Statistical Analysis

What I want to cover in this topic is to look at how to interpret results. Most of this is statistical techniques which you may have learned in your other course or perhaps not. I'm not interested in how to do it as much as what the techniques are applicable to and why the statistical procedures you have probably learned don't always work.

Readings
Artiola et al Chapter 3

Statistical Methods for Groundwater Monitoring - Gibbons
A good book with lots of examples geared towards compliance/detection monitoring.
Ch 10 on censored data discusses some of the fancier methods for non-detects, pg 211-214 discusses comparison of methods, Chp 11 discusses outliers, Chp 8 Control charts

Nondetects and Data Analysis - Helsel
Really covers a lot of possibilities for non-detect analysis, discusses PQL and MDL, discusses data storage problems and some ways of plotting
Read pg 1-19, 37-38, and the introductions and summaries for Chp 9 and 10.

Using Statistical Methods for Water Quality Analysis
G. MacBride
This is an excellent book, really covers all the issues well and is pretty easy to read. Good examples and even problem sets to work on. ANOVA 95-99

Statistical Methods in Water Resources
U.S. Geological Survey, Techniques of Water-Resources Investigations Book 4, Chapter A3
R. Helsel and R.M. Hirsch
http://pubs.usgs.gov/twri/twri4a3/
Written for USGS class, covers most of the types of water-quality questions commonly encountered, Chp 1 on summary data, Chp 2 on graphical methods

http://www.sportsci.org/resource/stats/index.html
A simplified but good site with a lot of definitions

EPA documents on statistics
Unified Guidance on the Statistical Analysis of Ground-Water Monitoring Data
http://www.hanford.gov/dqo/project/level5/statanal.pdf
http://www.epa.gov/correctiveaction/resource/guidance/sitechar/gwstats/gwstats.htm

Quality Guidance for Data Quality Assessment, Practical Methods for Data Analysis
EPA QA/G-9
http://www.epa.gov/QUALITY/qs-docs/g9-final.pdf

Guidance for Comparing Background and Chemical Concentrations in Soil for CERCLA Sites. EPA 540-R-01-003 OSWER 9285.7-41 September 2002
http://www.epa.gov/oswer/riskassessment/pdf/background.pdf

Other References:
Statistical Procedures for Analysis of Environmental Monitoring Data and Risk Assessment - McBean and Rovers
Environmental Statistics and Data Analysis Wayne Ott

Outline
Characteristics and presentation of water quality data
Graphical representations
Common statistical distributions
Censored data
Detecting Outliers
Confidence, Tolerance, prediction intervals
Control Charts
Hypothesis testing
Comparing two independent sets of data
Paired data sets
Comparing Several Independent Groups
Trend analysis

What kinds of problems/questions do we have to deal with in water?

Characteristics and presentation of water quality data
What are some measures of a dataset?
What is skewness, kutosis?

What do the following plots show:
" Stiff diagrams
" Schoeller diagrams
" Piper diagrams
" Contour maps
" Time series displays
" Histograms, cumulative frequency
" Boxplots, Box and whisker plots

What distributions are common to gw? How does this affect statistical testing?
Why is it so important to test for distribution?
What tests can be used to check for Normality? Which ones are recommended and not?

What is the importance of knowing the variance of your sample set?
What methods are available to check variances?

What is censored data? Why does it occur?
Discuss the following tests - what are they good for, limitations
½ DL
Cohen's method, Atchinson's method, Probablity plot for deciding
How do maximum likelihood estimators work?
What non-parametric tests work?

What is an outlier? Why may they occur?
What are some procedures for evaluating outliers?
How do you treat outliers? Should they be discarded?

What is the difference between confidence intervals, tolerance intervals, and prediction intervals? Where is each useful?

What are control charts all about? Where do they work?

Why do we do hypothesis testing?
What is a Type I error? A Type II?
How do we pick a hypothesis test?
What is the difference between a one-sided and two-sided test?
What is all the controversy over the pnull methods?
What are typical tests parametric and non for 2 samples, multiple samples, paired samples?

What is trend analysis good for?
What kind of trend tests are there?
What do we do about seasonality?
What is LOWESS?