One-Sample Tests

Kenneth J. Berry and Janis E. Johnston

Chapter Chapter 3 in Statistical Methods: Connections, Equivalencies, and Relationships, 2023, pp 55-89 from Springer

Abstract: Abstract Chapter 3 describes connections, equivalencies, and relationships relating to one-sample tests of null hypotheses. First, Student’s conventional one-sample t-test is described. Second, a permutation one-sample test is presented and the connection linking the two tests is established. An example analysis illustrates the differences in the two approaches and the connection linking the two tests. Third, measures of effect size for one-sample tests are presented for both Student’s one-sample t-test and the permutation one-sample test and the connections linking the various measures are set out. Fourth, Wilcoxon’s nonparametric one-sample signed-rank test is introduced for rank-score data and illustrated with an example analysis. A permutation alternative to Wilcoxon’s test is described and the connection linking the two tests is established. Finally, the connection linking a conventional one-sample z-test for proportions and Pearson’s chi-squared goodness-of-fit test is delineated.

Date: 2023
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DOI: 10.1007/978-3-031-41896-9_3

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