Comparison of Two Distribution-Free Procedures for Multiple Comparisons With a Control

Abstract

Chakraborti and Desu (1988) presented a distribution-free procedure for testing that k (≥1) distributions are equal to a control distribution. They compared their procedure, a generalization of the test proposed by Mathisen (1943), to the procedure proposed by Slivka (1970). They asserted that their procedure has shorter expected duration than Slivka's procedure in life-testing experiments where observations become available in an ordered manner. Here it is proven that, in fact, Slivka's procedure has shorter duration in such circumstances. Normal approximations are presented which indicate that their procedure requires a smaller sample size to guarantee a specified power for Lehmann alternatives and proportional hazard alternatives when all observations are to be observed.

Keywords:

• distribution-free
• multiple comparisons
• control distribution
• Lehmann
• alternatives
• proportional hazards alternatives