Nonparametric tests for homoscedasticity in randomized complete block designs

Abstract

Variance assessment is a key component in robust design, process improvement, and reliability analysis, among other practical venues. However, most statistical development in nonparametric statistics has been focused on the problem of location changes, whereas the development of tests for homoscedasticity has been scarce, limited, in most cases, to one-factor analysis. By considering a blocking element, in the sense of Friedman, more power can be obtained by extending the approach to be used with linear rank transformations sensitive to scale changes. In this research, a total of 96 different new linear rank tests for homoscedasticity have been created, and their robustness and power evaluated through extensive Monte Carlo simulations. 36 of these tests showed to be either distribution robust or distribution free. 5 approaches of within the remaining tests acted consistently with high power over scale changes, and only 3 (Fligner-Killeen, squared ranks, and Talwar-Gentle, the three are aligned with the overall median) of these tests remained powerful when dealing with scale and location changes. Based on their performance, and ease of use, practitioners and researchers might find the results and recommendations of this work compelling and useful for their practice of data analysis when dealing with nuisance factors in the form of blocks.