Permutation Tests and Bootstrapping

Never worry about a normal distribution again!

Course Outline

Day 1

• Why are permutation tests important to environmental science?
• What 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

Online at: