Abstract

1. When a number of objects are presented for ranking by an observer there sometimes arise cases in which he is unable to express a preference in regard to certain of them and ' ranks them equal ' or regards them as ' tying'. The effect may arise either because the objects really are indistinguishable, so far as the quality under consideration is concerned, or because the observer is unable to discern such differences as exist. Ties of this character are by no means uncommon—and indeed may be more the rule than the exception in some classes of work—and it is desirable to have a systematic method of dealing with them. In this paper I consider the effect of ties on coefficients of rank correlation, the estimation of rankings and the measurement of concordance in judges. RANK CORRELATIONS 2. The method of allocating ranking numbers to tied individuals in general use is to average the ranks which they cover. For instance, if the observer ties the third and fourth members each is allotted the number 3£, and if he ties the second to the seventh inclusive, each is allotted the number £(2 + 3 + 4+5 + 6+7) = 4$. This is known as the mid-rank method and is the only one I shall consider. In fact I have seen only two other courses