Читать книгу Applied Eugenics - Paul Popenoe - Страница 24

Whenever a large enough number of individuals is tested, these differences arrange themselves in the same general form. It is the form assumed by the distribution of any differences that are governed absolutely by chance.

Suppose an expert marksman shoots a thousand times at the center of a certain picket in a picket fence, and that there is no wind or any other source of constant error that would distort his aim. In the long run, the greatest number of his shots would be in the picket aimed at, and of his misses there would be just as many on one side as on the other, just as many above as below the center. Now if all the shots, as they struck the fence, could drop into a box below, which had a compartment for each picket, it would be found at the end of his practice that the compartments were filled up unequally, most bullets being in that representing the middle picket and least in the outside ones. The intermediate compartments would have intermediate numbers of bullets. The whole scheme is shown in Fig. 11. If a line be drawn to connect the tops of all the columns of bullets, it will make a rough curve or graph, which represents a typical chance distribution. It will be evident to anyone that the distribution was really governed by "chance," i.e., a multiplicity of causes too complex to permit detailed analysis. The imaginary sharp-shooter was an expert, and he was trying to hit the same spot with each shot. The deviation from the center is bound to be the same on all sides.

Fig. 11.—The "Chance" or "Probability" Form of Distribution.

Now suppose a series of measurements of a thousand children be taken in, let us say, the ability to do 18 problems in subtraction in 10 minutes. A few of them finish only one problem in that time; a few more do two, more still are able to complete three, and so on up. The great bulk of the children get through from 8 to 12 problems in the allotted time; a few finish the whole task. Now if we make a column for all those who did one problem, another column beside it for all those who did two, and so on up for those who did three, four and on to eighteen, a line drawn over the tops of the columns make a curve like the above from Thorndike.

Comparing this curve with the one formed by the marksman's spent bullets, one can not help being struck by the similarity. If the first represented a distribution governed purely by chance, it is evident that the children's ability seems to be distributed in accordance with a similar law.

With the limited number of categories used in this example, it would not be possible to get a smooth curve, but only a kind of step pyramid. With an increase in the number of categories, the steps become smaller. With a hundred problems to work out, instead of 18, the curve would be something like this:

Fig. 12.—Probability curve with increased number of steps.

And with an infinite number, the steps would disappear altogether, leaving a perfectly smooth, flowing line, unmarred by a single step or break. It would be an absolutely continuous distribution.

If then, the results of all the tests that have been made on all mental traits be studied, it will be found that human mental ability as shown in at least 95% of all the traits that have been measured, is distributed throughout the race in various degrees, in accordance with the law of chance, and that if one could measure all the members of the species and plot a curve for these measurements, in any trait, he would get this smooth, continuous curve. In other words, human beings are not sharply divided into classes, but the differences between them shade off into each other, although between the best and the worst, in any respect, there is a great gulf.

If this statement applies to simple traits, such as memory for numbers, it must also apply to combinations of simple traits in complex mental processes. For practical purposes, we are therefore justified in saying that in respect of any mental quality—ability, industry, efficiency, persistence, attentiveness, neatness, honesty, anything you like—in any large group of people, such as the white inhabitants of the United States, some individuals will be found who show the character in question in a very low degree, some who show it in a very high degree; and there will be found every possible degree in between.

NORMAL VARIABILITY CURVE FOLLOWING LAW OF CHANCE