THE CORRELATION COEFFICIENT OF A 
POLYCHORIC TABLE. 
By a. RITCHIE-SCOTT, B.Sc. 
§ 1. Introduction. 
We have at our disposal a considerable number of mctliods for finding the 
coefficient of correlation between two characters from a table of frequencies. These 
methods may be summarily named and classified as follows: 
1. Product Moment. 
2. Tetrachoric r. 
3. Marginal centroids. 
4. Biserial r. 
5. Three Row rj. 
6. Variate difference methods including the correlation of grades and ranks. 
7. Equiprobable tetrachoric r. 
8. Mean contingency. 
9. Mean square contingency. 
Each of these methods has its own specially appropriate field of usefulness, but 
there still remains one class of table for which no entirely satisfactory methods have 
been devised, namely those which contain more than 2x2 cells and fewer than 
4 X 4, to which the tetrachoric and mean square contingency methods respectively 
may be applied. 
It was with a view to investigating satisfactory methods for such tables that the 
following work was undertaken. Such tables arise under many circumstances, 
particularly when we can, as in many psychological investigations which depend 
upon the instinctive judgment of some character, definitely assign individuals with 
pronounced characters to either end of a scale, but are compelled to relegate 
doubtful cases to an intermediate but somewhat indefinite category. We have, in 
a word, good, indifferent, bad; present, doubtful, absent — classifications resulting 
in a frequency table with three categories for one or both characters. 
In the present memoir a normal distribution has been assumed as it has been 
found to be not infrequently applicable and its assumption has given fairly satis- 
factory results even with distributions which are not strictly normal. 
§ 2. Notation. 
Let the normal surface (when standard deviations are used as units) 
