An absolute deviation approach to assessing correlation

Gorard, S.

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.

Citation

Gorard, S. (2015). An absolute deviation approach to assessing correlation. British journal of education, society & behavioural science, 5(1), 73-81. https://doi.org/10.9734/bjesbs/2015/11381

• Journal Article Type: Article
• Acceptance Date: Sep 3, 2014
• Publication Date: Jan 1, 2015
• Deposit Date: Nov 12, 2014
• Publicly Available Date: Nov 21, 2014
• Journal: British Journal of Education, Society and Behavioural Science
• Electronic ISSN: 2278-0998
• Publisher: SCIENCEDOMAIN International
• Peer Reviewed: Peer Reviewed
• Volume: 5
• Issue: 1
• Pages: 73-81
• DOI: https://doi.org/10.9734/bjesbs/2015/11381
• Keywords: Mean absolute deviation, Correlation, Quantitative methods initiative, Statistical methods, The new statistics.
• Public URL: https://durham-repository.worktribe.com/output/1442289