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2 × 2 Tables: a note on Campbell's recommendation.

F M T A Busing1, B Weaver2, S Dubois2,3

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Summary

Egon Pearson's N - 1 chi-squared statistic offers more accurate p-values for 2 × 2 tables than Karl Pearson's. This method is readily available in statistical software, simplifying data analysis.

Keywords:
Mantel-Haenszel chi-squared statisticN − 1 chi-squared statisticPearson's chi-squared statisticsRSASSPSSStatarstatistical softwareχ2ϕ

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Area of Science:

  • Biostatistics
  • Statistical Methods

Background:

  • Traditional chi-squared tests for 2 × 2 tables have limitations.
  • Karl Pearson's chi-squared statistic is widely used but can be less accurate.

Purpose of the Study:

  • To highlight the theoretical advantages of Egon Pearson's N - 1 chi-squared statistic.
  • To demonstrate its practical utility and availability in statistical software.

Main Methods:

  • Comparison of Egon Pearson's N - 1 chi-squared statistic with Karl Pearson's chi-squared statistic for 2 × 2 tables.
  • Equivalence of Egon Pearson's N - 1 statistic to the Mantel-Haenszel chi-squared statistic for single tables.

Main Results:

  • Egon Pearson's N - 1 chi-squared statistic is theoretically more sound for 2 × 2 tables.
  • This statistic yields more accurate p values compared to Karl Pearson's.
  • The N - 1 statistic is equivalent to the Mantel-Haenszel statistic for a single 2 × 2 table.

Conclusions:

  • Egon Pearson's N - 1 chi-squared statistic is recommended for analyzing 2 × 2 tables due to its accuracy.
  • Its availability in common statistical packages (SPSS, SAS, Stata, R) facilitates its adoption.
  • This approach aids researchers in adhering to statistical best practices and recommendations.