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Exact-Permutation-Based Sign Tests for Clustered Binary Data Via Weighted and Unweighted Test Statistics

Author

Listed:
  • Janie McDonald

    (Clemson University)

  • Patrick D. Gerard

    (Clemson University)

  • Christopher S. McMahan

    (Clemson University)

  • William R. Schucany

    (Southern Methodist University)

Abstract

Clustered binary data occur frequently in many application areas. When analyzing data of this form, ignoring key features, such as the intracluster correlation, may lead to inaccurate inference, e.g., inflated Type I error rates. For clustered binary data, Gerard and Schucany (Comput Stat Data Anal 51:4622–4632, 2007) proposed an exact test for examining whether the marginal probability of a response differs from 0.5, which is the null hypothesis considered in the classic sign test. This new test maintains the specified Type I error rate and has more power, when compared to both the classic sign and permutation tests. The test statistic proposed by these authors equally weights the observed data from each cluster, regardless of whether the clusters are of equal size. To further improve the performance of the Gerard and Schucany test, a weighted test statistic is proposed and two weighting schemes are investigated. Seeking to further improve the performance of the proposed test, empirical Bayes estimates of the cluster-level success probabilities are utilized. These adaptations lead to 5 new tests, each of which are shown through simulation studies to be superior to the Gerard and Schucany (Comput Stat Data Anal 51:4622–4632, 2007) test. The proposed tests are further illustrated using data from a chemical repellency trial.

Suggested Citation

  • Janie McDonald & Patrick D. Gerard & Christopher S. McMahan & William R. Schucany, 2016. "Exact-Permutation-Based Sign Tests for Clustered Binary Data Via Weighted and Unweighted Test Statistics," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 698-712, December.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:4:d:10.1007_s13253-016-0261-6
    DOI: 10.1007/s13253-016-0261-6
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    References listed on IDEAS

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    1. Gerard, Patrick D. & Schucany, William R., 2007. "An enhanced sign test for dependent binary data with small numbers of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4622-4632, May.
    2. Martin S. Ridout & Clarice G. B. Demétrio & David Firth, 1999. "Estimating Intraclass Correlation for Binary Data," Biometrics, The International Biometric Society, vol. 55(1), pages 137-148, March.
    3. Dean A. Follmann & Michael A. Proschan, 1999. "Valid Inference in Random Effects Meta-Analysis," Biometrics, The International Biometric Society, vol. 55(3), pages 732-737, September.
    4. Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2007. "A weighted multivariate sign test for cluster-correlated data," Biometrika, Biometrika Trust, vol. 94(2), pages 267-283.
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    Cited by:

    1. Monjed H. Samuh & Fortunato Pesarin, 2018. "Applications of conditional power function of two-sample permutation test," Computational Statistics, Springer, vol. 33(4), pages 1847-1862, December.

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