Opinion
No. 79-2817.
December 7, 1981.
Carol Nelkin, Houston, Tex., for plaintiffs-appellants.
Lonny Zwiener, Asst. Atty. Gen., Austin, Tex., for defendants-appellees.
Appeal from the United States District Court for the Southern District of Texas, 471 F. Supp. 1054.
Before BROWN, COLEMAN and GEE, Circuit Judges.
ON PETITION FOR REHEARING AND SUGGESTIONS FOR REHEARING EN BANC [2] (Opinion August 28, 5 Cir. 1981, 654 F.2d 388)
In their petition for rehearing appellants press upon us for the first time the University of Houston's "Suggestion of Error in Presentation of Statistical Evidence." In the suggestion of error, the university admits that its expert on faculty compensation, Dr. Douns, erred when he testified that his first regression analysis model without a sex variable produced a table showing that men and women were treated equally with regard to pay. In fact, Dr. Douns was using his second regression analysis, which utilized a sex variable. The actual "sex-free" model showed that 49 percent of the males were overpaid, while only 31 percent of the females were overpaid, the relevant preponderance of underpaid women having less than 8 chances in 10,000 of occurring by chance.
This point casts doubt on our opinion on faculty compensation insofar as our prior opinion relied on the fact that "the only expert to testify on the subject stated that in his opinion the regression analysis did not establish that the university discriminated against women with respect to faculty compensation." 654 F.2d 388 at 403. Also incorrect is our discussion, id., at 404, of a "second inconsistency" in the results of the university's multiple regression analysis. Contrary to what we stated in our original opinion, it does appear on the basis of the university's own sex-free regression analysis that faculty women in general were paid less than the amount predicted by the model, while men were paid more. Nonetheless, we still adhere to our original conclusion and affirm the district court on the class plaintiffs' faculty compensation claim.
Nonetheless, the university's data that 49 percent of the males and 31 percent of the females were "overpaid" may or may not be statistically significant, depending on the validity of the model, as we discuss below. This data does not conclusively establish that female University of Houston faculty members were discriminated against in compensation.
The thrust of our original opinion on faculty compensation remains unchanged: plaintiffs have failed to demonstrate the validity of the multiple regression model as a whole. As we stated in our original opinion, "Multiple regression analysis is a relatively sophisticated means of determining the effect that any number of different factors have on a particular variable." 654 F.2d at 402-03. Since multiple regression analysis is subject to misuse, courts cannot be expected to accept at face value conclusions derived from such a model absent expert testimony concerning the validity of the model itself. In this case, the class plaintiffs are attempting to use the university's own data to establish a case of discrimination in faculty compensation. At trial, however, only one expert attempted — on the university's behalf — to lay a foundation for the validity of the model used. As we have seen, the value of this expert's testimony is now doubtful at best. Yet when the class plaintiffs purported to use the university's statistics for their own purposes, they did not fulfill their burden of showing that the multiple regression analysis model employed was valid. Without guidance, this court cannot be expected to resolve in the class plaintiffs' favor fundamental questions relating to the model itself.
Also undisturbed is our original discussion, 654 F.2d at 403, of the first inconsistency with the university's multiple regression analysis. Consideration of the university's "suggestion of error" does not change the fact that the model with sex as a factor explained only .8 percent more of the total variation around the average salary than did the model without sex.
As we pointed out in our original opinion, multiple regression analysis is based upon three major assumptions, and where these assumptions fail, "the use of multiple regression analysis is likely to be inappropriate." Fisher, Multiple Regression in Legal Proceedings, 80 Colum.L.Rev. 702 (1980). Neither the university's expert, Dr. Douns, nor the class plaintiffs have addressed whether these assumptions are valid in this case; "neither have other questions, such as those relating to the relationship among the independent variables, whether a linear model is appropriate in this case, whether variables have been erroneously included or excluded in the model, and whether the fact that the model explains only 52 to 53 percent of the total variation in average salary means that the model as a whole is not very reliable." 654 F.2d at 404-05.
We have examined with some care class plaintiffs' other contentions in their petition for rehearing and conclude that none have merit.
The petition for rehearing is DENIED, and no member of this panel nor judge of this Administrative Unit in regular active service having requested that the Court be polled on rehearing en banc, Rule 35, Federal Rules of Appellate Procedure; Local Fifth Circuit Rule 16; Fifth Circuit Judicial Council Resolution of January 14, 1981, the suggestions for rehearing en banc are DENIED.