Measures of Interindividual Variation: Definition and Computation

Abstract

Measures of interindividual variation are rarely used or studied in descriptive/inference statistics, despite constituting a third approach to describing data variability, alternative to ranges (the difference between two extreme measures of position) and to the mean or median of the distances of the data from a measure of central tendency. The aim of this article is to present point and interval estimation (asymptotic and bootstrap) for four absolute measures of variation based on interindividual differences and one relative measure, to develop an R script for their computation, and to demonstrate the performance of the script using two examples. One example is based on a large sample ( n = 1000) drawn from a bounded continuous distribution with negative skewness (PERT (0, 8, 10)), which may simulate data from a knowledge–ability test; the other is based on a medium-sized sample ( n = 100) drawn from a bounded discrete distribution with positive skewness (BN ( n = 10, p = 0.25)), which may simulate the recording (present/absent) of a behavior in independent observations. Both distributions are slightly platykurtic and non-normal. With the measure based on the median of interindividual differences, difficulties arise when generating its sampling distribution for discrete data, but not for continuous data. The absolute measures converge to a normal distribution, whereas the relative measure does not. It is concluded that the script enables the appropriate computation of interindividual variation statistics. Its use is recommended, and further investigation of these measures through simulation studies is encouraged.