Guidelines for selecting variability measure in limited-size ANOVA experiments

Abstract

Abstract Graphical representation of variability is essential for accurately communicating scientific results in applied sciences. In ANOVA experiments with a low number of replicates (n), the selection between pooled or individual standard deviations (SDs) poses a methodological challenge. The aim of this study is to offer practical guidelines to help researchers decide whether to use pooled or individual SDs in tables and figures, when the number of replicates is low. This study uses extensive Monte Carlo simulations (over 2,000 scenarios) to investigate the distributional behaviour of SD estimates across different replications and heterogeneity levels. We compare the performance of pooled versus individual SDs using the Mean Absolute Deviation (MAD) from the true population values, and we evaluate the utility of Levene’s and F max (Hartley’s) tests in guiding this choice. Results show that pooled SDs offer superior accuracy under homogeneity or low heterogeneity conditions, particularly with n  ≤ 4, while individual SDs are preferable when variance heterogeneity is moderate to high and the replication number is higher ( n  ≥ 5). Levene’s test generally outperforms the F max test in supporting the correct selection of the variability measure, especially in multi-group settings. The guidelines proposed can be directly applied to many experimental settings in applied sciences, where the number of replicates and treatments is often limited.