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Statistical Hypothesis Testing with SAS and R by Dirk Taeger, Sonja Kuhnt

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Chapter 9

Tests on scale difference

In this chapter we present nonparametric tests for the scale parameter. Actually, it is tested if two samples come from the same population where alternatives are characterized by differences in dispersion. These tests are called tests on the scale, spread or dispersion. The most famous one is the Siegel–Tukey test (Test 9.1.1). The introduced tests can be employed if the samples are not normally distributed, but the equality of median assumption is crucial.

9.1 Two-sample tests

9.1.1 Siegel–Tukey test

Description: Tests if the scale (variance) of two independent populations is the same.
Assumptions:
  • Data are measured at least on an ordinal scale.
  • Samples c09-math-0001 and c09-math-0002 are independently drawn from the two populations, c09-math-0003.
  • The random variables c09-math-0004 and c09-math-0005 are independent with continuous distribution functions c09-math-0006 and , scale parameters and median . It holds that .

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