Statistics, down to Earth
Course Outline
Our
flagship course, taught over 4.5 days.
DAY 1
Describing Data in a
Group
What's your best estimate?
How noisy is it?
Dealing with outliers
When to transform the scale
How Hypothesis Tests Work
Their common denominators
Their jargon explained
Tips and tricks for computer and hand
calculation
1-sided and 2-sided tests
Exercise: testing means
Statistical intervals
Coping with uncertainty
Coping with skewed data
Confidence, prediction, tolerance
intervals
Exercise: the UCL95 and other
intervals
Contingency Tables
Does the frequency change between
groups?
Use with censored data
Exercise: uranium in drinking water
DAY 2
Comparing Two Groups of
Data
Are means, medians different?
Parametric and nonparametric tests
Paired data
Have standards been met?
The quantile test
Exercise: Precipitation chemistry
How many observations do I
need?
Weaknesses of standard formulae
Interactions between variation, power, and
dollars
Software available
Comparing Three or More
Groups
one- and two-factor ANOVA
non-parametric 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
PROBLEM: variability of
concentrations
Correlation
Linear and monotonic correlation
r, rho and tau
Kendall’s linear model
Exercise: Three correlation
coefficients
DAY 3
Linear Regression
Building a good regression model
determining improvements over background
noise
hypothesis tests, confidence and
prediction intervals
Exercise: estimating total load
Multiple Regression
measures of a good model
plot the data !
multi-collinearity
model selection methods better than
stepwise
Exercise: estimating urban non-point
loads
DAY 4
Analysis of Covariance
Do two lines differ?
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
Logistic Regression
regression for categorical responses
application to nondetects, ratings,
qualitative field methods
Exercise: regression for atrazine
concentrations with nondetects
Equivalence Tests
difference from standard statistical
tests
testing for differences that are "big
enough"
equivalence between groups, trends
Class Discussion and
Applications