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* Always when the assumptions for the specific test (as there are many parametric tests) are fulfilled. * When you want to say something about a statistical parameter.
Nonparametric tests are sometimes called distribution free statistics because they do not require that the data fit a normal distribution. Nonparametric tests require less restrictive assumptions about the data than parametric restrictions. We can perform the analysis of categorical and rank data using nonparametric tests.
What is DC parametric tests
Parametric statistical tests assume that your data are normally distributed (follow a classic bell-shaped curve). An example of a parametric statistical test is the Student's t-test.Non-parametric tests make no such assumption. An example of a non-parametric statistical test is the Sign Test.
Parametric tests assume that your data are normally distributed (i.e. follow a classic bell-shaped "Gaussian" curve). Non-parametric tests make no assumption about the shape of the distribution.