If we have small samples, the one and two sample t tests and the test of comparing K means are all valid only if we are sampling from normal populations. This week we study methods for comparing the distribution of populations that do not require the normality (or any other distributional assumption). There are two basic points to be made:
1. The distribution-free methods are valid for any
distribution of the populations being compared, that is, if we
specify a certain 
value, then the true type I error
probability is .
2. If the populations being compared do in fact have the normal distribution, then the previous methods (t tests and so on) are in fact better than the distribution-free methods we will study. They are better in the sense that if the populations are different, then the parametric procedures have a better chance of concluding they are different (that is, they are more powerful).
These two points are illustrated in the ``Comparing Parametric and Nonparametric Tests'' concept lab.