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The Nature of Statistics

W. Allen Wallis and Harry V. Roberts
Dover Publications
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Robert W. Hayden
, on

What we have here is a Dover reprint of an initial segment of an innovative introductory statistics textbook originally published in 1956. The shorter book is something of a classic and has been available in a variety of formats from a variety of publishers over the years. The content is material beginners really need to know, but that is not included in most other textbooks. Such textbooks tend to focus on getting the computations done, while the book at hand focuses on the more important issues of designing a study and interpreting its results.

The first chapter deals with the field of statistics in general, and, more broadly, with scientific method. There is an emphasis on the need for careful design prior to doing any arithmetic. The second chapter consists of more than two dozen short examples of the use of statistics. These are meaty, real applications that give the reader a sense of the power of statistics. Both of these chapters would make excellent supplementary reading for students. The third chapter discusses three applications in much greater detail. Students rarely get any sense of what a scientific study looks like as a whole, so these examples are valuable. However, they are so detailed that a reasonable assignment might be to ask students to choose one of the three to read.

Chapter 4 is similar to Chapter 2, but this time we get many examples of misuses of statistics. This too would make excellent supplementary reading. Chapter 5 is about samples and populations. It contains a very early use of a simulation to explain the idea of sampling variability. Handy readers may even want to try to build the sampling apparatus described. This material is covered well by some but not all textbooks. and so may or may not be a useful supplement. This would apply as well to Chapter 6 on randomness and it role in statistical inference.

Chapter 7 discusses issues involved in making sound measurements and observations. Some of this gets rather philosophical but the many examples remain excellent. More fine supplementary reading, as is Chapter 8 about designing and conducting surveys. Chapter 9 is on reading a table and provides a thorough analysis of one complex table. The example table, and the terseness of the explanation, make one wonder if this belongs in an introductory course. On the other hand, we do generally assume that students can read a contingency table, which may be optimistic. Having students make a couple of contingency tables by hand from raw data might be an exercise on tables more directly relevant to a first course.

To place this work in the context of other, similar books, we can say that it is similar to Huff’s How to Lie with Statistics but with a lot more depth, yet without a higher reading level. Perhaps complementing it are the various case study collections that focus more on the analysis than on design or interpretation.

One disappointment is that there is not a treatment of experiments parallel to the treatment of surveys, but that is absent from most other textbooks as well. In a few places the book shows its age, but a surprising number of the examples hold up well. Most deal with issues that have not changed since the book was written. A useful assignment for students might be to find and evaluate more recent examples.

This book covers essential information for students in a first course in statistics and is one one of the best supplements one could use for that material. The modest price makes it even more attractive. Highly recommended.

After a few years in industry, Robert W. Hayden ( taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.

1. The Field of Statistics

2. Effective Uses of Statistics

3. Psychoses, Vitamins, and Rain-Making: Three Extended Examples

4. Misuses of Statistics

5. Samples and Populations

6. Randomness

7. Observation and Measurement

8. Kinds of Data

9. How to Read a Table