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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?

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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.

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  • $\begingroup$ If this is routine work (you say "in my daily work") with same sort of data, join many data sets (maybe of residuals) and test the for normality (or plot them qq-plots) jointly. If this is far from normal, consider switch to some more robust tests. $\endgroup$
    – kjetil b halvorsen ♦
    May 3, 2020 at 19:55
  • $\begingroup$ @kjetilbhalvorsen,what's the more robust tests.? $\endgroup$
    – kittygirl
    May 3, 2020 at 20:00
  • $\begingroup$ Could be Wilcoxon test. Search this site! $\endgroup$
    – kjetil b halvorsen ♦
    May 3, 2020 at 20:01
  • $\begingroup$ Does t.test(paired =TRUE) include above pre test? $\endgroup$
    – kittygirl
    May 3, 2020 at 20:01
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    $\begingroup$ @kittygirl No it doesn’t, and the point of my post is that pre-testing isn’t worth doing. Graphical examination is the way to go. If you see severe deviations from normality, consider another kind of test. $\endgroup$
    – Dave
    May 3, 2020 at 20:10

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