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ANOVA (Analysis of Variance) and Tukey's HSD (Honestly Significant Difference) test are commonly used in scientific papers even when the data are not normalized because these methods are robust to certain violations of their assumptions. ANOVA is particularly robust to non-normality when sample sizes are equal or large, which tends to mitigate the effects of non-normal distributions¹[4].

The central limit theorem supports this robustness, suggesting that with a sufficiently large sample size, the distribution of the sample means will approximate a normal distribution, even if the underlying population distribution is not normal. This allows ANOVA to produce reliable results despite non-normality in the data.

Tukey's HSD test is often used in conjunction with ANOVA as a post hoc analysis to determine which specific group differences are significant. It controls for the family-wise error rate, which is the probability of making one or more Type I errors when performing multiple comparisons²[5].

However, it's important to note that if the data are heavily skewed or have outliers, transformations or non-parametric alternatives might be more appropriate. Non-parametric equivalents, like the Kruskal-Wallis test, can be used when the assumptions of ANOVA are not met, and for post hoc comparisons, the Dunn's test can serve as a non-parametric counterpart to Tukey's HSD³[7].

In practice, researchers may choose ANOVA and Tukey's HSD for their simplicity and the availability of software that supports these tests. They also may be following conventions within their field or the expectations of peer reviewers and journals. Nonetheless, it's crucial for researchers to justify their choice of statistical methods and ensure that the assumptions underlying these methods are reasonably met in their data. If there's significant deviation from these assumptions, alternative methods should be considered.

Source : conversation avec Bing, 27/04/2024
(1) Can I trust ANOVA results for a non-normally distributed DV?. https://stats.stackexchange.com/questions/5680/can-i-trust-anova-results-for-a-non-normally-distributed-dv.
(2) A Guide to Using Post Hoc Tests with ANOVA - Statology. https://www.statology.org/anova-post-hoc-tests/.
(3) Is there a nonparametric equivalent of Tukey HSD?. https://stats.stackexchange.com/questions/17342/is-there-a-nonparametric-equivalent-of-tukey-hsd.
(4) ANOVA with Tukey's HSD Post Hoc Test in SPSS. https://www.youtube.com/watch?v=JiyeE7uzSbQ.
(5) Tukey Method - One-Way ANOVA. https://www.youtube.com/watch?v=zQr190cacC0.
(6) ANOVA : TWO FACTOR WITH REPLICATION & TUKEY TEST ON EXCEL. https://www.youtube.com/watch?v=3-nRXmq-Zng.
(7) Tukey's test of additivity - Wikipedia. https://en.wikipedia.org/wiki/Tukey%27s_test_of_additivity.
(8) What Is the Tukey HSD Test? | Sciencing. https://sciencing.com/what-is-the-tukey-hsd-test-12751748.html.

ANOVA with Tukey's HSD Post Hoc Test in SPSS This video demonstrates how to conduct an ANOVA with a Tukey’s HSD post hoc test in SPSS. The results of pairwise comparisons with a Bonferroni correction ar...

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