Those of us who have taught a Chance course have used a supplementary textbook and find this helpful. It is useful for students to have a resource where they can get a systematic treatment of statistical concepts at an elementary level. It is important that this book be elementary and very clear so that students with no formal background can read it on their own. It is useful if this book is non-mathematical and organized into chapters that may be understood if read in a non-linear order. Two books that have met these requirements are David Moore's Statistics: Concepts and Controversies (3rd edition, paperback, 1991, W.H. Freeman) [Moore] and Freedman, Pisani, Purves, and Adhikari's Statistics (2nd edition, hardback, 1991, W.W. Norton) [FPPA].
Moore is the more elementary of the two. It contains 3 major parts: I - ``Collecting Data'', II - ``Organizing Data'', and III - ``Drawing Conclusions from Data''. Part I has very lively and intuitive chapters on sampling, experiments, and measurement with lots of real life examples. Part II has good explanation of what are now standard descriptive and EDA statistics, including an excellent chapter on relationships including both qualitative variables (cross-classifications, controlling for extraneous variables), and quantitative variables (regression, correlation). All of this is done at the descriptive level with the emphasis being on what relationships mean. Part III treats probabilities as a frequentist and thinks of their computation as a job for simulations. This paves ground for a very intutive final chapter on statistical inference, with the emphasis on what a confidence interval is and what a statistical test is and their uses and abuses.
FPPA has much the same material as Moore but at a slightly deeper level. For example, FPPA discusses residuals and the root-mean-square-error for the regression line while Moore does not. FPPA does a lot more with probability than Moore. FPPA discusses conditional probability, teaches computing probability by a few simple rules, and has a chapter on the binomial. FPPA then devotes 3 entire chapters to computing probabilities for sums (and averages) of draws (with replacement) from a box of numbered tickets - so-called ``box models''. This discussion culminates in the central limit theorem. It is done in a highly conversational, non-technical way, free of mathematical proof or notation. Yet it clearly demands much more of the student than does Moore.
While both books can be used with a beginning audience, FPPA will demand more of the student and so may require a bit more help or should perhaps be used with students who are a bit more quantitatively gifted.
Both Moore and FPPA contain excellent exercises. We recommend assigning some of these to the students on a regular basis to be counted in the course grade. Some of us assign these exercises on a daily basis to be handed in and graded like normal homework. Others have had the students keep these in a looseleaf journal, to be self-graded and commented on by the students, and handed in 3 or 4 times during the semester. Since class discussion rarely revolves explicity around these assignments we are still feeling our way around the notion of getting our students to understand this material.
What follows is an identification of the various topics with portions of these two textbooks that pertain to those topics. We have chosen to list statistical topics followed by Chance topics. In the list of Chance topics you should find most of the topics that at least one of us has taught. Attached to this document is a copy of the table of contents of each book.
Statistical topic: Surveys and sampling
Chance topics: Public opinion polls and survey sampling; Census undercount
Statistical topic: Experiments and observational studies
Chance topics: Clinical trials, experiments, and other studies
Since many discussions in our Chance courses have centered on media reports of some new scientific study this material is central to much of the course. For this reason it might be good to include this reading early in the course. These readings and discussions typically do not require statistical inference.
Statistical topic: Probability
Chance topics: Paradoxes, coincidences, gambling, DNA fingerprinting, streaks and runs (e.g., in sports), card shuffling, lotteries, etc.
Statistical topic: Statistical tests
Chance topics: Statistics in the law and more advanced articles on clinical trials and experiments
Note: Journal articles on an experiment will typically require knowledge of statistical tests and P-value.
Statistical topic: Basic descriptive statistics
Chance topics: A variety of Chance topics require knowledge of means, standard deviations, basic graphical procedures, and the normal curve.
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