I have been reading several sources mentioning that when you have large enough sample sizes (some say 20, others above 200?) then parametric tests, such as t-test, are robust against non-normality and even should be preferred when the data is best represented by means.
https://doi.org/10.1186/1471-2288-12-78; 10.1016/j.cct.2009.06.007.
There's an argument that are misusing non-parametric tests
But it has been common (or even considered the proper?) for normality tests or plots to be used (such ada K-S or Q-Q/P-P) and to choose non-parametric tests when the data are skewed.
I have talked to some people, and they still generally believe even with very large sample sizes (e.g. n=2000, 2 groups) that normality tests are done then choosing non-parametric if non-normal distribution.
I wonder if anyone can give an input? Is this a problem with statistical textbooks or practices in the field that did not evolve as we have larger and larger study sizes? Or were I wrong?
Secondly, I can't seem to find a package on SPSS of non-parametric that could deal unequal variances (for instance the Brunner-Munzel tests; yes MWM U test may be used depending of the H0 but I'm looking for a test that disregard homogeneity of variances), anyone know of such test that comes with SPSS?
Watch this video to understand which statistical analysis to run for large sample sizes - Parametric or Non-parametric tests :
https://youtu.be/Xu6-kU8s-ls
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some pointers in the discussion below
https://www.researchgate.net/post/What_are_some_tests_used_for_data_that_is_not_normally_distributed_even_after_trimming
but since then i came accross the following (excellent) post
https://stats.stackexchange.com/questions/141314/question-about-normality-assumption-of-t-test
and i do not know what to think anymore !
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Hello Lee,
While the central limit theorem suggests that, as sample size approaches infinity, the distribution of sample means approaches normality (no matter the shape of the parent population), what is unknown is exactly how large does a sample have to be for complete confidence that the parametric method will hold? The answer depends on, among other things, how much discrepancy there is between the parent population shape and that of a normal distribution.
Options?
1. Use exact / resampling / bootstrap methods. These allow you to evade the usual concerns about normality and homogeneity.
2. Use the non-parametric methods, though these do (in the case of group comparisons, such as Mann-Whitney or Kruskal-Wallis) require homogeneity. As well, note that the non-parametric methods test somewhat different hypotheses than do the parametric tests.
3. Try a lower-inference method, such as Cliff's dominance statistic (or the closely related A statistic). The definitional form of the Common Language Effect Size (the proportion of cases in which the score for a randomly selected case from group "A" exceeds that of a randomly selected case for group "B") also works. None of these assumes normality or homogeneity. See: Cliff, N. (1993). Dominance statistics: Ordinal analyses to answer ordinal questions. Psychological Bulletin, 114(3), 494–509. https://doi.org/10.1037/0033-2909.114.3.494
Good luck with your work.
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