Methods involving rankings have been used by psychologists for half a century; and, although in their early development they were subjected to severe criticism, recent years have brought their rehabilitation and extension in new directions. Current interest in ranking methods has been displayed in several papers published in this Journal and very recently in the correspondence by Burt and Morris (1953). The present paper investigates theoretically the magnitude of the correlation between observations and the rank values by which they are sometimes replaced. It is found that in samples from the two most commonly considered types of statistical distribution, the normal and the uniform, this correlation is very high. With a sample as small as 25, it is .94 for the normal distribution and .96 for the uniform distribution; and these values increase, with sample size, towards limits of .98 and 1 respectively. In these circumstances there is justification for replacing the original observations by their ranks, since the consequent saving in computation entails very little loss of efficiency. The results of the investigation also turn out to have bearing on other matters of theoretical interest.
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Alan Stuart (1954) studied this question.