An Improved Hollander's Distribution-Free Test for Parallelism

摘要

Hollander (1970) proposed a distribution-free signed rank test for testing parallelism of two regression lines. Hollander's test requires that the number of pairs of data in the two datasets must be equal and even. This requirement of the test is met by discarding observation pairs randomly from one or both datasets as needed. In this article, we propose that instead of discarding the observation pairs randomly, we add observation pairs randomly in one or both datasets as needed to meet the requirement of Hollander's test. By using simulation technique we show that the new test is a significant improvement over the original test of Hollander since the new test is consistently more powerful than the original test and provides narrower confidence intervals for the difference of the two slopes of the regression lines.