Since its inception, ridit analyses has been in widespread use in epidemic-logic studies where the data are ordered but are not on an interval scale. However, no mathematical properties of ridits have been given. In this paper, we use a squared error loss function to show that, for a particular class of distribution functions, ridits form a best invariant estimate of the unknown distribution function. Under another class of distribution functions, we derive another estimate, m-ridits, of the distribution function. Data are used to compare these two scores with the scores obtained from the empirical distribution function and the original scores used on the data. The results indicate that, although these scores are numerically different, the same inferences can be drawn.
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