In each diagram a heavy diagonal line shows approximately where the plotted points would fall if the relationship were perfect between the numbers of errors in the educational measurements and the other measure of ability. It is clear that the relationship shown in each diagram is far from perfect, but it is not clear from the diagrams which rating of the teacher is most nearly approximated by the educational measurement scores. To discover this relative degree of relationship, a mathematical calculation must be made. For the purposes of testing the correspondence between the scores in the various Mentimeter tests and the production records or supervisor’s ratings of the group of persons tested, it is sufficient to calculate what is best called “a coefficient of coördination.”[7] Footnote 7: Calculated by a somewhat more complex formula, approximately the same measure of relationship might be found, called by the more familiar name “coefficient of correlation.” The first step in the calculation of a coefficient of coördination is the transformation of the original scores into figures indicating order of merit. In the case of the sixth-grade class here referred to, the teacher’s ratings of intelligence need not be changed, for they are exactly the kind of ratings necessary: 1 indicating the brightest and 28 the dullest pupil, so far as the teacher was able to judge her pupils at the end of a year’s work. Since the educational measurements scores reported are the number of errors made by each child, the rank of the child making the smallest numbers of errors will be 1, while the rank of the pupil making the largest number of errors will be 28. On the other hand, the scholarship marks are the summaries of the teacher’s percentage marks for a half year, hence the best pupil is the one making the highest percentage. In scholarship, then, the highest percentage should get the rank of 1 and the lowest percentage a rank of 28. [Illustration: Graphic picture of relation between test results and intelligence ratings given by teacher] [Illustration: Graphic picture of relation between test results and scholarship marks given by teacher]