PHILADELPHIA — Who can forget the morass of statistics used in the O.J. Simpson double-murder trial? What did the cited DNA probabilities mean? Did the jury and the public grasp the mathematics undergirding the numbers?
More recently, the issues of race, death and mathematics have again subtly entertwined. This time, the misunderstanding arises because the technical meaning of a common phrase differs substantially from its informal meaning. What at first glance may seem like semantic nitpicking has significant consequences for public policy and perceptions.
In a study published in The Times, there appeared a potentially inflammatory, although ostensibly correct, statement. In reporting on death sentences in Philadelphia, the study asserted that the odds of blacks convicted of murder receiving a death sentence were four times the odds faced by other defendants similarly convicted. The Times article, as well as accounts in other newspapers, then transmuted that statement into the starkly inequivalent one that blacks were four times as likely to be sentenced to death as whites. The author of the study used the technical definition of odds, not the more familiar idea of probability, and, as a consequence, most readers were seriously misled.
The difference between "probability" and "odds" is crucial. The odds of an event is defined as the probability it will occur divided by the probability that it will not occur. Consider a coin flip. The probability of it landing heads is one-half, or .5, and the probability of not landing heads is also one-half, or .5. Hence: The odds of the coin landing heads is 1 to 1 (.5 divided by .5). Now consider rolling a die and having it land on 1,2,3,4 or 5. The probability of this event is five-sixths, or .83, and the probability of the die not landing on 1,2,3,4,, or 5 is one-sixth, or .17. Hence: The odds of the die landing on one of these five numbers is 5 to 1 (.83 divided by .17). More serious discrepancies between probabilities and odds occur for events with higher probabilities.