A Generalized Wilcoxon Test for Comparing Interval Data Samples
A distribution-free two-sample test is proposed that is an extension of the Wilcoxon test to interval-censored data or more generally to interval data samples. Interval-censored data are often observed in medical or biological studies and the idea of interval data is extension of interval-censored data. We define a generalized sign of difference between two observations based on their interval data under the estimated distribution of each observation. The generalized sign may be interpreted as the probability that the one is larger than the other. The test statistic is defined as the sum of the generalized signs based on all combinations of the two samples. The test is conditional on the pattern of observations. The null hypothesis is H0 : F (t) = G (t) against either H1 : F (t) < G(t) or H2 : F(t) < G(t) or F(t) > G(t), where F, G are cumulative distribution functions of the observations. The test is shown to be asymptotically normal. Working examples are presented and the tests are performed by a BASIC program which was developed for the proposed test.