Does paired sample `t test` need pre test?

Question

Paired t-test can be used only when the difference d is normally distributed. This can be checked using Shapiro-Wilk test.

This sentence come from http://www.sthda.com/english/wiki/paired-samples-t-test-in-r

In my daily work, I always use t.test(data~group,alternative = 'two.sided',paired =TRUE) to paired sample t-test. I never do above mentioned pre test.

Does paired sample t test need pre test?

Answer 1

The general sentiment on Cross Validated is that formal testing of normality is not helpful: either you have too few observations to reject, or you have so many that the tests become sensitive to deviations from normality that are not practically significant because your data are “normal enough”. Graphical examination such as histograms, kernel density estimates, and normal quantile-quantile plots will be your friend.

The t-test happens to be rather robust to deviations from normality, too. Also remember that you’d assess the differences between the groups, not the groups themselves.