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.
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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.
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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.
There are several reasons, including the following, in no particular order:I suspect that many or most people learn the parametric alternatives first, or learn mainly the parameteric alternatives.When the correct conditions hold, the parametric alternatives provide the best power.In some situations, such as the more complicated ANOVA and related methods, there are no nonparametric alternatives.Often data that do not appear to satisfy the requirements for parametric procedures can be transformed so that they do, more or less.Parametric procedures have been shown to be robust in the face of departures from the assumptions on which they were based, in many cases.
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