Misleading Gender Discrimination Statistics

Here is a link to a nice example about how statistics can be misleading in subtle ways that most people will not think of.  The moral of the story is "Don't jump to conclusions suggested by statistics unless you understand them - and don't jump to the conclusion that you understand them."

A snippet.
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To illustrate Simpson’s paradox, I found more detailed data for a similar situation at the University of California in a 1973 gender discrimination case:

               Applications           Successful

Male          8442                       44%

Females     4321                       35%

Because 44% of all male applicants and 35% of all female applicants were accepted to their graduate schools in 1973, gender discrimination seemed rather obvious…until you took a closer look

                          Men             Men           Women        Women
Department      Applicants     Admitted     Applicants     Admitted

     A                  825               62%            108               82%

     B                  560               63%             25                68%

     C                  325               37%            593               34%

     D                  417               33%            375               35%

     E                  191               28%            393               24%

     F                  272                 6%            341                 7%

As you can see, more women applied to more competitive departments. Meanwhile more men competed for spots in departments with high acceptance rates. Combined, these stats conveyed the impression that women experienced discrimination. However, if we consider the relationship between the proportion of female applications and admissions rates the data point us in a different direction.