Environmental
Statistics
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