As we have discussed elsewhere, to use the t-test for independent samples, the data in each sample must be normal (or at least symmetric) and the presence of outliers should not distort the results. In the case of paired samples the differences in measurements must be normal or at least symmetric and there shouldn’t be significant outliers in these difference measurements.
In case one of these conditions is not met, we have the following choices:
- Check the data – in particular, make sure that that the problematic data are true outliers and not errors in copying
- Ignore the problem – not recommended since this will usually cause problems
- Transform the variable, the Box-Cox transformation can be especially useful
- Use a non-parametric test
- Use robust estimators of the mean and variance – e.g. use the median (which is more resilient to outliers than the mean)