Paired t-Test in R - checking normality assumption

// Paired t-Test in R - checking normality assumption //

The main requirement of the paired sample t-test, next to the interval or ratio level for the test variable, is normal distribution. However, not the test variable itself has to be approximately normally distributed. Rather, the residuals need to be. The residuals are simply the difference of the measurements for each individual.

Despite there being three ways to test for normal distribution, the Shapiro-Wilk-test, a histogram or a Q-Q-plot, I will only show the latter for the following reason:
As with all analytical tests, large samples have more power and will “find” significant deviations from normal distribution, even if those deviations are negligible. Therefore, caution is advised when blindly trusting a p-value.

Please refer, among many other publications, to Lantz, B. (2013). The large sample size fallacy. Scandinavian journal of caring sciences, 27(2), 487-492.

Eventually, put emphasis on the plots, mainly a histogram or a q-q-plot. I prefer the latter since one can manipulate the histogram with a proper "bin width".

Final note: a z-standardization before plotting a histogram or q-q-plot is optional. You will only see a slightly different histogram (reminder of the bin width) with less cliffs on the inside. The q-q-plot is not affected, hence my advise to use this as a test for normal distribution.

⏰ Timestamps:
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0:00 Introduction and overview
0:23 Calculating residuals
0:35 Possible ways to test for normal distribution
0:57 Q-Q-Plot for the residuals

If you have any questions or suggestions regarding the normal distribution testing for the paired samples t-test, please use the comment function. Thumbs up or down to decide if you found the video helpful.
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[odaimaihoub]

Thank you Dr. Björn!

Please can you correct me if my understanding is wrong?

If we have paired data ( before treatment, after treatment)
first we need to check normality assumption ( for residuals NOT for each group separately ) using Shapiro-wilk

then if p_value > 0.05, the data is normally distributed, so we can use paired T-test
if p_value <0.05, the data is not normally distributed, so we can use Mann-Whitney Wilcoxon test.

thanks again.