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Asymptotic confidence intervals for the Pearson correlation via skewness and kurtosis
Author(s) -
Bishara Anthony J.,
Li Jiexiang,
Nash Thomas
Publication year - 2018
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/bmsp.12113
Subject(s) - kurtosis , pearson product moment correlation coefficient , skewness , statistics , confidence interval , mathematics , correlation , econometrics , geometry
When bivariate normality is violated, the default confidence interval of the Pearson correlation can be inaccurate. Two new methods were developed based on the asymptotic sampling distribution of Fisher's z ′ under the general case where bivariate normality need not be assumed. In Monte Carlo simulations, the most successful of these methods relied on the (Vale & Maurelli, 1983, Psychometrika , 48, 465) family to approximate a distribution via the marginal skewness and kurtosis of the sample data. In Simulation 1, this method provided more accurate confidence intervals of the correlation in non‐normal data, at least as compared to no adjustment of the Fisher z ′ interval, or to adjustment via the sample joint moments. In Simulation 2, this approximate distribution method performed favourably relative to common non‐parametric bootstrap methods, but its performance was mixed relative to an observed imposed bootstrap and two other robust methods ( PM 1 and HC 4). No method was completely satisfactory. An advantage of the approximate distribution method, though, is that it can be implemented even without access to raw data if sample skewness and kurtosis are reported, making the method particularly useful for meta‐analysis. Supporting information includes R code.