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When should a pre-test for normality only without a pre-test for equality of variances be performed before location tests like this paper did ((Rochon, J., Gondan, M. & Kieser, M. To test or not to test: Preliminary assessment of normality when comparing two independent samples. BMC Med Res Methodol 12, 81 (2012). https://doi.org/10.1186/1471-2288-12-81))

Whereas, other papers focus on the two pre-tests for normality and equality variances before location tests such as ((Rasch D, Kubinger KD, Moder K: The two-sample t test: pretesting its assumptions does not pay. Stat Papers. 2011, 52: 219-231. 10.1007/s00362-009-0224-x.)).

my question is when focus on the pre-test for the normality test and ignore the pre-test for equality of variances, and when we focus on both pre-tests for normality and equality of variances?

Statistical scientist
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    My opinion: Don't do any formal hypothesis tests for "assumptions". See this post on normality testing to get a few ideas why it's usually ill advised. – COOLSerdash Feb 12 '24 at 12:23
  • See also https://stats.stackexchange.com/questions/551264/when-to-check-model-assumptions for an answer to a more general question, and for a very special case see https://stats.stackexchange.com/questions/434928/unequal-variance-in-randomized-experiments-to-compare-treatment-with-control – kjetil b halvorsen Feb 12 '24 at 18:36

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