Permutation Tests

Never worry about a normal distribution again!

Course Outline

Day 1

Basics

Why are permutation tests important to environmental science?

iWhat are the advantages over parametric test methods?

Bootstrap intervals

Advantages over t-intervals for skewed data

Statistical foundations for bootstrapping

Bootstrap confidence and other intervals

Exercise: UCL95 for background data

Permutation Tests

Statistical foundations for permutation tests

Power of parametric vs permutation tests

How permutation tests obtain p-values

Software and references

Permutation Tests for Paired Data

Paired perm test vs sign and signed-rank tests

Computation of the paired permutation test

Exercise: comparing inflow and outflow data

Day 2

Permutation Tests for Independent Two-Sample Data

Permutation tests vs t-test and Mann-Whitney (rank-sum) test

Computing the two-sample permutation test

Exercise: comparing background to elevated site concentrations

Permutation Tests for Three or More Groups

Permutation tests vs ANOVA and Kruskal-Wallis tests

Computing the one-factor permutation test

Exercise: comparing difference in means between groups

Comparing blocked permutation tests to the Friedman test

Computing the blocked permutation test

Exercise: trends over time at multiple sites

Comparing permutation tests to contingency tables

Computing the permutation (exact) test for tables

Exercise: testing differences in counts of organisms

Permutation Tests for Regression

Permutation tests for the linear regression setup

Permutation tests as an alternate to transforming the y variable

Permutation tests vs Thiel-Sen regression

Bootstrapped intervals for linear regression

Exercise: computing regression with non-normal residuals