Permutation Hypothesis Testing with Example | Statistics Tutorial # 37 | MarinStatsLectures

Permutation Hypothesis Testing in Statistics with Examples: What is a Permutation Test? How to Do a Permutation Test in Statistics and Research? 👉🏼Related: Bootstrapping Concept and Bootstrapping in R Videos: (https://bit.ly/2GL6AYS) ; Permutation Hypothesis Test with R    • Permutation Hypothesis Test in R with...   👍🏼Best Statistics & R Programming Language Tutorials: ( https://goo.gl/4vDQzT )
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In this video, we present the general concept of a Permutation Test. Permutation tests also get referred to as “Exact Hypothesis Tests”, and serve as an alternative approach to large-sample parametric approaches.

In mathematics, a permutation is the act of taking the members of a set (in this case, the set of all observations from the sample), and rearranging or reordering them. The total number of permutations for a set is the total number of unique re-orderings of the elements of a set. For example, if a set consists of (A, B, C), there are 3!=6 total permutations (ABC, ACB, CAB, BAC, BCA, CBA).

A Permutation hypothesis test makes use of the concept of permutations. The underlying concept of a Permutation Test is as follows. First, a test statistic is defined, and calculated for the observed sample data. Then, all possible permutations of the data are considered, and the test statistic is calculated for all possible permutations of the data. A p value is then calculated as the total percentage of permutation test statistics that are greater than or equal to the test statistic calculated for the observed sample data. In this sense, the p value is helping us to get an idea of how extreme the observed test statistic for the sample data is.

Because a permutation test considers all possible permutations, it gets referred to as an exact test, and calculates an exact p-value. In a real world, the total number of permutations for a set of data is extremely large, and in practice a random sample of all permutations is generally taken to work with (so in this sense, a permutation test often results in an approximate p value, even though it is usually referred to as being an exact test).

In this statistics video tutorial, we lay out the general procedure and concept of a permutation test. While the idea is presented in reference to a specific example (with X=categorical/factor/qualitative, and Y=numeric/continuous/quantitative), we present the concepts as generally as possible, so that the concept can be easily extended to permutation tests using different types of variables.

Accompanying this video is a separate video implementing the permutation test using the statistical software R (using RStudio).



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