Rank Correlation Between Two Variables, One of Which Is Ranked, the Other Dichotomous

Rank correlation is one of the most useful statistical techniques available for the treatment of data arising in experimental and applied psychological research. Chambers (1946) has indicated the type of data most frequently occurring in these fields, and has pointed out the advantages of Kendall's r over Spearman's p or any form of transformation to ordinal form. Given the use of T when tied rankings are present (Kendall, 1946) it seemed possible to extend the method to cover a very common problem in psychology, namely, determination of the relation between two variables, one of which is expressed as a ranking and the other as a dichotomy. In applied or field work the relation of a psychological 'measurement' and an external criterion nearly always appears in this form. The usual method of determining the relationship consists of reducing the ranking to a dichotomy and calculating x2 for the 2 x 2 table which results. That this may lead to inaccuracy can be seen from the following example: