"For every 100 black defendants, 18 were sentenced to death, revealing that black defendants on average face a significantly higher risk of receiving the death sentence than all other defendants committing similar crimes."

The above attention grabbing statements based on researchers' conclusions from a study of death penalty cases in Philadelphia appeared in an article on abc.com on June 4, 1998. But while statistics such as "40% higher" and "4 times more likely" are clearly alarming, what do they really mean?

To begin with, to conclude that the fact that 18 out of every 100 blacks are sentenced to death translates into higher risk for blacks, you would first need a figure for nonblacks to compare it against. Without a number to compare it against, words such as higher and lower have no meaning.

As for the statement "40% higher," once again the article fails to report the actual rate for each group, without which the figure is extremely misleading. Using the reported rate of 40% higher rate, we can calculate the risk for nonblacks to be 13%, or 13 out of every 100. The absolute difference is actually only 5%, a figure that while possibly significant, is far less alarming.

Similarly, the statement that "blacks are four times as likely" is also misleading. It is an interpretation of numbers based on the precise definition of odds. In fact, such a statement would be true when comparing events that occur 99% of the time versus 96%. To say, for example, that "blacks were sentenced to death 99% of the time for a particular type of murder versus nonblacks who were sentenced to death 96% of the time" is clearly not nearly as striking as the statement, "blacks are four times as likely to receive the death penalty." Nevertheless, they mean the same thing. The odds for an event occurring 99% of the time is 99-to-1 (.99/.01) while the odds for an event occurring 96% of the time is 24-to-1 (.96/.04), resulting in a relative difference of 4.125 times.

The study was conducted by University of Iowa professors David Baldus and George Woodworth, who reviewed 667 murder cases over a decade and found that 18% of black defendants in murder cases were sentenced to death compared to 13% of nonblacks. Upon a closer look at the numbers underlying the study, however, it appears that the statements in the article were likely the result of the media’s desire to sensationalize statistical conclusions without examining how those conclusions were actually reached.

More Lies, Damned Lies