In parametric tests we make assumptions about the distribution of the population and each parametric test is specific to a population parameter such as mean or variance, for example, a z-test.
A nonparametric test is not concerned with a parameter or makes minimal assumptions about the population being sampled.
A nonparametric test is primarily used in three situations:
- when data does not meet distributional assumptions
- when data are given in ranks
- when the hypothesis we are addressing does not concern a parameter