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

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Chapter 13

Tests on randomness

Section 13.1 deals with run tests. The Wald–Wolfowitz runs test, also known as the single-sample runs test, and the runs up and down test are the most common ones. For the definition of a run please refer to the Glossary (Appendix C). Section 13.2 covers successive difference tests (tests based on the difference of consecutive observations). We introduce the von Neuman test and its rank version also known as Bartels' test. All these tests are useful to test if a dataset is sampled randomly from the same distribution.

13.1 Run tests

13.1.1 Wald–Wolfowitz runs test

Description: Tests if a sample is sampled randomly from an underlying population.
Assumptions:
  • Data are at least measured on a nominal scale.
  • Let c13-math-0001 be a sequence of binary random variables with observations c13-math-0002. These may also be derived as dichotomized versions of random variables with originally multinomial or quantitative output.
  • The c13-math-0003 observations thereby contain c13-math-0004 elements with one of the outputs and with the other one.
Hypotheses: (A) Sequence is randomly generated
vs Sequence ...

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