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Multiple Comparison Procedures for the Differences of Proportion Parameters in Over-Reported Multiple-Sample Binomial Data

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  • Dewi Rahardja

    (U.S. Department of Defense, Fort Meade, MD 20755, USA
    Disclaimer Statement: This research represents the author’s own work and opinion. It does not reflect any policy nor represent the official position of the U.S. Department of Defense nor any other U.S. Federal Agency.)

Abstract

In sequential tests, typically a (pairwise) multiple comparison procedure (MCP) is performed after an omnibus test (an overall equality test). In general, when an omnibus test (e.g., overall equality of multiple proportions test) is rejected, then we further conduct a (pairwise) multiple comparisons or MCPs to determine which (e.g., proportions) pairs the significant differences came from. In this article, via likelihood-based approaches, we acquire three confidence intervals (CIs) for comparing each pairwise proportion difference in the presence of over-reported binomial data. Our closed-form algorithm is easy to implement. As a result, for multiple-sample proportions differences, we can easily apply MCP adjustment methods (e.g., Bonferroni, Šidák, and Dunn) to address the multiplicity issue, unlike previous literatures. We illustrate our procedures to a real data example.

Suggested Citation

  • Dewi Rahardja, 2020. "Multiple Comparison Procedures for the Differences of Proportion Parameters in Over-Reported Multiple-Sample Binomial Data," Stats, MDPI, vol. 3(1), pages 1-12, March.
    • Handle: RePEc:gam:jstats:v:3:y:2020:i:1:p:6-67:d:331473
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    References listed on IDEAS

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    1. Stamey, James D. & Bratcher, Tom L. & Young, Dean M., 2004. "Parameter subset selection and multiple comparisons of Poisson rate parameters with misclassification," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 467-479, April.
    2. Dewi Rahardja & Ying Yang, 2015. "Maximum likelihood estimation of a binomial proportion using one-sample misclassified binary data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 272-280, August.
    3. Alberto Gianinetti, 2020. "Basic Features of the Analysis of Germination Data with Generalized Linear Mixed Models," Data, MDPI, vol. 5(1), pages 1-42, January.
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    Cited by:

    1. Dewi Rahardja, 2022. "Omnibus Tests for Multiple Binomial Proportions via Doubly Sampled Framework with Under-Reported Data," Stats, MDPI, vol. 5(2), pages 1-14, April.
    2. Marian Reiff & Erik Šoltés & Silvia Komara & Tatiana Šoltésová & Silvia Zelinová, 2022. "Segmentation and estimation of claim severity in motor third-party liability insurance through contrast analysis," Equilibrium. Quarterly Journal of Economics and Economic Policy, Institute of Economic Research, vol. 17(3), pages 803-842, September.

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