@article {10.3844/jmssp.2026.61.76,
article_type = {journal},
title = {Absolute Measures of Interindividual Variation: A Simulation Study },
author = {Rubia, José Moral la},
volume = {22},
year = {2026},
month = {Aug},
pages = {61-76},
doi = {10.3844/jmssp.2026.61.76},
url = {https://thescipub.com/abstract/jmssp.2026.61.76},
abstract = {Four absolute measures and one relative measure of interindividual variability have been defined, together with their point and interval estimation (bootstrap and asymptotic), and an R script has been developed for their computation. However, further simulation studies are required to strengthen their methodological evaluation. This study focused on the three absolute measures with potentially better regularity conditions, Mean Interindividual Differences (MID), Interindividual Variance (IVAR), and Interindividual Standard Deviation (ISD). Its objectives were: (1) To examine whether bootstrap and asymptotic approaches for these statistics show comparable performance, assessed through their standard errors and confidence interval widths; and (2) To determine whether their sampling distributions converge to normality. Using Monte Carlo simulation, 1000 samples were generated for each of 65 conditions (13 sample sizes ×5 distributions). Within each condition, mean Wald-type and bootstrap confidence interval widths, as well as log-transformed asymptotic and bootstrap standard errors, were compared using paired t tests. Equality of variability between asymptotic and bootstrap standard errors was evaluated with the Pitman–Morgan test. Normality of the bootstrap sampling distributions was assessed using the Shapiro–Francia test. The results support asymptotic equivalence between asymptotic and bootstrap standard errors and between Wald-type and Bias-Corrected and accelerated (BCa) confidence interval widths, with faster convergence for MID and ISD and slower convergence for IVAR. The bootstrap sampling distributions of MID and ISD showed clear convergence to normality, whereas IVAR converged more slowly. Overall, the three statistics exhibit regularity properties that justify the application of asymptotic methods. Their use in empirical research is recommended.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}