Chance Guide to Supplementary Texts

# Chance Guide to Supplementary Texts

## Thomas Moore

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

• from MOORE: The Introduction to Part I (pages 1 - 3) plus Chapter 1, sections 1 - 5 form the essential reading. This covers the need for good sampling, investigates basic concepts and terminilogy, without going beyond simple random samples. Moore gives lots of real life examples of good and bad surveys, and discusses concepts of bias, precision, and confidence interval. The remaining sections of chapter 1 give the rest of the story including other kinds of probability sampling, as well as good discussions of policy and ethical issues. In chapter 8, sections 1 and 2, Moore discusses confidence intervals more fully and includes formulas for confidence intervals. To understand these sections it helps if the student knows the rudiments of the normal curve, which he/she can get from section 5 of chapter 4. It also helps to have read the probability material from Moore, but neither of these prerequesites is absolutely necessary.

• from FPPA: Chapter 19 has an excellent overview of survey samples with good historical examples of good and bad samples to motivate the need for proper design. This chapter covers the concept of chance error in samples but does not explicitly introduce confidence intervals. To get this story the reader must read somewhat more technical chapters 20, 21, and 23. A hearty student could read sections 1 - 3 of chapter 21, ignoring the few technical references and gain insight into the meaning of a confidence interval. To properly understand chapters 20, 21, and 23 it is necessary to have read and understood at least chapters 13, 16, and 17 on basic probability and on setting up and working with box models. These chapters form the basic information for any Chance topic about probability.

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.

• from Moore: The Introduction to Part I (pages 1 - 3) plus Chapter 2 on experimentation is the essential material. This is full of good examples and is highly non-technical.

• from FPPA: Chapters 1 and 2 on controlled experiments and observational studies provide all the basic information.

Statistical topic: Probability

Chance topics: Paradoxes, coincidences, gambling, DNA fingerprinting, streaks and runs (e.g., in sports), card shuffling, lotteries, etc.

• from Moore: Moore has a very basic approach to probability in chapter 7. This reading will provide the student with the concept of long-range relative frequency, the law of averages, equally likely models, simulation, and expected value. This is a spare toolkit, so the instructor should be prepared to supplement as needed.

• from FPPA: Chapters 13 and 14 introduce the bare essentials to tackle many probability topics. Chapter 13 includes the long-range frequency definition, the definition of conditional events and the product rule for a sequence of two possibly dependent events, independent events and the implications of indendence, and uses the famous Collins case as a final example. Chapter 14 adds the notion of equally likely models and the addition rule for mutually exclusive events to compute probabilities. These 2 chapters are really sufficient to handle any of the example topics listed above with the exception of gambling, which seems to need the notion of expected value. To gain this concept one must read chapters 16 and 17 of FPPA which tell the reader how to compute probabilities for sums (or averages) of draws from a box using the normal approximation. Chapter 17 includes roulette examples.

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.

• from Moore: Two sections give the essence: sections 3 and 5 of Chapter 8. (Section 4 is an optional and more technical section.) It would be advantageous to have read Moore's probability material, but it is not absolutely necessary. Section 3 introduces tests, P-value, and statistical significance. Section 5 discusses ``uses and abuses'' of these concepts.

• from FPPA: Sections 1 - 5 of Chapter 26 and Chapter 29 form the core. In Chapter 26 we learn what a statistical test is, about P-value, and about statistical significance. It really helps to know how sample means vary (chapter 16 and 17) when reading Chapter 26. Chapter 29 includes the ``uses and abuses'' discussion and is important.

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.

• from Moore: Chapters 4 and 5 give the core and are very readable. Especially important sections from Chapter 5 are section 1 on cross-classified data and section 3 on correlation and causation.

• from FPPA: Chapters 4, 5, 8, and 9 form the core. Chapter 5 gives the normal curve a thorough going over, but is accessible by most students. One could skip sections 3 and 4 of chapter 8 (one need not know how to compute ). Chapter 9 is must reading.