A NOTE OF THE INTERPRETATION OF THE RIDIT AS A QUANTILE RANK1

Abstract

Kantor, S. (2211 Main St., Buffalo, N. Y. 14214), W. Winkektein, Jr. and M. A. Ibrahim. A note on the interpretation of the rid it as a quantile rank. Amer. J. Epid., 1968, 87: 609–615.—Ridit analysis was introduced by Bross to summarize data which cannot be optimally described by means of a nominal classification but do tot satisfy the requirements of a refined measurement system. Although alluding \o the ridit's relationship to rank-order statistics, Bross did not describe the precise lature of this relationship. The importance of such a description is underscored by the understandable reluctance of epidemiologists to utilize a statistic whose explicit meaning is unclear or overly The precise relationship is as Follows: in ranking an array of observations, the quantile (or percentile) rank is *he proportion of observations lying below the corresponding integer rank (adjusted upward one-half unit). In ordered categorical data each category may be represented numerically by an integer rank. If, in addition. It is desired to make he value of the category's rank proportionate to the number of observations it rontalnj, one can assign to the category the Median or Mean of the intra-category ranks. Correspondingry, the average quantile rank, or ridit, is the proportion of observations lying below the average integer rank of each category.