I understand that the Wilcoxon paired test is non-parametric and can be used for data that is not normally distributed, and that the paired t-test is considered parametric and is typically used when the data is normally distributed (although I have read that it is supposedly robust against the normality distribution assumption as well).
I just wanted to gather opinions on this topic, as I am thinking about reporting both the Wilcoxon paired test and include the paired t-test just in case, although it is a bit redundant.
I have a paired grouping of a sample size of n = 41 with a time 1 and time 2. At first glance, using the Central Limit Theorem (CLT), this may seem to be normally distributed based on the CLT, but I checked the data using the Shapiro-Wilk test and it is not normally distributed according to the Shapiro-Wilk test (using an α = 0.05 threshold). I used the Wilcoxon paired test.
I have another one that is smaller unforunately with a sample size of n = 25, also time 1 and time 2. It did not pass the Shapiro-Wilk test for normality as well, and I used the Wilcoxon paired test.
I also have paired t-tests that were run for both of them. I just wanted to hear people's thoughts on this. I will have to explain this to the PI since I think the PI wanted to use paired t-tests. As a middle ground, I could probably report both of them in the paper, although a bit redundant (both tests came out statistically significant, with p values below the α = 0.05 threshold).
Hello Peter,
In general, I would think that it makes more sense to choose a method that best fits the specific research question, nature of the variable(s) involved, and data collection method and use it rather than run a set of tests on the same data. In a single study, that can mean using different analyses for different dependent variables.
If the chief concern for your variables in your study is about normality, then one approach which will work and is widely available is to run the t-test, but use bootstrap/resampling as the method for determining the probability of a result as or more extreme than that observed under your null hypothesis. Here are some links that introduce and explain the process:
1. http://www.stat.ucla.edu/~rgould/110as02/bshypothesis.pdf
2. https://garstats.wordpress.com/2019/07/25/boott/
3. https://www.uncg.edu/mat/qms/Resampling%20Methods%20Using%20R.pdf
4. https://www.youtube.com/watch?v=L275hyiqSVs
Good luck with your work.
I agree with David Morse , it makes more sense to pick one method that best fits the statistical assumptions and circumstances regarding your data. This is akin to trying out varying statistical tests until you find a test that shows what you want it to show, it simply isn't correct. Additionally, if these tests showed different results, which one do you trust?
Thank you so much. Yes, I'll keep that in mind as well. The results for either statistical test were the same (both report as statistically significant).
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