The appropriateness of a statistical test, which depends on underlying distributional assumptions, is generally not a problem if the population distribution is known in advance. If the assumption of normality is known to be wrong, a nonparametric test may be used that does not require normally distributed data. Difficulties arise if the population distribution is unknown—which, unfortunately, is the most common scenario in medical research.
Many statistical textbooks and articles state that assumptions should be checked before conducting statistical
tests, and that tests should be chosen depending on whether the assumptions are met (e.g., [22,28,47,48]).
Various options for testing assumptions are easily available and sometimes even automatically generated within
the standard output of statistical software (e.g., see SAS or SPSS for the assumption of variance homogeneity for
the t test; for a discussion see [42-45]).