Popular Statistical Tests

Konstantin M. Zuev ()
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Konstantin M. Zuev: California Institute of Technology, Department of Computing and Mathematical Sciences

Chapter 10 in Fundamentals of Statistical Inference, 2026, pp 213-261 from Springer

Abstract: Abstract In the previous chapter, we discussed a general framework for hypothesis testing. Our next goal is to consider several specific statistical tests that are often used in practice. In this chapter, we will learn the Wald test and the t-test for testing simple hypotheses, the Kolmogorov-Smirnov test for testing the equality of probability distributions, the likelihood ratio test, which, thanks to its power, is one of the most widely used tests in parametric inference, and an elegant nonparametric permutation test for testing whether two samples were generated by the same data generating process. To illustrate how these tests can be used in applications, we will consider two case studies: we will compare the cholesterol levels in men and women and will statistically test Mendel’s theory of inheritance.

Keywords: Wald test; Student’s test; Kolmogorov-Smirnov test; permutation test; likelihoodratio test (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-03848-7_10

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