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An absolute deviation approach to assessing correlation.

Gorard, S. (2015) 'An absolute deviation approach to assessing correlation.', British journal of education, society and behavioural science., 5 (1). pp. 73-81.

Abstract

This paper describes two possible alternatives to the more traditional Pearson’s R correlation coefficient, both based on using the mean absolute deviation, rather than the standard deviation, as a measure of dispersion. Pearson’s R is well-established and has many advantages. However, these newer variants also have several advantages, including greater simplicity and ease of computation, and perhaps greater tolerance of underlying assumptions (such as the need for linearity). The first alternative approach simply divides the co-variance by the mean absolute deviation(s) instead of the standard deviation as in Pearson’s R. The second alternative uses the sum of each pair of deviations in x and y instead of the covariance, and again uses the mean absolute deviation(s) as the denominator. All three are compared to one another using 30,000 simulations based on 100 pairs of random numbers. The substantive findings are the same for each approach, and the ‘coefficients’ correlate with each other (using R) at +0.99 to 1.00. The three approaches also give the same substantive findings when trialled with real-life secondary datasets. This introduction of simpler kinds of correlation forms part of an attempt to simplify the use of numeric analysis, to make it more ‘everyday’, for the benefit of both analysts and consumers of evidence.

Item Type:Article
Keywords:Mean absolute deviation, Correlation, Quantitative methods initiative, Statistical methods, The new statistics.
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.9734/BJESBS/2015/11381
Publisher statement:© 2015 Gorard; This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Date accepted:03 September 2014
Date deposited:21 November 2014
Date of first online publication:January 2015
Date first made open access:No date available

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