Yates' Correction

Yates' correction is an adjustment made to chi-square values obtained from 2 by 2 contingency table analyses (e.g., Pearson chi-square and McNemara chi-square). More fully, it is known as the Yates' correction for continuity and was first proposed by Yates (1934). The logic of Yates' correction rests upon the fact that because contingency table analyses are based on dichotomous data, and the statistical chi-square distribution is continuous (rather than dichotomous), an adjustment must be applied to contingency table analyses, so as to obtain more accurate results. The correction consists of subtracting .5 from each absolute difference between the observed and expected cell frequencies.

Despite the fact that the correction is commonly observed in the literature, there is a compelling amount of Monte-Carlo simulation research which suggests that the Yates' correction is overly conservative, even in small sample sizes, which suggests that it should not be applied in practice (Camilli & Hopkins, 1978, 1979; Feinberg, 1980; Larntz, 1978; Thompson, 1988).

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Camilli, G. & Hopkins, K. D. (1978). Applicability of chi-square to 2 * 2 contingency tables with small expected frequencies. Psychological Bulletin, 85, 163-167.

Camilli, G. & Hopkins, K. D. (1979). Testing for association in 2 * 2 contingency tables with very small sample sizes. Psychological Bulletin, 86, 1011-1014.

Feinberg, S. E. (1980). The analysis of cross-classified categorical data. Cambridge: MIT.

Larntz, K. (1978). Small sample comparisons of exact levels for chi-square goodness of fit statistics. Journal of the American Statistical Association, 73, 253-263.

Thompson, B. (1988). Misuse of chi-square contingency-table test statistics. Educational and Psychological Research, 8(1), 39-49.

Yates, F. (1934). Contingency tables involving small numbers and the chi-square test. Journal of the Royal Statistical Society, 1, 217-235.