Methods of computation
Coefficients of Correlation and Regression from a Double-Frequency Table. A short-cut method of calculating coefficients of simple correlation from double-frequency tables is given in previous editions (pages 455 to 457 in the second edition). It is omitted from this edition.
Use of the Check Sum. Where a number of different variables are involved, every operation in making the extensions, computing the averages and corrections, and solving the normal equations through to the "back solution," can be verified by an automatic check known as the "check sum." The way in which the check sum is used will be illustrated by a small problem, carried through every step in turn, but it is equally applicable to any other other method of tabulation and is especially valuable with machine tabulation, where it serves as an overall control on the accuracy of the machine processes.
THE CHECK SUM AS A CHECK IN EXTENDING. The values in the following table (Table A2.1) may be used to illustrate the use of the check sum.
The values in the columns X2, X3, X4, and X1, are the three independent factors and the dependent factor, which are to be correlated. The values in the column headed "∑X" are the arithmetic totals of the values for the four other variables, and are designated "the check sum."
As the first step, each of these five columns is added. Since, for each line, X2 + X3 + X4 + X1 = ∑X it also holds true that ∑X2 + ∑X3 + ∑X4 + ∑X1 = ∑(∑X)