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Cochran's rules

(NL: Cochran's regels)

Cochran's rules are a set of rules to determine whether the results of a chi-square test are reliable. More specifically, there should be "sufficient" observations in each category of a contingency table or frequency table to apply the chi-square test. Cochran's rules determine how much "sufficient" exactly is.

The rules are typically formulated as follows:

  1. Each cell in the table should have an expected frequency of at least 1.
  2. In at least 80% of the cells, the expected frequency should be at least 5 (or at most 20% of the cells may have an expected frequency of less than 5).

The rules are named after the American statistician William G. Cochran to whom they are attributed, based on his work in the 1950s (Cochran, 1952; 1954, p.420). For an extensive discussion of Cochran's rules, see Kroonenberg & Verbeek (2018).

References

Cochran, W. G. (1952). The χ2 test of goodness of fit. The Annals of Mathematical Statistics, 23(3), 315-345. https://doi.org/10.1214/aoms/1177729380

Cochran, W. G. (1954). Some Methods for Strengthening the Common χ 2 Tests. Biometrics, 10(4), 417-451. https://doi.org/10.2307/3001616

Kroonenberg, P. M., & Verbeek, A. (2018). The Tale of Cochran’s Rule: My Contingency Table has so Many Expected Values Smaller than 5, What Am I to Do? The American Statistician, 72(2), 175–183. https://doi.org/10.1080/00031305.2017.1286260