These web pages were created to supplement chapters 1-7 of Millard and Neerchal's text, Environmental Statistics with S-Plus (CRC Press, 2001). However, they are independent of the text and are intended to stand on their own.
A lot of written material is available in the Class notes section. You can navigate forth and back through the notes, or plunge in by following one of the highlighted links in this table:
| Page | Contents |
| Characterizing Distributions | Graphical and numerical illustration of different techniques used to compute percentiles and plotting positions. |
| Probability plots | Extended discussion of Q-Q plots and probability plots. Normal probability paper is available for creating probability plots by hand. |
| Geometric means, exponentials, and logs | Self-contained introduction leading to methods for rapid calculation with logarithms. An extended discussion, with many examples, also appears at the Logarithms page. |
| Probability paradoxes and simulation | Analysis of the "sibling mystery," the "three coins problem," and the "envelope problem." |
| Ticket-in-a-box tutorial | Brief tutorial, with progressive questions and answers, setting forth the "ticket in a box" model of probability used throughout this course. |
| Properties of distributions
and The Chebyshev UCL Proposal |
Self-contained exposition of Chebyshev's theorem (including a graphical proof) and a critical evaluation of its proposed application to compute UCLs (upper confidence limit) of the mean for environmental applications. |
| Simulation with Excel | Instructions for creating simple Monte-Carlo simulations using Excel (without any commercial add-ons). Examples are available as The Monty Hall puzzle and The Three Coins problem spreadsheets. |
| Decision Theory | Detailed discussion of statistical tests and estimators in a rational decision theory framework (according to Wald, Lehmann, and Kiefer). Contains detailed worked examples of statistical risk functions, including a case involving a non-traditional loss function discussed under the heading "how and why people lie with statistics." This loss function is offered as a model of the behavior of some self-monitoring facilities, such as those in the U.S. EPA's RCRA groundwater detection monitoring program. |
| The 75%-10X rule | Analysis of the operating characteristics of Pennsylvania's "75%/10X" rule. PA's Land Recycling Act ("Act 2") recommends using this ad-hoc test for comparing a median concentration to a standard. In some ways the test is very good and in other ways it is poor, so the discussion concludes with recommendations about when to consider using it and when not to. |
| Hypothesis Tests | An illustration showing how hypothesis testing fits within the rational decision theory framework. The example is designed to illustrate how much of the popular description of statistical testing is nonsensical or meaningless. |
The How To ... pages link to Excel spreadsheets and other DOS/Windows programs for performing simulations and various statistical computations and graphics. Some of these spreadsheets contain macros implementing hard-to-find functions such as Finney's function (for computing minimum variance unbiased estimators for the Lognormal distribution) and the non-central T distribution (for computing Normal-theory tolerance limits and power functions). A few contain tables (such as Land's "H statistics" used for computing 95% UCLs of the mean in the Lognormal setting).
Disclaimer: The software, spreadsheets, and tables available here are not warranted to be correct or free from all defects. Use them for instructional purposes only. If you believe you have detected an error, please be so kind as to e-mail whuber @ quantdec.com with the details.
Eleven Excel spreadsheets available at the Data page contain real environmental data of all types in all media, ranging from soil gas measurements to cone penetrometer test (CPT) measurements. They have been chosen for their tractability and suitability for practice with the techniques taught in the course, but they are also realistically messy: very few of these data sets appear Normal or Lognormal; a few contain typographical errors; they may have additional information (which may or may not be relevant) but more often are missing information the careful analyst would like to have; there are many outliers; some data are censored; and so on. In short, these data are typical of what a practicing environmental statistician is routinely faced with.
A large number of quizzes (over 30), most with detailed solutions, are available at the Quizzes page. The quizzes were used to emphasize fundamental concepts and measure student progress. Some of them cover material of current interest, such as arsenic in drinking water (Quiz 9) and the Centers for Disease Control (CDC) National Report on Human Exposure to Environmental Chemicals (Quiz 10).
Any environmental statistician would make short work of these quizzes. The students, however, found some of them very difficult on the first attempt. A common reaction was "once you really understand the material, they are easy, but until then, you can waste a lot of time in calculations and still get the wrong answer."
Some eleven collections of homework problems, occasionally with solutions, augment the end-of-chapter questions available in the text and provide more worked examples to illustrate the statistical techniques. See the Homework page.
Most of the Class notes pages begin with a carefully selected list of links to other sites on the Web. Usually there is a "terminology" section containing short careful definitions of statistical terms discussed within the notes.
The Links page lists general-purpose references, including a commented bibliography of printed reference material used for this course. This bibliography supplements the larger one presented in the textbook and is intentionally incomplete, but it still covers a lot of ground.
Detailed comments and errata for chapters 1, 3, 4, and 5 of the course textbook appear beginning with Notes on Chapters 1 and 3. They are keyed to chapter and page. For a first printing the book is remarkably free of errors, but some do crop up occasionally. Mainly, however, these comments consist of clarifications and nitpicks.
Return to the Environmental Statistics home page
This page was created 3 May 2001 and last updated 4 May 2001.
Copyright (c) 2001 Quantitative Decisions and William A. Huber. Please cite this page as