Basic Statistics for Environmental Studies: A Distance-Learning Course

Richard Cellarius, Ph.D., Prescott College, Prescott, AZ

e-mail: ; Phone: 928-778-6724; Web:

Texts:     Triola, Mario F. (2001).   Elementary Statistics Using Excel . (1st Ed,)   Boston: Addison-Wesley Longman. ISBN 0-201-69942-7
[This edition is specifically required.]

Moore, David S.(2001).   Statistics: Concepts and Controversies (5th Ed.).  New York: W. H. Freeman.   ISBN 0-7167-4008-7
[This edition is specifically required.]

Tools:     Hand calculator with statistical functions (graphing calculator not required); Microsoft Excel spreadsheet program

Credit:   2-3 semester credits, depending on number of topics completed, Minimum 2 credits for Topics 1-3; 1 credit additional for Topics 4-5 combined.

I have prepared a series of five reading and problem assignments based on the above texts.   In each assignment, I provide a brief overview of the essential points to focus on.  I also provide a series of PowerPoint presentations and video files that assist in the elaboration of the concepts and problem-solving techniques.   The problems from the texts are to be worked either on paper and hand calculator or using Excel. For the full 3-credit course, these will be due as indicated on the attached schedule, usually about 3 weeks from when the assignment is made, based on a time commitment of about 9-10 hours per week. Some folks will find a slower pace will fit their other obligations better; however, completion of Topics 1-3 is essential for a basic understanding of the statistical approach to data analysis. The instructor will review your work and return it promptly. Specific details with be worked out on an individual basis. Contact the Prescott College Master of Arts Program (MAP) office or Environmental Studies Faculty for information on setting up the course and access to the course materials.

IMPORTANT--PLEASE NOTE: The recommended process is for a student to include the course on his or her enrollment form and in his or her semester's study plan. It is up to the student and advisor to determine the process for evaluation. A set of pdf answer files is available from me. They are password protected, and once you have finished one of the five topics, the student or advisor can contact me for the specific file and the  password to the answer file(s) for that topic.  The recommended evaluation process is when the student has completed a topic, the student and advisor evaluate the student's answers using the answer key(s). The student's final self-evaluation for the course should summarize what the student learned and how the learning was accomplished. The advisor's evaluation could support that conclusion based on the student's reporting of the student's overall performance. One simple alternative for stronger evaluation is to have your GA review and correct your answers to the problems specifically identified as "self-evaluation" at the end of Topics 3 etc.

NOTE: Right click on topic number to download a pdf file with the topic instructions; right click on supplementary file names to download those needed files.

Topic 1 : Overview; Descriptive Statistics -- Sampling, the Nature of Data, Displaying Data

This first installment introduces some of the initial concepts of data acquisition and description .  This topic covers a great many topics that might be review of previous learning, at least in part.   The fundamental issue here is to understand the different types of data and how data should properly be obtained and displayed.   Data can often be displayed in a way that misleads or hides critical information, and it is important to be able to recognize this and evaluate those data more correctly. Contact

Topic 2 : Probability and Probability Distributions; Sampling Distributions and the Central Limit Theorem

Probability is one of the most fundamental concepts underlying statistical analysis: given a number of events, what is the probability that a specific event will occur or, if there are repetitive events, what is the proportion of a specific kind of event that is likely to occur.  For statistics, probability can be approached with a full-blown coverage of probability analysis or with a survey of the basic fundamentals sufficient to demonstrate that the statistical procedures encountered later have an adequate mathematical basis.  I have chosen a route closer to the latter, which does not require learning elaborate notations or doing excessive calculations.   The ultimate conclusions to focus on are the nature of probability distributions including the Normal Distribution, sampling distributions , and the Central Limit Theorem , which provides the fundamental rationale for relying on random samples of a population to make statistical conclusions about the entire population.  (Supplementary files The Uniform Distribution.pdf , Excel-Central Limit Theorem.pdf , and 16Sheets.xls )

Topic 3 : Introduction to Inferential Statistics -- Confidence Intervals; Hypothesis Testing and Tests of Significance

The two parts of this Topic introduce the essential concepts and tools of Inferential Statistics , the science and art of making conclusions about populations from statistical samples of those populations.   In the first part, the task is to determine the probable range within which the "true" population value of the quantity in question lies based on analysis of the sample data.  In the second part, the process is extended to make comparative statements or conclusions based on hypotheses about the population, again on the basis of the sample data from that population.  (Supplementary file Temps-Table 6-1.xls )

Topic 4 : More Tests of Hypotheses: Inferences from Two Samples; Multinomial Experiments and Contingency Tables

The two tools covered in this Topic are among the most widely used statistical procedures.   The first, "Inferences from Two Samples," generally follows quite directly and quite simply from the hypothesis testing of a single sample that was the subject of the previous topic; here one of two questions is asked: (1) "are the means of the populations represented by two different samples the same or different?" or (2) "has the population changed as the result of the treatment?"  The second tool involves making inferences from data gathered when there are a number of categories, for example races of people or varieties of trees.   Again we will consider two different types of questions, (1) "how does the distribution in the categories compare with an assumed distribution?" which applies when you're dealing with a sample from a single population--a multinomial experiment--often referred to as a Chi-Square Test by biologists, or (2) "are the distributions among the various categories the same or different in the different samples?" which involves analysis of contingency tables. (Supplementary file Ch 8&10 AltMeth.xls )

Topic 5 : Two Important Analysis Tools: Analysis of Variance (ANOVA) and Correlation & Regression

The two tools described here are again two of the most important tools used in statistical analysis, and for the purposes of this course, they complete our study of basic statistical analysis techniques.  W cover them in the reverse order that they are discussed in the text, primarily because Analysis of Variance (ANOVA) is a logical extension to multiple samples of the hypothesis testing of sample data encountered in one and two sample tests (Topics 3 and 4).  In contrast Correlation and Regression deal with the analysis of a different type of data: pairs of sample data, such as weight and height of individuals, weight and girth of bears, or time and distance for a mode of travel or a race. (Supplementary file Chs 11 & 9.xls )


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Posted January 24, 2002, by Richard Cellarius  

New links added March 17, 2002 and August 16, 2002; Minor editing changes made August 5, 2003; February 10, 2004., May 4, 2006; January 25, 2007, November  8, 2007, March  1, 2011