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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?

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