The permutation test: a simple way to test hypotheses

Quantitative researchers can use permutation tests to conduct null hypothesis significance testing without resorting to complicated distribution theory. A permutation test can reach conclusions in hypothesis testing that are the same as those of better-known tests such as the t-test but is much easier to understand and implement.

To introduce and explain permutation tests using two real examples of independent and dependent t-tests and their corresponding permutation tests.

This article traces the history of permutation tests, explains the possible reason for their absence in textbooks and offers a simple example of their implementation. It provides simple code written in the R programming language to generate the null distributions and P -values for the permutation tests.

Permutation tests do not require the strict model assumptions of t -tests and can be robust alternatives.

Permutation tests are a useful addition to practitioners' research repertoire for testing hypotheses.