TABLE Z 2.

Individual highest places attained in competition within each class.

age in this table is only 29 (line 24). So that the question at the present stage is: Shall we try to force 82% of high-school men to go first to college for one or two years to develop highest powers, if, after all, 71% in the 82% will not develop such powers? Obviously, in this paper we venture merely to put the question, because the number of C2 men here under test was too small for safely making broad generalizations. But we do put the question; because if these figures are verified on a larger scale, it seriously affects the utility of the proposed measureat least so far as the proposal rests on some assumed benefits to legal scholarship.

FOURTH TEST.
TABLES Q1, 2.

This test consists in finding for each student a single figure representing his net percentage-grade of attainment, and then in arranging them according to decimal sections; thus, upon ascertaining how many of each group (H and C) fall into the several decimal sections, respectively, the median value appears. By transmuting these numbers of each section into an identical percentage-scale, and by plotting the numbers in a curve, the distribution can be appreciated graphically with more ease.

This method, it should be explained, has been publicly advocated as the most scientific by Dr. Winfield Scott Hall, Associate Dean of the Medical Faculty of Northwestern University, and Professor of physiology in that Faculty. In three articles' published by him he has expounded the scientific basis and the utility of this test. Briefly stated, his articles remind us that the anthropological researches of Quetelet, Galton, and others, have shown that for relatively small numbers of observed instances in biological data the median value is more trustworthy than the average value. He exhibits researches of his own in confirmation.

1" Changes in the Proportions of the Human Body," Journ. Anthrop. Inst., London, 1895; "Evaluation of Anthropometric Data," Journ. Amer. Medical Assoc., Chicago, Dec. 21, 1901; "Guide to the Equitable Rating of Students," School Science, 1906.

He notes that the psychologists also use this median value.' He further points out that the intellectual process of studious attainment is a biological process which must conform to biological laws; and that, therefore, the results of examinations have a normal line of distribution. Any variance from this normal line of distribution indicates some peculiarity in either the instructor who marks or in the class which is examined. He further believes he has demonstrated that the normal curve of distribution corresponds to the curve of a series of binomial coefficients, raised in the usual way on the binomial theorem. Without dwelling on this special discovery of his (extraordinary and significant, no doubt), we note here merely that this table purports to use the test of median value, as employed by anthropologists, i. e., the value or grade of attainment possessed by the middle person in the group. The average value would be the total values divided by the number of individuals; the median value is that of the middle person in the total series of persons, who is thus the type of the group.

To ascertain this value, the following process was used: Each student's marks of each grade were reduced to a single net percentage by multiplication and division; i. e., his units of A marks were multiplied by 95, B by 75, C by 50, and D by 30; this total was then divided by the total units of all his marks; for example, for a student having the record A 20, B 40, C 10, D 2, the 20 was multiplied by 95, and so on, the sum divided by 72 (his total marks), giving 76 as his percentage figure. On a decimal scale the total number of individuals in each decimal section was placed (Table Q 1). But since the total numbers of persons in the groups H and C were different, a just comparison required these section totals to be turned into percentages of the group totals; this result is shown in Table Q 2. Then these section totals were plotted on a curve graphically (Table Q 3).

1

1 Professor Palmer uses it in his recent volume, "The Teacher," p. 185 (1909).

2

Since the lowest possible per cent would be 30, and the highest possible per cent would be 95, the ends of the curve are not in exact relation. But with the A, B, C, D system of marking, no closer approach to percentages is possible.

The Table Q shows four varieties of results: (1) The median value, (2) the attainments of the bulk of the group, (3) the highest attainments, (4) the lowest attainments.

(1) The median value, i. e., the percentage-quality of work done by the middle man in each group is revealed as follows: Ha, 73; Hb, 73.7; H, 73.3; C2, 76.4; C4, 78.5; C, 78.2; HC,

TABLE 1.-Median value (actual numbers).

75.8. Thus, between H and C, is found a difference of only

4.9 per cent.

(2) The attainments of the bulk of each group fall between 60 and 90 per cent; i. e., 90 per cent of the H group and 90 per cent of the C group fall within grades of passable and high quality.

(3) The lowest attainments fall exclusively in the H group; i. e., 7.5 per cent fall below the 60 per cent grade.