What is the difference between a parametric and a nonparametric test?
Parametric tests assume underlying statistical distributions in the data. Therefore, several conditions of validity must be met so that the result of a parametric test is reliable. For example, Student’s t-test for two independent samples is reliable only if each sample follows a normal distribution and if sample variances are homogeneous.
Nonparametric tests do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met.
Parametric tests often have nonparametric equivalents. You will find different parametric tests with their equivalents when they exist in this grid.
What is the advantage of using a nonparametric test?
Nonparametric tests are more robust than parametric tests. In other words, they are valid in a broader range of situations (fewer conditions of validity).
What is the advantage of using a parametric test?
The advantage of using a parametric test instead of a nonparametric equivalent is that the former will have more statistical power than the latter. In other words, a parametric test is more able to lead to a rejection of H0. Most of the time, the p-value associated to a parametric test will be lower than the p-value associated to a nonparametric equivalent that is run on the same data.