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Sociological Methods & Research
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Simple Approximations to Null Sampling Variances

Goodman and Kruskal's Gamma, Kendall's Tau, and Somers's dxy

Robert H. Somers

Pacific Telephone and Telegraph Company

Procedures for significance testing and confidence interval estimation of several employed measures of association have been available for several years, but rarely used, possibly because of the lengthy computations entailed. Simple formulas involving the sample size and the number of rows and columns in the cross-classification have been found to closely approximate formulas suitable for significance testing under a wide variety of circumstances. Although this remarkable stability of the asymptotic variances extends to many non-null populations, the use of the simple formulas to approximate confidence intervals is not recommended.

Sociological Methods & Research, Vol. 9, No. 1, 115-126 (1980)
DOI: 10.1177/004912418000900107
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[Abstract]