve for men than women. We all know what happened next. But if you missed it, a concise summary can be found here: http://media.swarthmore.edu/bulletin/?p=145 The point was that while there may not have been a difference in average ability, there was in variability (at both tails). As the Swarthmore essay notes, a well-known researcher, Janet Hyde "partially" confirmed Summers. Not any more, she doesn't. Here's the abstract from Psychological Bulletin, just published. Lindberg, Sara M.; Hyde, Janet Shibley; Petersen, Jennifer L.; Linn, Marcia C. New trends in gender and mathematics performance: A meta-analysis. Psychological Bulletin, Vol 136(6), Nov 2010, 1123-1135. Abstract In this article, we use meta-analysis to analyze gender differences in recent studies of mathematics performance. First, we meta-analyzed data from 242 studies published between 1990 and 2007, representing the testing of 1,286,350 people. Overall, d = 0.05, indicating no gender difference, and variance ratio = 1.08, indicating nearly equal male and female variances. Second, we analyzed data from large data sets based on probability sampling of U.S. adolescents over the past 20 years: the National Longitudinal Surveys of Youth, the National Education Longitudinal Study of 1988, the Longitudinal Study of American Youth, and the National Assessment of Educational Progress. Effect sizes for the gender difference ranged between -0.15 and +0.22. Variance ratios ranged from 0.88 to 1.34. Taken together, these findings support the view that males and females perform similarly in mathematics. (PsycINFO Database Record (c) 2010 APA, all rights reserved) And just when Summers thought it might be safe to go back to Harvard. 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=13251.645f86b5cec4da0a56ffea7a891720c9&n=T&l=tips&o=6259 or send a blank email to leave-6259-13251.645f86b5cec4da0a56ffea7a89172...@fsulist.frostburg.edu --- 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=6261 or send a blank email to leave-6261-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
