Assumption of dependent t-test

Question

Some sources (i.e. https://statistics.laerd.com/spss-tutorials/dependent-t-test-using-spss-statistics.php) include assumption about outliers. "There should be no significant outliers in the differences between the two related groups". However, the text book that I read, does not.

My question is, should I check for existence of outliers or normality test is enough to conduct dependent t-test? if yes, what does "significant" outliers mean here?

The number of outliers? Extreme outliers (outlier > IQR*3+Q3 / outlier < Q1 - IQR*3) ?

Can I still conduct t-test if my data are normally distributed but there are mild outliers? (not extreme)

If my data are not normally distributed I use Wilcoxon signed-rank test. Are mild outliers problem for this test as well?

Answer 1

In this context, outliers could be defined as any data point that makes the distribution deviate from normality. So, looking for outliers and checking for normality are both to satisfy the same assumption.

Exactly what constitutes and outlier is pretty subjective though.

Mild outliers might not be a problem for the t-test if you have a big enough sample size — the central limit theorem will allow you to do the test if your distribution is close to normal even without a huge sample size.

Outliers are not a problem for the Wilcoxon test because normality is not a necessary condition.