Full House by Stephen Jay Gould Read Free Book Online

than politics: fifty pounds is the lower limit for sustaining life, and no one can get any thinner. Therefore, although citizens are now free to alter their weight, only one direction of change is possible. The great majority of inhabitants remain content with the old ways and elect to maintain themselves at fifty pounds. Fifteen percent of the population revels in its newfound freedom and begins to gain weight with abandon. Six months later, these fifteen individuals average seventy-five pounds; after a year, one hundred pounds; and after two years, 150 pounds.
    The statistical spin doctors for the fat fifteen now step in. They argue that their clients’ point of view is sweeping through the whole society, as clearly indicated by the steady increase of mean weight for the entire population. And who can deny their evidence? They even present a fancy graph (shown here as Figure 3). Before the liberation, average weight stood at fifty pounds; after six months the mean rises to 53.8 pounds (the average for eighty-five remaining at fifty pounds, and fifteen rising to seventy-five pounds); after a year to 57.5 pounds; and after two years to sixty-five pounds (an increase of 30 percent from the original fifty)—a steady, unreversed, and substantial rise.
    Again, you may view this example as silly (and purposely chosen to illustrate the obvious nature of the point, once you understand the whole system and its variation). Few people would be fooled, so long as they grasped the totality of the story, and knew that most members of the population had not changed their weight, and that the steady increase in mean values arises as an artifact produced by amalgamating two entirely different subpopulations—a majority of stalwarts with a minority of revolutionaries. But suppose you didn’t appreciate the whole tale, and only listened to the statistical spin doctors for the fat fifteen. Suppose, in addition, that you tended to imbue mean values (as I fear most of us do) with a reality transcending actual individuals and the variation among them. You might then be persuaded from Figure 3 that a general trend has swept through the population, thrusting it as a whole toward greater average weights.

    FIGURE 3 Average weight of my hypothetical population plotted against time to show how a false impression of an overall trend may be generated.
    We are more likely to be fooled by the second case, where limits to variation on one side of the average permit change in only one direction. The rise of mean values isn’t "false" in this second case, but the supposed trend is surely misleading in the sense of Mark Twain’s or Disraeli’s famous line (the quote has been attributed to both) about three kinds of falsification—"lies, damned lies, and statistics." I will present the technicalities later, but let me quickly state why such false impressions can emerge from correct data in this case—as so often exploited by economic pundits and political spin doctors. As in the cliché about skinning cats, there is more than one way to represent an "average." The most common method, technically called the mean, instructs us to add up all the values and divide by the number of cases. If ten kids have ten dollars among them, the mean wealth per kid is one dollar. But means can be grossly misleading—and never more so than in the type of example purposely chosen above: when variation can expand markedly in one direction and little or not at all in the other. For means will then drift toward the open end and give an impression (often quite false) that the whole population has moved in that direction.
    After all, one kid may have a ten-dollar bill, and the other nine nothing. One dollar per kid would still be the mean value, but would such a figure accurately characterize the population? Similarly, to be serious about real cases, spin doctors for politicians in power often use mean incomes to paint dishonestly bright pictures. Suppose that, under a