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1975•The Annals of StatisticsOpen access

Unbiasedness of the Chi-Square, Likelihood Ratio, and Other Goodness of Fit Tests for the Equal Cell Case

Arthur Cohen, Harold B. Sackrowitz

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Abstract

The chi-square test, likelihood ratio test, and other goodness of fit tests in a family are shown to have monotonic power functions, and hence are unbiased, for testing a simple hypothesis that all cell probabilities are equal. The chi-square test is also shown to be Type D for this situation.

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The chi-square test, likelihood ratio test, and other goodness of fit tests in a family are shown to have monotonic power functions, and hence are unbiased, for testing a simple hypothesis that all cell probabilities are equal. The chi-square test is also shown to be Type D for this situation.

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Available abstract

The chi-square test, likelihood ratio test, and other goodness of fit tests in a family are shown to have monotonic power functions, and hence are unbiased, for testing a simple hypothesis that all cell probabilities are equal. The chi-square test is also shown to be Type D for this situation.

Key concepts: Mathematics, Goodness of fit, Statistics, Chi-square test, Likelihood-ratio test, Pearson's chi-squared test, Square (algebra), Monotonic function

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