must form a contingency table, in which the rows are the distributions of mental capacity in each school, so that in the case of the boys we have a five x twelvefold contingency table, and in the case of the girls a five x thirteen-fold contingency table. If now the contingency coefficients be calculated from these tables, we have two numbers which express the degree of heterogeneity among the boys' and girls' schools respectively. If the proportions in each grade of mental capacity were the same for all the schools, then this coefficient would be zero, while the maximum amount of divergence would be represented by a coefficient of unity, and the higher the coefficient the greater the degree of heterogeneity. Actually those coefficients were found to be: In the face of such divergence as is represented by these numbers we are compelled to assert that either the schools, and each department of the schools, represent highly differentiated grades of intelligence, or that there has been far too much scope left for the play of personal equation. There can be little doubt that personal equation and not local differentiation contributes the bulk of the heterogeneity. No conventional use of the word "brilliant" would admit of our returning 33 per cent. of the scholars—even in a middle-class scholarship preparatory school-as of "brilliant" intelligence. The word has evidently been used in a personal sense peculiar to the head master or mistress. We may be satisfied that the "brilliant" class in this school has intelligence of a higher grade than those classed as "above the average " in the same school, but it is clearly impossible to pool such estimates with those of another school in which the "brilliant" children form only 4 per cent., say, of the population. It is clear that each school must be dealt with separately, and this immensely increases the labour of reduction and decreases the certainty of and weight to be given to our conclusions. Believing that the heterogeneity above measured is principally due to personal equation, it will not be without interest to observe how far the individual schools differ from the average of all schools in the use of the terms employed by the teachers, by estimating the relative heterogeneity of the individual schools. To do so we must form a contingency table consisting of two rows only, one row consisting of the mental capacity distribution of a single school, and the other row, of the distribution of all the other schools taken together. The contingency coefficient found from this table gives a measure of the relative agreement of the individual schools with the general "norm". These coefficients are given in Table III. This table confirms what has already been found from Table II, that the estimation by the teachers of the mental capacity of the children has not been reduced to any standard value. In all probability this is due to the fact that a system of marks such as that adopted and the rather loose categories "average", under the average", &c., which they represent, did not demand sufficient preliminary thought on the part of the teachers. 66 Much better results were obtained by Professor Pearson's more elaborate and more definite scale of mental capacity.* But it must be remembered that in Professor Pearson's investigation, all those who sent in returns were volunteers, and the bulk of them secondary school teachers, while in the present case the return was compulsory and was probably resented by a few as an extra, and perhaps in their opinion an unnecessary duty. It is probable also that some teachers imagined that to enter any children as very dull and backward" would in some way or other be to their disadvantage. A little consultation, however, between head master or head mistress and the members of the staff, followed by a slight examination of the returns, would probably have eliminated some of the greater divergences. 66 It will be seen at once that from this standpoint this pioneer survey has a most valuable lesson to teach us. There must be a preliminary standardization of the teachers who are called upon to estimate the intelligence of their pupils. It is idle to assert that there is no such thing as "general intelligence"; it may be difficult to find a satisfactory means of measuring it, but measure it we must if we are to obtain any useful facts from these school surveys. In the battle of life * Biometrika, vol. v, p. 107. it is general intelligence which grades men, and that is what we seek to measure, imperfectly it may be, by the system of examinations or in practical affairs by our experience of men. Under a good system of closely defined categories we believe that two experienced teachers will show only a small percentage of divergence in classifying pupils with whose work they have been familiar for some time. But even without this system, would not the results of general examinations for each standard provide a better test of general intelligence than we have had to deal with above? It is usual in this country for a child to advance a standard a year, and the place in the standard is usually known each year by examination. We might therefore propose to adopt as our standard the grade of the child, i. e. 100 × place in standard ÷ number examined. This would require correction for age, but this correction might be made once for all by ascertaining the correlation for the same standard between place and age. Thus a child's intelligence would be measured by the deviation of its grade in the standard from the mean grade of children of that age in the standard. This would very considerably reduce the personal equation, especially in the case of teachers who are not apt psychological observers. Some day we may hope that examinations may be skilfully devised for the very purpose of grading the intelligence of school children; these examinations would be accompanied by various psychological tests, but we are somewhat removed from this at present, and also from being able to base a satisfactory measure of general intelligence even on the results of such mental tests, if they were made. The wisest course at present seems to be to determine place in standard, corrected for age, and compare this with the teacher's estimate of the intelligence of the children obtained by carefully defined verbal categories. (5) GENERAL SCALE OF INTELLIGENCE. Even with such heterogeneous material, however, there is some advantage to be gained by a study of the distribution of the mental capacity of all the children of the same sex together. The numbers and percentages of boys and girls in each grade of intelligence are given in Table IV. TABLE IV. THE NUMBERS AND PERCENTAGES IN FIVE GRADES OF MENTAL CAPACITY. It will be seen that the percentages of "brilliant" and "above the average boys are somewhat higher than in the case of the girls, but the differences are small and not necessarily significant. If we now make the assumption that mental capacity follows the normal or Gaussian curve of errors, it is possible to express this qualitative scale in quantitative form. Taking first of all as our unit the standard deviation of mental capacity, σ, we can find the range of each grade of intelligence, the whole range ∞ to + ∞. extending from The results are given in Table V, and we see that in the case of the boys the "brilliant" group extends from + ∞ to +1.294 σ, the "above the average group from 1.294 o to +414 o, the " + group + σ from 414 to 815, and so on. average TABLE V. RELATIVE SCALES OF MENTAL CAPACITY WITH THE STANDARD DEVIATION AS UNIT AND WITH MEANS SUPPOSED TO BE IDENTICAL. These results may now be compared with a similar distribution found for the school children of Professor Pearson's investigation, which has already been quoted. The results are given in the second part of Table V, and the results are also compared graphically in Fig. 1. Such a method of comparison, however, assumes that the average intelligence in the two series is the same, and also the variability is the same; but there is no reason for supposing that this is the case. Each series is selected from the |