Asymptotic confidence intervals for the Pearson correlation via skewness and kurtosis

Abstract

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 0 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 0 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 (PM1 and HC4). 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.

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“…Genetic analysis allows confirmation of the diagnosis by revealing a deletion of mitochondrial DNA in all tissues (at least 1000 base pairs deleted). This syndrome is rarely diagnosed in the neonatal period and must be diagnosed in the presence of sideroblastic macrocytic anemia, which should lead to the rapid performance of a myelogram and then a genetic analysis based on a blood sample [27]. Histological examination shows erythroid precursors with vacuolation typical of hematopoietic precursors, and presence of ring sideroblastic [28].…”

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