Sidelining the Mean: The Relative Variability Index as a Generic Mean-Corrected Variability Measure for Bounded Variables

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Abstract

Variability indices are a key measure of interest across diverse fields, in and outside psychology. A crucial problem for any research relying on variability measures however is that variability is severely confounded with the mean, especially when measurements are bounded, which is often the case in psychology (e.g., participants are asked “rate how happy you feel now between 0 and 100?”). While a number of solutions to this problem have been proposed, none of these are sufficient or generic. As a result, conclusions on the basis of research relying on variability measures may be unjustified. Here, we introduce a generic solution to this problem by proposing a relative variability index that is not confounded with the mean by taking into account the maximum possible variance given an observed mean. The proposed index is studied theoretically and we offer an analytical solution for the proposed index. Associated software tools (in R and MATLAB) have been developed to compute the relative index for measures of standard deviation, relative range, relative interquartile distance and relative root mean squared successive difference. In five data examples, we show how the relative variability index solves the problem of confound with the mean, and document how the use of the relative variability measure can lead to different conclusions, compared with when conventional variability measures are used. Among others, we show that the variability of negative emotions, a core feature of patients with borderline disorder, may be an effect solely driven by the mean of these negative emotions.

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