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Abstract
In measuring visual acuity, the extremes of a set of normally distributed measures are of concern, together with one or more covariates. This leads to a model in which (X, Y 1, Y 2) are jointly normally distributed with Y 1, Y 2 exchangeable and (X, Y i ) having a common correlation. Inferential procedures are developed for correlations and linear regressions among X and the ordered Y values. This requires determination of the covariance matrix of X, Y (1) = min{Y 1, Y 2} and Y (2) = max{Y 1, Y 2}. The inadequacy of certain estimates that ignore the nonnormality of {X, Y (1), Y (2)} is also discussed. Although the bivariate case is emphasized because of the context of the visual acuity model, many results are given for the more general multivariate case.
