Most types of hypothesis test require that the population conforms to a particular distribution, usually the normal distribution. Where this is not the case a nonparametric test can be used.
Nonparametric tests make no assumptions about the type of distribution (although they may require symmetry, or some other property). The disadvantage is that nonparametric tests are not as efficient; for a given data set the nonparametric test will give a higher p-value.
Nonparametric Tests include:
Parametric tests include ANOVA, the t test, the F test and the chi-square test.