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Robust Correlation Analyses: False Positive and Power Validation Using a New Open Source Matlab Toolbox

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      Pearson’s correlation measures the strength of the association between two variables. The technique is, however, restricted to linear associations and is overly sensitive to outliers. Indeed, a single outlier can result in a highly inaccurate summary of the data. Yet, it remains the most commonly used measure of association in psychology research. Here we describe a free Matlab (R) based toolbox ( that computes robust measures of association between two or more random variables: the percentage-bend correlation and skipped-correlations. After illustrating how to use the toolbox, we show that robust methods, where outliers are down weighted or removed and accounted for in significance testing, provide better estimates of the true association with accurate false positive control and without loss of power. The different correlation methods were tested with normal data and normal data contaminated with marginal or bivariate outliers. We report estimates of effect size, false positive rate and power, and advise on which technique to use depending on the data at hand.

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      Most cited references 20

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        Assessing the accuracy of prediction algorithms for classification: an overview.

        We provide a unified overview of methods that currently are widely used to assess the accuracy of prediction algorithms, from raw percentages, quadratic error measures and other distances, and correlation coefficients, and to information theoretic measures such as relative entropy and mutual information. We briefly discuss the advantages and disadvantages of each approach. For classification tasks, we derive new learning algorithms for the design of prediction systems by directly optimising the correlation coefficient. We observe and prove several results relating sensitivity and specificity of optimal systems. While the principles are general, we illustrate the applicability on specific problems such as protein secondary structure and signal peptide prediction.
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          Alternatives to the Median Absolute Deviation


            Author and article information

            1Brain Research Imaging Center, Division of Clinical Neurosciences, University of Edinburgh Edinburgh, UK
            2Department of Psychology, University of Southern California Los Angeles, CA, USA
            3Centre for Cognitive Neuroimaging, Institute of Neuroscience and Psychology, College of Medical, Veterinary and Life Sciences, University of Glasgow Glasgow, UK
            Author notes

            Edited by: Holmes Finch, Ball State University, USA

            Reviewed by: Jill S. Budden, National Council of State Boards of Nursing, USA; Michael Smithson, Australian National University, Australia

            *Correspondence: Cyril R. Pernet, Brain Research Imaging Center, Western General Hospital, Crewe Road, Edinburgh, EH4 2XU, UK. e-mail: cyril.pernet@

            This article was submitted to Frontiers in Quantitative Psychology and Measurement, a specialty of Frontiers in Psychology.

            Front Psychol
            Front Psychol
            Front. Psychology
            Frontiers in Psychology
            Frontiers Media S.A.
            04 December 2012
            10 January 2013
            : 3
            Copyright © 2013 Pernet, Wilcox and Rousselet.

            This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and subject to any copyright notices concerning any third-party graphics etc.

            Figures: 9, Tables: 3, Equations: 0, References: 30, Pages: 18, Words: 9786
            Methods Article

            Clinical Psychology & Psychiatry

            robust statistics, outliers, matlab, correlation, power


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