review · Heliyon
Post-hoc comparison tests determine which group means differ following a significant analysis of variance, but their valid application depends on meeting assumptions such as normality, balanced group sizes, and equal variance. A review of literature across environmental and biological sciences identified ten distinct post-hoc tests in use. Over the past twenty years, Tukey HSD, Duncan's, and Fisher's LSD emerged as the most frequently employed tests, accounting collectively for the majority of cases. Conversely, Games-Howell, Holm-Bonferroni, and Scheffe's tests were rarely selected. The selection of a specific test often depended on the prior statistical method. Crucially, the underlying statistical assumptions required for these procedures were frequently left unverified by researchers. Verification of normality and equal variance occurred primarily alongside only a few widely used tests, highlighting widespread inadequacies in current data analysis practices.
Biological and environmental research relies on sound data analysis to produce credible, reproducible findings. When researchers apply post-hoc statistical tests without checking foundational requirements such as variance equality and normal distribution, they risk drawing flawed conclusions. Ensuring the correct selection and validation of these statistical tools strengthens scientific integrity and prevents misleading experimental interpretations.
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Post-hoc comparison procedures are commonly used to determine which group means differ after a significant analysis of variance (ANOVA). Several post-hoc tests have been proposed, but their use requires certain assumptions to be met, such as normality, equality of variance, and balanced group size. This review examined the statistical literature on post-hoc tests and their use in the environmental and biological sciences. Through this review, we found that post-hoc tests are effective but often inadequately used in these sciences. We conducted a search of reputed search engines to identify articles in which post-hoc tests were used and found ten post-hoc tests used in the environmental and biological literature. Tukey HSD (30.04%), Duncan's (25.41%) and Fisher's LSD (18.15%) were the most commonly used post-hoc tests over the past 20 years, whereas the Games-Howell (1.13%), Holm-Bonferroni (1.25%), and Scheffe's tests (2.25%) were the least used. The choice of post-hoc test depended on the statistical method used prior. In addition, the assumptions of applying post-hoc tests were not always verified. In fact, the normality condition was mostly only checked in the cases of Tukey HSD, Duncan's, and Fischer's LSD tests, and equality of variance was often met for the Tukey HSD, Duncan's, Fischer's LSD, and Bonferroni tests. This review opens a new avenue for comparing post-hoc test performance in ANOVA using linear or generalised mixed effect models.
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DOI: 10.1016/j.heliyon.2024.e25131
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