Quantile-based Nonparametric Test for Comparing Two Diagnostic Tests

Diagnostic test results, which are approximately normal with a few number of outliers, but non-normal probability distribution, are frequently observed in practice. In the evaluation of two diagnostic tests, Greenhouse and Mantel (1950) proposed a parametric test under the assumption of normality but this test is inappropriate for the above non-normal case. In this paper, we propose a computationally simple nonparametric test that is based on quantile estimators of mean and standard deviation, instead of the moment-based mean and standard deviation as in some parametric tests. Parametric and nonparametric tests are compared with simulations under the assumption of, respectively, normality and non-normality, and under various combinations of the probability distributions for the normal and diseased groups.