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