Naked Statistics: Stripping the Dread from the Data

by Charles Wheelan

Suppose that you have a potentially fatal illness. The good news is that a new drug has been developed that might be effective. The drawback is that it’s extremely expensive and has many unpleasant side effects. “But does it work?” you ask. The doctor informs you that the new drug increases the median life expectancy among patients with your disease by two weeks. That is hardly encouraging news; the drug may not be worth the cost and unpleasantness. Your insurance company refuses to pay for the treatment; it has a pretty good case on the basis of the median life expectancy figures. Yet the median may be a horribly misleading statistic in this case. Suppose that many patients do not respond to the new treatment but that some large number of patients, say 30 or 40 percent, are cured entirely. This success would not show up in the median (though the mean life expectancy of those taking the drug would look very impressive). In this case, the outliers—those who take the drug and live for a long time—would be highly relevant to your decision.