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One of the hardest things in environmental statistics has been to test differences in group means, and compute useful confidence intervals, when data are strongly skewed. Traditional t-tests and analysis of variance look for differences in means, but have low power when data are strongly skewed. Transformation to logarithms often addresses skewness, but the resulting tests on logs evaluate differences in geometric means, not means. Rank-based nonparametric tests look for differences in medians. What’s a scientist to do?

Our Permutation Test and Bootstrapping course introduces and explains how permutation and bootstrap methods resolve these problems. Permutation alternatives to t-tests, analysis of variance, and bootstrap confidence intervals allow inferences about the mean, and confidence intervals around the mean, to be made without assuming normality and without transforming variables.

Topics include:
  • What are the advantages of permutation tests over parametric tests?
  • How do permutation tests work?
  • Power of parametric vs nonparametric vs permutation tests
  • What is bootstrapping and how does it work?
  • Computing bootstrapped confidence intervals
  • Permutation tests for paired data
  • Permutation tests for two groups (t-test situation)
  • Permutation tests for 3+ groups (ANOVA situation)

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Course Outline