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A weighted test of internal symmetry

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  • Thomas Smith
  • Cornelius McKenna

Abstract

This study examines extensions of McNemar's Test with multinomial responses, and proposes a linear weighting scheme, based on the distance of the response change, that is applied to one of these extensions (Bowker's test). This weighted version of Bowker's test is then appropriate for ordinal response variables. A Monte Carlo simulation was conducted to examine the Type I error rate of the weighted Bowker's test for a cross-classification table based on a five-category ordinal response scale. The weighted Bowker's test was also applied to a data set involving change in student attitudes towards mathematics. The results of the weighted Bowker's test were compared with the results of Bowker's test applied to the same set of data.

Suggested Citation

  • Thomas Smith & Cornelius McKenna, 2011. "A weighted test of internal symmetry," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2111-2118.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:10:p:2111-2118
    DOI: 10.1080/02664763.2010.545117
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    References listed on IDEAS

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    1. Franklin Satterthwaite, 1941. "Synthesis of variance," Psychometrika, Springer;The Psychometric Society, vol. 6(5), pages 309-316, October.
    2. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer;The Psychometric Society, vol. 12(2), pages 153-157, June.
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