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Testing the equality of several binomial proportions to a prespecified standard

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  • Kulkarni, Pandurang M.
  • Shah, Arvind K.

Abstract

Testing the equality of several binomial proportions was first proposed by Pearson (1900) and the discussion of this test can be found in standard statistics books. In this article we consider testing the equality of several binomial proportions to a known standard. For testing such a hypothesis against a two sided alternative, an intuitive test statistic and its null distribution have been mentioned in Rohatgi (1976). Here we study the non-null distribution of that statistic and provide a simple way of calculating the approximate power via a moment approximation method (MAM). A procedure of constructing simultaneous confidence intervals is also given here. Additionally, we propose test statistics for testing the above null hypothesis against one sided alternative hypotheses. We give simple methods of obtaining the p-value and the power for these test statistics. Finally, two examples are given to illustrate the techniques.

Suggested Citation

  • Kulkarni, Pandurang M. & Shah, Arvind K., 1995. "Testing the equality of several binomial proportions to a prespecified standard," Statistics & Probability Letters, Elsevier, vol. 25(3), pages 213-219, November.
    • Handle: RePEc:eee:stapro:v:25:y:1995:i:3:p:213-219
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    References listed on IDEAS

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    1. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
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    Cited by:

    1. Cai, Yong & Krishnamoorthy, K., 2005. "A simple improved inferential method for some discrete distributions," Computational Statistics & Data Analysis, Elsevier, vol. 48(3), pages 605-621, March.
    2. Man Lai Tang & Ka Ho Wu, 2005. "A unified sequential test procedure for simultaneous testing the equality of several binomial proportions to a specified standard," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(6), pages 617-624.
    3. Krishnamoorthy, K. & Thomson, Jessica & Cai, Yong, 2004. "An exact method of testing equality of several binomial proportions to a specified standard," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 697-707, May.

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