On the Regularity and Sampling Behavior of the Median Interindividual Difference

The Median Interindividual Difference (MEID), defined as the median of all positive pairwise differences within a sample, has been proposed as an absolute measure of variability with both asymptotic and bootstrap procedures for interval estimation; however, its finite-sample behavior requires further evaluation. This Monte Carlo simulation examined whether bootstrap and asymptotic approaches show comparable performance in terms of standard errors and confidence interval widths, and whether the sampling distribution of the MEID converges to normality under different distributional conditions. For each of 65 conditions (13 sample sizes × 5 distributions), 1000 samples were generated. Within each condition, mean Wald-type and bootstrap confidence interval widths and log-transformed standard errors were compared using paired t-tests; equality of variability was assessed with the Pitman–Morgan test, and normality of bootstrap-generated sampling distributions was evaluated using the Shapiro–Francia test. Results did not support overall equivalence between asymptotic and bootstrap inference. Practical equivalence emerged under approximately regular continuous distributions and large samples, whereas discrepancies persisted under strong asymmetry. In discrete distributions, the MEID converged to a constant as the sample size increased, resulting in near-zero bootstrap variability and limiting the practical usefulness of certain resampling-based confidence interval procedures. Convergence toward normality occurred only in continuous settings and increased with sample size. These findings delineate the conditions under which the MEID yields stable, interpretable inference.