Grouping for Testing Trends in Categorical Data

In many studies there is believed to be a trend in a categorical variate with a continuous variate. Often in these cases it is desired to test for the trend using k groups formed from the continuous variable. This article is concerned with the grouping problem where the goal is essentially to maximize the asymptotic efficiency of the test. Optimal classes are given for k = 2, 3, 4, 5 and 6 for the uniform, normal and exponential distributions. Also, the number of groups to use and the “robustness” of the optimal grouping are investigated. It is noted that the “mathematical problem” in determining the optimal classes appears in other studies; a rationale for this is presented.