A Note on a New Class of Distribution-Free Tests for the Two-Sample Scale Problem Based on Subsample Medians

Abstract

A fundamental problem encountered in statistics is that of testing the equality of two population parameters those measure variability. There are several tests available in the literature for the two-sample scale problem. However, much attention has not been given to the tests that take care of

Two Sample Test for Censored Data Based on Sub-Sample Medians

“…In case of uncensored data, for comparative studies between two treatments most commonly used nonparametric procedures are Kochar [6], Deshpande and Kochar [7], Stephenson and Ghosh [8], Kumar [9], Kumar et al [10], Shetty and.Pandit [11], Shetty and Umarani [12], Mahajan et al [13], Kössler and Kumar [14], Kumar and Goyal [15], Goyal and Kumar ([16], [17]). Brookmeyer and Crowley [18] introduced a method for comparing medians of several survival distributions for right censored data.…”

Class of Tests Based on Subsample Quantiles for Two-sample Scale Problem

“…Tests due to [1,2,3,4] are some of the earlier tests designed based on the two-sample U-statistics. Also, [5][6][7][8][9][10][11][12][13] study this problem using U-statistics approach. The asymptotic properties of the U-statistics are discussed in [1].…”

“…The asymptotic properties of the U-statistics are discussed in [1]. Some more distribution-free tests proposed for two-sample scale problem that explore [9] are ‫ܵܤ‬ ଵ due to [14], ‫ܵܤ‬ ଶ and ‫ܵܤ‬ ଷ due to [15], ‫ܵܤ‬ ସ and ‫ܵܤ‬ ହ due to [16], ‫ܵܤ‬ due to [17] and ‫ܵܤ‬ due to [18]. The test in [14] is based on the subsample medians and hence is resistant to the outliers in both the samples.…”

“…In this paper, we propose a class of tests based on subsample quantiles, ܳ ఈ,ఉ ሺܾ, ݀ሻ for two-sample scale problem. This is a general class of tests that includes [2,3,9,[14][15][16][17][18] as its subclasses. Also, it includes the classes of tests which are resistant to outliers in ܻ-sample and extract information from tails of the distribution of ܺsample discussed in this paper.…”

A Nonparametric Test For Homogeneity Of Variances: Application To GPAs Of Students Across Academic Majors

“…If the population centers are unknown and unequal, then Moses (1963) and Blair and Thompson (1992) rank-like procedures are among the very few truly distribution-free tests for the two-sample scale problem. For a literature review on the two-and multi-sample scale problems, see Duran (1976), Daniel (1979), Conover et al (1981) and Shetty et al (2004). To better understand the proposed procedure, we first need to summarize (in Section 2) Bakir's (1989) ANOMR procedure for testing the equality of several population means.…”