Course Outline

Our flagship course, taught online, or over 4.5 days

DAY 1

Describing Data
• When to use a median vs a mean
• Dealing with skewed, non-normal data
• Dealing with outliers
• When to transform the scale

Seven Urban Legends in Environmental Statistics
• Do parametric methods have more power than nonparametric tests?
• Why t-tests on logarithms don't test differences in means
• Why t-tests don't test whether one group has higher values than the second
and more....

How Hypothesis Tests Work
• Structure of hypothesis testing
• Their jargon explained
• Parametric, nonparametric and permutation tests. When to use each.
• 1-sided and 2-sided tests
• Checking data distributions
• Illustration: How tests obtain a p-value

Statistical Intervals
• Confidence, prediction, tolerance intervals
• Intervals with small sample sizes
• Coping with skewed data
• Bootstrap intervals — and why to use them instead of t-intervals
• Exercise: the UCL95 and other intervals

DAY 2

Comparing Two Groups of Data
• Are means, medians different?
• Parametric, nonparametric and permutation tests
• Testing paired data
• Have standards been met?
• The quantile test
• Permutation tests — test the mean for non-normal distributions

Comparing Three or More Groups
• One- and two-factor ANOVA
• Nonparametric Kruskal-Wallis test
• Multiple comparison tests: who’s different?
• Permutation one-factor test: never worry about a normal distribution again!

Contingency Tables
• Does the frequency change between groups?
• Application to nondetect and other cateogories
• Bootstrapping contingency tables

Testing differences in Variability/Precision
• Characterizing differences in variability
• Levene’s & Fligner-Killeen tests
• Why NOT to use Bartlett’s test

DAY 3

Correlation
• Linear and monotonic correlation
• r, rho and tau
• Permutation test for Pearson’s r correlation
• The Theil-Sen line: a linear median

Linear Regression
• Building a good regression model
• Better measures of quality than r-squared
• Hypothesis tests, confidence and prediction intervals
• Consequences of transforming the Y variable
• Bootstrapping tests for significance - an alternative to transformations

Multiple Regression
• How to build a good multiple regression model
• Why plots of Y vs each X don't work, and what to do instead
• Multi-collinearity
• Model selection methods better than r-squared or stepwise
• Bootstrapping tests for significance - an alternative to transformations

DAY 4

Analysis of Covariance
• Testing whether there is one or more than one regression line
• Are there differences in intercept and slope?
• Modeling seasonal changes

Trend Analysis
• Selecting a trend test
• Regression vs. Mann-Kendall approaches
• Monotonic vs. step trends
• Dealing with seasonality: the Seasonal-Kendall test for trend
• Detecting consistent regional trends across sites
• R routines for trend testing

Final Exam

DAY 5

(half day)

Handling Nondetect Data Correctly (In-person course only)
• Why not substitute 1/2 the detection limit?
• Simple methods without substitution
• Introduction to survival analysis methods

Logistic Regression
• Regression for categorical responses
• Effect of X variables on the odds
• Modeling nondetects, qualitative methods, and the probability of something bad happening
• Multicollinearity and hypothesis tests