Part 7 (1/2)
FIG. 10.--When deviations in all directions are equally probable, as in the case of shots fired at a target by an expert marksman, the ”frequencies” will arrange themselves in the manner shown by the bullets in compartments above. A line drawn along the tops of these columns would be a ”normal probability curve.” Diagram by C. H.
Popenoe.]
Whenever a large enough number of individuals is tested, these differences arrange themselves in the same general form. It is the form a.s.sumed 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 a.n.a.lysis. 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.
[Ill.u.s.tration: 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:
[Ill.u.s.tration: 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 cla.s.ses, 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.
[Ill.u.s.tration: NORMAL VARIABILITY CURVE FOLLOWING LAW OF CHANCE
FIG. 13.--The above photograph (from A. F. Blakeslee), shows beans rolling down an inclined plane and acc.u.mulating in compartments at the base which are closed in front by gla.s.s. The exposure was long enough to cause the moving beans to appear as caterpillar-like objects hopping along the board. a.s.suming that the irregularity of shape of the beans is such that each may make jumps toward the right or toward the left, in rolling down the board, the laws of chance lead to the expectation that in very few cases will these jumps all be in the same direction, as is demonstrated by the few beans collected in the compartments at the extreme right and left. Rather the beans will tend to jump in both right and left directions, the most probable condition being that in which the beans make an equal number of jumps to the right and left, as is shown by the large number acc.u.mulated in the central compartment. If the board be tilted to one side, the curve of beans would be altered by this one-sided influence. In like fas.h.i.+on a series of factors--either of environment or of heredity--if acting equally in both favorable and unfavorable directions, will cause a group of men to form a similar variability curve, when cla.s.sified according to their relative height.]
The consequences of this for race progress are significant. Is it desired to eliminate feeble-mindedness? Then it must be borne in mind that there is no sharp distinction between feeble-mindedness and the normal mind. One can not divide sheep from goats, saying ”A is feeble-minded. B is normal. C is feeble-minded. D is normal,” and so on.
If one took a scale of a hundred numbers, letting 1 stand for an idiot and 100 for a genius, one would find individuals corresponding to every single number on the scale. The only course possible would be a somewhat arbitrary one; say to consider every individual corresponding to a grade under seven as feeble-minded. It would have to be recognized that those graded eight were not much better than those graded seven, but the drawing of the line at seven would be justified on the ground that it had to be drawn somewhere, and seven seemed to be the most satisfactory point.
In practice of course, students of r.e.t.a.r.dation test children by standardized scales. Testing a hundred 10-year-old children, the examiner might find a number who were able to do only those tests which are pa.s.sed by a normal six-year-old child. He might properly decide to put all who thus showed four years of r.e.t.a.r.dation, in the cla.s.s of feeble-minded; and he might justifiably decide that those who tested seven years (i.e., three years mental r.e.t.a.r.dation) or less would, for the present, be given the benefit of the doubt, and cla.s.sed among the possibly normal. Such a procedure, in dealing with intelligence, is necessary and justifiable, but its adoption must not blind students, as it often does, to the fact that the distinction made is an arbitrary one, and that there is no more a hard and fast line of demarcation between imbeciles and normals than there is between ”rich men” and ”poor men.”
[Ill.u.s.tration: CADETS ARRANGED TO SHOW NORMAL CURVE OF VARIABILITY
FIG. 14.--The above company of students at Connecticut Agricultural College was grouped according to height and photographed by A. F. Blakeslee. The height of each rank, and the number of men of that height, is shown by the figures underneath the photograph. The company const.i.tutes what is technically known as a ”population” grouped in ”arrays of variates”; the middle rank gives the median height of the population; the tallest array (5 ft., 8 in.) is the mode. If a line be drawn connecting the upper ends of the rows, the resulting geometric figure will be a ”scheme of distribution of variates” or more briefly a ”variability curve,” such as was shown in several preceding figures. The arrangement of h.o.m.ogeneous objects of any kind in such form as this is the first step in the study of variation by modern statistical methods, and on such study much of the progress of genetics depends.]
[Ill.u.s.tration: FIG. 15.--Height is one of the stock examples of a continuous character--one of which all grades can be found. As will be seen from the above diagram, every height from considerably under five feet to considerably over six feet can be found in the army, but extreme deviations are relatively rare in proportion to the amount of deviation.
The vertical columns represent the total number of individuals of a given height in inches. From Davenport.]
If a group of soldiers be measured as the children were measured for arithmetical ability, their height will be distributed in this same curve of probability. Fig. 14 shows the cadets of Connecticut Agricultural College; it is obvious that a line drawn along the tops of the files would again make the step-pyramid shown in Figures 10, 11 and 13. If a larger number were taken, the steps would disappear and give place to a smooth curve; the fact is well shown in a graph for the heights of recruits to the American Army (Fig. 15).
The investigation in this direction need not be pursued any farther. For the purpose of eugenics, it is sufficient to recognize that great differences exist between men, and women, not only in respect of physical traits, but equally in respect of mental ability.
This conclusion might easily have been reached from a study of the facts in Chapter I, but it seemed worth while to take time to present the fact in a more concrete form as the result of actual measurements. The evidence allows no doubt about the existence of considerable mental and physical differences between men.
The question naturally arises, ”What is the cause of these differences?”
The study of twins showed that the differences could not be due to differences in training or home surroundings. If the reader will think back over the facts set forth in the first chapter, he will see clearly that the fundamental differences in men can not be due to anything that happens after they are born; and the facts presented in the second chapter showed that these differences can not be due in an important degree to any influences acting on the child prior to birth.