I am comparing 21 subjects´ results (before and after) but I am not sure if this sample requires a T-test (Parametric) or the WILCOXON HODGES_LEHMAN (Non parametric). Someone did the test for normality (Shapiro-Wilk) and told me that because of the results I could do the t-test. But another colleague told me that because I am dealing only with 21 subjects the t-test is not appropriate but the Wilcoxon, and even more so, if I want later to break down in three groups the sample to see if there are any differences due to language proficiency and I may end up with a group of 4, another group of 8 and the other of 9 participants. Any guidance you may give me will be certainly appreciated.
Hello Julio,
Sample size is not the determining factor for deciding whether to use a parametric or non-parametric test; it's the other considerations/assumptions and the nature of the scores that should guide the decision. Whenever assumptions for a parametric test are in doubt, one can always use exact/permutation tests as an alternative.
In general, small sample sizes, no matter what kind of test you elect to use, will have lower statistical power to detect some target magnitude of effect (if it exists) than will larger sample sizes.
Good luck with your work.
Thank you for your answer, David. In fact, I am replicating the analysis (they used non-parametric Wilcoxon) of a study that also explored writing development but two people who have helped me double check the results pointed me into different directions and that got me confused. What are those exact/permutation tests that you refer to in your answer? I would like to check into that
Hello again Julio,
Here are a couple of links that will get you started:
1. A starting intro: http://www.utstat.toronto.edu/~brunner/oldclass/appliedf12/lectures/2101f12PermutationRandomization.pdf
2. A great list of relevant references: Article Exact Permutation/Randomization Tests Algorithms
3. A somewhat brief (18 min) video: https://www.youtube.com/watch?v=X87lzluILjU
Good luck with your work.
David, thank you for the links and the video. I really appreciate it. I will check them carefully.
- Badges
- Science topic
- Similar topics
- Philosophy
- Ethics