# Chapter 5

# The Two-Sample Dispersion Problem and Other Two-Sample Problems

# Introduction

In this chapter the data once again consist of two independent random samples, one sample from each of two underlying populations. This is the same as the data setting considered in Chapter 4, where we discussed procedures designed for statistical analyses in which the primary interest was on possible differences in the locations (medians) of the populations. In this chapter we deal with statistical procedures designed to make inferences about possible differences other than location between two populations.

In Section 5.1 we present a distribution-free rank test for the hypothesis of equal scale parameters when the two underlying populations have a common median. Section 5.2 is devoted to an asymptotically distribution-free test for equality of scale parameters when the assumption of common medians is not justified. In Section 5.3 we consider a distribution-free rank test for the dual hypothesis of equal location and equal scale parameters for the underlying populations. Section 5.4 contains a distribution-free test of the general hypothesis that two populations are identical in all respects. Some aspects of the asymptotic relative efficiencies of the procedures in this chapter with respect to their normal theory counterparts are discussed in Section 5.5.

**We obtain observations and**

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