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      cocor: A Comprehensive Solution for the Statistical Comparison of Correlations

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      PLoS ONE
      Public Library of Science

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          Abstract

          A valid comparison of the magnitude of two correlations requires researchers to directly contrast the correlations using an appropriate statistical test. In many popular statistics packages, however, tests for the significance of the difference between correlations are missing. To close this gap, we introduce cocor, a free software package for the R programming language. The cocor package covers a broad range of tests including the comparisons of independent and dependent correlations with either overlapping or nonoverlapping variables. The package also includes an implementation of Zou’s confidence interval for all of these comparisons. The platform independent cocor package enhances the R statistical computing environment and is available for scripting. Two different graphical user interfaces—a plugin for RKWard and a web interface—make cocor a convenient and user-friendly tool.

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          Most cited references29

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          Comparing correlated correlation coefficients.

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            Tests for comparing elements of a correlation matrix.

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              Toward using confidence intervals to compare correlations.

              G Zou (2007)
              Confidence intervals are widely accepted as a preferred way to present study results. They encompass significance tests and provide an estimate of the magnitude of the effect. However, comparisons of correlations still rely heavily on significance testing. The persistence of this practice is caused primarily by the lack of simple yet accurate procedures that can maintain coverage at the nominal level in a nonlopsided manner. The purpose of this article is to present a general approach to constructing approximate confidence intervals for differences between (a) 2 independent correlations, (b) 2 overlapping correlations, (c) 2 nonoverlapping correlations, and (d) 2 independent R2s. The distinctive feature of this approach is its acknowledgment of the asymmetry of sampling distributions for single correlations. This approach requires only the availability of confidence limits for the separate correlations and, for correlated correlations, a method for taking into account the dependency between correlations. These closed-form procedures are shown by simulation studies to provide very satisfactory results in small to moderate sample sizes. The proposed approach is illustrated with worked examples. Copyright (c) 2008 APA.
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                Author and article information

                Contributors
                Role: Academic Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                2015
                2 April 2015
                : 10
                : 4
                : e0121945
                Affiliations
                [1 ]Department of Experimental Psychology, University of Duesseldorf, Duesseldorf, Germany
                University of New South Wales, AUSTRALIA
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Wrote the paper: BD JM. Software development: BD.

                Article
                PONE-D-14-48849
                10.1371/journal.pone.0121945
                4383486
                25835001
                32c2e0a3-3e11-487d-9c1c-a8b531f83eba
                Copyright @ 2015

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

                History
                : 30 October 2014
                : 5 February 2015
                Page count
                Figures: 3, Tables: 3, Pages: 12
                Funding
                The authors have no support or funding to report.
                Categories
                Research Article
                Custom metadata
                The cocor R package can be downloaded from http://cran.r-project.org/package=cocor. A web front-end to conveniently access the functionality of the cocor package is available at http://comparingcorrelations.org.

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