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Art of Computer Programming, Volume 2, The: Seminumerical Algorithms by Donald E. Knuth

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3.3.1. General Test Procedures for Studying Random Data

A. “Chi-square” tests. The chi-square test (χ2 test) is perhaps the best known of all statistical tests, and it is a basic method that is used in connection with many other tests. Before considering the idea in general, let us consider a particular example of the chi-square test as it might be applied to dice throwing. Using two “true” dice (each of which, independently, is assumed to yield the values 1, 2, 3, 4, 5, or 6 with equal probability), the following table gives the probability of obtaining a given total, s, on a single throw:

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For example, a value of 4 can be thrown in three ways: ...

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