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Testing for positive evidence of equally likely outcomes

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  • Frey, Jesse

Abstract

Goodness-of-fit tests allow one to conclude that k possible outcomes are not equally likely. In this paper, we develop an exact equivalence test that allows one to conclude that k possible outcomes are approximately equally likely. We show that the power properties of the test compare favorably to those of possible alternative tests, and we develop an associated simultaneous confidence interval procedure. We apply the test to data sets on the digits of [pi], winning roulette numbers, and winning numbers from the Pennsylvania Lottery.

Suggested Citation

  • Frey, Jesse, 2012. "Testing for positive evidence of equally likely outcomes," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 48-57, January.
    • Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:48-57
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    References listed on IDEAS

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    1. Rachel Croson & James Sundali, 2005. "The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos," Journal of Risk and Uncertainty, Springer, vol. 30(3), pages 195-209, May.
    2. Neil H. Spencer, 2009. "Overcoming the multiple‐testing problem when testing randomness," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 543-553, September.
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    Cited by:

    1. A. Hayter, 2014. "Recursive formulas for multinomial probabilities with applications," Computational Statistics, Springer, vol. 29(5), pages 1207-1219, October.

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