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Chapter 8 Statistical tests

Having discussed the idea of hypothesis testing, we can now move to the discussion of specific tests. In this chapter, we will start the discussion with the tests for the means of random variables, then move towards the variance and to the comparison of several variables. The tests in this chapter are introduced based on the needs of an analyst. We finish the chapter with a discussion of how to select the appropriate statistical test for your problem.

Before we proceed, we need to define two terms, which will be used in this chapter. Parametric statistical test is the test that fully relies on distributional assumptions about the random variable. For example, we can assume that the variable follows Normal distribution and thus we can use a parametric test. Non-parametric statistical test is the test that does not rely on distributional assumptions. These types of test are typically conducted on ranked data rather than on the original one, reducing the scale of information to the ordinal one (see Section 1.2). The parametric ones are typically more powerful than their non-parametric counterparts if the assumptions hold. If they do not, the non-parametric ones become more powerful.