6ΣD2

Spearman's Equation is r= 1—

in which

N(N21)

r is the coefficient of correlation;

D is the difference in rank of a pair of scores;

N is the number of cases in the array under consideration;
Σ is the sum.

The quantity ED2 is obtained by finding the D's in each of the twenty cases, squaring each, and adding. Taking A in Table I we find that his rank in scholarship is 7 and in activities 1. Since 7 is 6 more than 1 we place 6 in the plus column under "Differences in Rank." For L we find that the rank in scholarship, 9.5, is less than the rank in activities by 3.5. We, therefore, enter 3.5 under the minus column. Since no student in this class had the same rank in both of the qualities under consideration, no entry is made in the zero column which would indicate that there is no difference in rank. It should be noted here that the sum of the positive differences must equal the sum of the negative differences. Otherwise an error in computation is indicated. In this table the sum of the differences for each is 49.

In Table I ΣD 2 is found to be 659.5. N is 20 in this as in all the tables. Substituting these values, the solution for the coefficient of correlation is as follows: