Skip to main content
Log in

Testing Marginal Homogeneity in Matched-Pair Polytomous Data

  • Statistics
  • Published:
Drug information journal : DIJ / Drug Information Association Aims and scope Submit manuscript

Abstract

Statistical tests for assessing marginal homogeneity of matched-pair polytomous data can be classified as a score-type test or a Wald-type test; the Wald-type Bhapkar test is a more powerful alternative to the score-type Stuart–Maxwell test, and the Bhapkar test tends to be liberal. Extending the authors’ earlier work, an additional test of each classification is proposed for testing marginal homogeneity, and the relationships among the available test statistics are established. The results from some limited simulation study suggest that the new proposals are very competitive alternatives to the extant methods. These results are the basis of the authors’ recommendations to practitioners. Information from SAS procedure PROC CATMOD regarding Bhapkar’s test statistic and the relationship among the test statistics make their implementation and calculation convenient and accessible to interested researchers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. McNemar Q. Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika. 1947;16:153–157.

    Article  Google Scholar 

  2. Stuart A. A test for homogeneity of the marginal distributions in a two-way classification. Biometrika. 1955;42:412–416.

    Article  Google Scholar 

  3. Maxwell AE. Comparing the classification of subjects by two independent judges. Br J Psychiatry. 1970;116:651–655.

    Article  CAS  Google Scholar 

  4. Bhapkar VP. A note on the equivalence of two test criteria for hypotheses in categorical data. J Am Stat Assoc. 1966;61:228–235.

    Article  Google Scholar 

  5. Yang Z, Sun X, Hardin JW. Testing marginal homogeneity in clustered matched-pair data. J Stat Plan Infer. 2011;141:1313–1318.

    Article  Google Scholar 

  6. Obuchowski NA. On the comparison of correlated proportions for clustered data. Psychometrika. 1998;17:1495–1507.

    CAS  Google Scholar 

  7. Bennett BM. Tests of hypotheses concerning matched samples. J Roy Stat Soc B. 1967;29:468–474.

    Google Scholar 

  8. Ireland CT, Ku HH, Kullback S. Symmetry and marginal homogeneity of an r × r contingency table. J Am Stat Assoc. 1969;64:1323–1341.

    Google Scholar 

  9. Krauth J. A comparison of tests for marginal homogeneity in square contingency tables. Biometrical J. 1985;27:3–15.

    Article  Google Scholar 

  10. Keefe TJ. On the relationship between two tests for homogeneity of the marginal distributions in a two-way classification. Biometrika. 1982;69:683–684.

    Article  Google Scholar 

  11. Shoukri MM. Measures of interobserver agreement. New York, NY: Chapman & Hall/CRC; 2004.

    Google Scholar 

  12. Westlund KB, Kurland LT. Studies on multiple sclerosis in Winnipeg. Manitoba and New Orleans, Louisiana. Am J Hyg 1953;57:380–396.

    CAS  PubMed  Google Scholar 

  13. Sun X, Yang Z. Generalized McNemar’s test for homogeneity of the marginal distributions. SAS Global Forum 2008. https://doi.org/www2.sas.com/proceedings/forum2008/382-2008.pdf.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhao Yang PhD.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, Z., Sun, X. & Hardin, J.W. Testing Marginal Homogeneity in Matched-Pair Polytomous Data. Ther Innov Regul Sci 46, 434–438 (2012). https://doi.org/10.1177/0092861512442021

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1177/0092861512442021

Keywords

Navigation