Calling Bullshit: The Art of Skepticism in a Data-Driven World

by Carl T. Bergstrom

Reporting numbers as percentages can obscure important changes in net values. For example, the US incarcerates African Americans at a shockingly high rate relative to members of other groups. African Americans are more than five times as likely as whites to be in jail or prison. In the year 2000, African Americans composed 12.9 percent of the US population but a staggering 41.3 percent of the inmates in US jails. Given that, it would seem to be good news that between the year 2000 and the year 2005, the fraction of the jail population that was African American declined from 41.3 percent to 38.9 percent. But the real story isn’t as encouraging as the percentage figures seem to indicate. Over this period, the number of African Americans in US jails actually increased by more than 13 percent. But this increase is obscured by the fact that over the same period, the number of Caucasians in US jails increased by an even larger fraction: 27 percent. This is an example of a more general issue with comparisons that involve fractions or percentages: Changing denominators obscure changes in numerators. The numerator—the top part of the fraction, here the number of jailed African Americans—increased substantially from 2000 to 2005. But the denominator—the bottom part of the fraction, here the total number of jailed Americans—increased by an even larger proportion over the same period. As a result, African Americans made up a smaller fraction of the incarcerated population in 2005 than...