Prisoner sex-ratio dispersion has not always decreased as the median prisoner sex ratio has decreased. In the U.S. from 2000 to 2010, the median prisoners sex ratio across U.S. states decreased from 10.9 to 9.3. However the sex-ratio dispersion index increased from 0.39 to 0.41. Scaling effects should be symmetric. From 1880 to 1910, the median prisoner sex ratio across U.S. states increased from 16.3 to 23.7. The dispersion index, however, fell from 1.43 to 0.89.

Both internationally and across states within the U.S., the dispersion in the prisoner sex ratio has decreased over time. That’s not simply a scaling effect from a decreasing median prisoner sex ratio.