A statistical hypothesis test that rearranges the labels on data points to assess the likelihood of observing a statistic as extreme as, or more extreme than, the observed statistic. Implementation of this procedure leverages the capabilities of a particular statistical computing language and environment widely used for data analysis, statistical modeling, and graphics. For example, one might use this method to determine if the difference in means between two groups is statistically significant, by repeatedly shuffling the group assignments and calculating the difference in means for each permutation. The observed difference is then compared to the distribution of differences obtained through permutation, thereby determining a p-value.
This non-parametric approach holds value as it makes minimal assumptions about the underlying data distribution. This makes it suitable for analyzing data where parametric assumptions, such as normality, are violated. The method provides a robust alternative to traditional parametric tests, especially when sample sizes are small or when dealing with non-standard data types. Historically, the computational burden of exhaustive permutation limited its widespread use. However, advances in computing power and the availability of programming environments have made this technique accessible to a broader range of researchers.
