Environmental
Statistics
Statistics, down to Earth
Course Outline
Our flagship course, taught over 4.5 days.
DAY 1
Describing Data in a Group
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 Stats
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
Bootstrapping
Exercise: the UCL95 and other intervals
DAY 2
Comparing Two Groups of Data
Are means, medians different?
Parametric and nonparametric tests - which is better? 
Testing paired data
Have standards been met?
The quantile test
Exercise: Precipitation chemistry
How many observations do I need?
Power and sample size
Which units to use?
Numbers of obs for parametric and non-parametric tests
Software available
Comparing Three or More Groups
One- and two-factor ANOVA
Nonparametric alternatives
Multiple comparison tests: who’s different?
Exercise: Metals at six locations
Testing differences in Variability/Precision
Characterizing differences in variability
Levene’s & Squared Ranks tests
Exercise: testing differences in precision
DAY 3
Correlation
Linear and monotonic correlation
r, rho and tau
The Theil-Sen line: a linear median
Exercise: Three correlation coefficients
Linear Regression
Building a good regression model 
Better measures of quality than r-squared
Hypothesis tests, confidence and prediction intervals
Load estimation
Multiple Regression
Measures of a good model
Why plots of Y vs each X don't work, and what to do instead
Multi-collinearity
Model selection methods better than stepwise
Exercise: estimating urban non-point loads
DAY 4
Analysis of Covariance
Do two lines differ in intercept and slope?
Seasonal changes
Exercise: how many regression lines are needed?
Trend Analysis
Selecting a trend test
Regression vs. Mann-Kendall approaches
Monotonic vs. step trends
Dealing with seasonality
Detecting regional trends
Example: Seasonal Kendall test for trend
FINAL EXAM
DAY 5
Handling Nondetect Data Correctly
Why not substitute 1/2 the detection limit?
Invasive data
Simple methods without substitution
Contingency Tables
Does the frequency change between groups?
Use with censored data
Exercise: uranium in drinking water
Logistic Regression
Regression for categorical responses
Application to nondetects, ratings, qualitative field methods
Exercise: regression for atrazine concentrations with nondetects