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Omnibus Tests for Multiple Binomial Proportions via Doubly Sampled Framework with Under-Reported Data

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  • Dewi Rahardja

    (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

Previously, Rahardja (2020) paper (in the first reference list) developed a (pairwise) multiple comparison procedure (MCP) to determine which (proportions) pairs of Multiple Binomial Proportions (with under-reported data), the significant differences came from. Generally, such an MCP test (developed by Rahardja, 2020) is the second part of a two-stage sequential test. In this paper, we derived two omnibus tests (i.e., the overall equality of multiple proportions test) as the first part of the above two-stage sequential test (with under-reported data), in general. Using two likelihood-based approaches, we acquire two Wald-type (Omnibus) tests to compare Multiple Binomial Proportions (in the presence of under-reported data). Our closed-form algorithm is easy to implement and not computationally burdensome. We applied our algorithm to a vehicle-accident data example.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:2:p:24-421:d:800597
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    References listed on IDEAS

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    1. Gordon J. Prescott & Paul H. Garthwaite, 2002. "A Simple Bayesian Analysis of Misclassified Binary Data with a Validation Substudy," Biometrics, The International Biometric Society, vol. 58(2), pages 454-458, June.
    2. Dewi Rahardja, 2019. "Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample," Stats, MDPI, vol. 2(1), pages 1-10, February.
    3. 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.
    4. Mary J. Morrissey & Donna Spiegelman, 1999. "Matrix Methods for Estimating Odds Ratios with Misclassified Exposure Data: Extensions and Comparisons," Biometrics, The International Biometric Society, vol. 55(2), pages 338-344, June.
    5. Boese, Doyle H. & Young, Dean M. & Stamey, James D., 2006. "Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3369-3385, August.
    Full references (including those not matched with items on IDEAS)

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