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Approximate confidence intervals for the correlation from data in two‐by‐two tables
Author(s) -
Bedrick Edward J.
Publication year - 1991
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1991.tb00968.x
Subject(s) - statistics , confidence interval , mathematics , cdf based nonparametric confidence interval , pearson product moment correlation coefficient , statistic , robust confidence intervals , sample size determination , correlation coefficient , credible interval , correlation , divergence (linguistics) , polychoric correlation , pearson's chi squared test , fisher transformation , test statistic , statistical hypothesis testing , linguistics , philosophy , geometry
The family of power divergence statistics is used to construct approximate confidence intervals for the correlation between two variables from data in 2×2 tables. This family includes confidence intervals obtained by inverting the likelihood ratio, Pearson chi‐squared and Freeman–Tukey statistics. Small‐sample calculations show that several power divergence intervals, and in particular the confidence interval constructed from the Pearson chi‐squared statistic, have coverage probabilities closer to nominal levels than the interval based on the normal approximation to the tetrachoric correlation coefficient.