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To the editor,
This letter concerns the article written by Robert Lerner and Althea Nagai titled "Reverse Discrimination by the Numbers," appearing in your summer 2000 issue.
I must express my disappointment in the level of scholarship found in that article. I think that the authors are probably correct in the conclusions that are drawn from the data, however, the representation of science and statistics is simply not professional. Speaking as someone who has taught graduate methods and statistics for 15 years and edited books and a journal dealing with these issues, the representations were frankly awful.
I will mention four of the more serious errors in the text. The problem is that all the errors cast a very negative reflection on the quality of scholarship and call now into question the accuracy and confidence anyone can have in the analysis.
First, the mathematical representations about causality are exceedingly strange (pages 74 and 81) and simply incorrect. The idea that a "large correlation" indicates a less ordered or causal system as opposed to a "small" correlation is incorrect. Take the following model, which indicates a "spurious" relationship between A and B.
There is a correlation between A and B, but the correlation is not causal because actually A and B are correlated because they are caused by a common underlying event X. Basically, X causes A and B to occur, but if you measured only A and B you would find a correlation existing between A and B but neither variable would cause the other.
Now mathematically, you can calculate the correlation between A and B by multiplying the correlations (X with A and X with B). Suppose X and A are correlated at .90 and X and B are correlated at .90 as well. The correlation between A and B would be .81 (very large using the Cohen system the authors mention) but it would not be causal, it would be extraneous. This simple example, one I use to teach undergraduates, is an examination of what happens when you try to use mathematical methods to substitute for theoretical methods.
The second issue is the "signature" issue they use on page 75. Basically, signature evidence is established when you have either base rate information or an established "footprint" for the process and can seek to verify the existence of the footprint. The problem is that the authors in this piece do not have such a process; they are seeking to establish the process rather than using an existing process and verifying various components. This is simply a misuse of the example.
The third issue deals with the problems of multicollinearity. Several of the variables (verbal SAT, math SAT, HS rank) are collinear (that is, they are correlated and indicators of the same underlying construct--this is a central argument made by Hernnstein and Murray, whom the authors cite). As a result of multicollinearity, that outcome is a regression equation where the multiple R is accurate but the individual estimates for the predictors are unstable and usable (any basic book on multiple regression will establish that). The problem is that the outcomes comparing various features are suspect and useless. Had the authors published a zero order correlation matrix among all the variables, this could have been assessed. As it is, I cannot evaluate the problem, but it is obviously present and no conclusions can be drawn from the analysis--in fact it is inappropriate.
The last issue deals with underlying causal issues among the predictors. Again the Bell Curve (which they cite) argues for causality among the racial issues that generate …