A Permutation S-sample Test Against Ordered Alternatives Based on Interval Data Samples
A distribution-free test is proposed that is an extension of the test by Jonckheere to interval data samples. Interval data are often obtained in the experiments in which the observation for each subject is specified only by an interval. We define a generalized sign of difference between two observations based on their interval data under the estimated distribution of each observation. The test statistic J is based on these generalized signs instead of ranks. Using the statistic J based on generalized signs, the hypothesis of no difference among the s treatments is tested against the alternatives of a definite order of these treatments. When s and sample sizes are small, we can derive the probability distribution of test statistic J exactly, but for large values of s and sample sizes the computations are impracticable. However, as J is then approximately normally distributed about zero, one requires the variance of J. We illustrate an easy calculation method of the variance of J and present a numerical example.