0

I have a large sample, 200 participants in each group, and normality is violated (the shapiro-wilk test showed that all data were non- normally distributed p<0.05) but i assume that can still perform a t-test because the sample is large enough to accept asymptotic normality according to the central limit theorem. However I found that the homogeneity was also violated (using Levene test) Am I still able to perform a t-test for independent samples according to the central limit theorem?

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
khouloud
  • 1
  • 1
  • The question is not clear to me. Where is normality violated? Also, the sample size looks quite good to me. – Peaceful May 24 '21 at 11:13
  • @Peaceful Sample size alone tells you nothing concerning the applicability of the t-test. See https://stats.stackexchange.com/questions/69898 for an example. – whuber May 24 '21 at 11:36
  • thank you for your answers normality was tested using the shapiro-wilk test that which showed that all data were non- normally distributed as for Levene test for variance homogeneity some data were homogenious and some other were not – khouloud May 24 '21 at 12:15
  • It'd be useful to get an idea of how non-normal the data are since the t-test can be fairly robust within reasonable violations of these assumptions. Additionally, have you looked at any transformations of the of data? While transformations can make it harder to interpret your results, they sometimes are useful, especially if your analysis software is limited in terms of statistical options – Billy May 24 '21 at 13:15
  • thank you @Billy, please what do you mean by "how non-normal" what should I clarify exactly ? and unfortunately I have no idea about data transformations – khouloud May 24 '21 at 13:38
  • https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless – Dave May 24 '21 at 14:05
  • As outlined in the discussion linked by @Dave, there are lots of ways of inspecting non-normality outside of the p-value for a S-W. I'd suggest checking skew and kurtosis as well. Like other statistical tests, with larger and larger samples, you'll get false positives p < .05 with S-W. QQ plots are helpful as well – Billy May 24 '21 at 16:04
  • @Billy that is false. The goodness-of-fit tests like Shapiro-Wilk give false positives at the correct rate (uniform distribution of p-values), even when sample sizes are gigantic. The trouble is that such tests will give true positives when there is a trivial (but existent) difference, so small that the practitioner need not be concerned. This is a feature of hypothesis testing, not a bug, but it often makes p-value screening an inappropriate tool for checking normality assumptions. – Dave May 24 '21 at 16:18
  • @Dave, you're correct - I shouldn't have been so broad in the implication of a false positive: I do mean exactly that the result can be statistically significant but practically unimportant. In much the same vein of hypothesis testing, I usually don't recommend the S-W for assumption testing because it rests on accepting the null hypothesis – Billy May 24 '21 at 16:24
  • Can you please show us qqplots for each of the samples? – kjetil b halvorsen May 24 '21 at 17:21
  • For what it's worth, I found this post on another question and thought it might be helpful to you OP: https://stats.stackexchange.com/questions/111010/interpreting-qqplot-is-there-any-rule-of-thumb-to-decide-for-non-normality?rq=1 – Billy May 25 '21 at 13:02
  • Thank you, I'm actually thinking of using Mann-whitney U test instead of T test – khouloud May 26 '21 at 09:55

0 Answers0