The Determination of Intra-Class and Inter-Class Equivalent Probability Coefficients of Correlation

In many cases individuals which must be classified in two alternative categories (such as male or female, died or survived) are associated for some logical reason into groups or classes. Thus, for example, a family of w children may contain x males and y females. Again, out of a series of plantings each of w seeds, x may produce plants while y may fail to germinate. When individuals of character x and y are thus associated in classes of size w for some biological reason, the question must frequently arise as to whether such individuals of character x (or y) are distributed among the classes at random, or whether there is a statistically significant deviation from a random distribution due to some factor or factors which tend to produce a definite excess of individuals of character x (or y) in certain classes and a corresponding deficit in other classes. Heretofore such problems have generally been dealt with by comparison of the empirical frequency distributions, or of some constant of the empirical frequ...