When parametric test assumptions are violated
In the previous chapter, we discussed parametric tests. Parametric tests have strong statistical power but also require adherence to strong assumptions. When the assumptions are not satisfied, the test results are not valid. Fortunately, we have alternative tests that can be used when the assumptions of a parametric test are not satisfied. These tests are called non-parametric tests, meaning that they make no assumptions about the underlying distribution of the data. While non-parametric tests do not require distributional assumptions, these tests will still require the samples to be independent.
Permutation tests
For the first non-parametric test, let’s look more deeply at the definition of a p-value. A p-value is the probability of obtaining a test statistic at least as extreme as the observed value under the assumption of the null hypothesis. Then, to calculate a p-value, we need the null distribution and an observed statistic...
