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Introduction to Statistical Investigations

Nathan Tintle, Beth L. Chance, George W. Cobb, Allan J. Rossman, Soma Roy, Todd Swanson, Jill VanderStoep
Publication Date: 
Number of Pages: 
[Reviewed by
Robert W. Hayden
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This book is authored by a star-studded cast of statistics educators and reflects current thinking in the statistics education community on what we should be doing in a first course. The book is innovative in many ways, so perhaps one form a review might take is to look through the authors’ list of claimed goals and innovations. For once, that list signals a book that really is different.

The first novelty the authors claim is emphasis on a six-step process for statistical investigations. The common cook book textbook focuses almost entirely on their Step 4, which involves doing some calculations. The earlier steps focus on design and the later steps on interpretation. What one can learn from a study depends almost entirely on the design, and whether one learns it depends on the interpretation, so an emphasis on these issues is welcome.

The authors generally carry through on this, with an extended explanation of the steps early on, and many examples in the exposition in later chapters. In places the exercises seemed to fall behind, with long stretches of “do a hypothesis test” type problems, though those usually did ask for more interpretation than is usually found in cookbooks. There are a few “How would you design a study to answer this research question?” exercises. Many more would be welcome. Consideration of different design approaches can shed a lot of light on interpreting the study results later on.

The second innovation is the incorporation of randomization-based inference procedures. The usual reasons given for doing this are that students find it easier to understand than approaches based on theory, and randomization methods are useful techniques in their own right. The drawback is that this adds new topics to a course that is already overcrowded.

The authors’ third innovation seems to be an elaboration of the first, and the fourth does not sound particularly innovative. The fifth is the use of online applets to get the computing done. Here a choice has been made to use software designed primarily for pedagogical purposes. Given the other innovations, it might be hard to find a standard software package that both supports the program and is easy for students to use. However, this does have the cost that students leave the course not knowing a standard package that could be used in later courses or in their own research.

The underlying issue is that a first course tries to meet the needs of two groups of students. Some just need to interpret what they read in the news, or what their doctor tells them, but will never do a research study themselves. Others will take more research courses and actually do research, or at least read a lot of journal articles. Every textbook for a first course has to strike a balance between the needs of these two audiences. Whether this book strikes the correct balance will depend largely on the actual audience for a particular course at a particular school.

The last innovation is the use of real data from real studies. Elsewhere the authors indicate they want studies of some importance, not just bunches of numbers used as fodder for arithmetic practice. The authors do well with this, but many other authors have as well, going all the way back to Snedecor and Cochran, the original statistics textbook for beginners.

The authors go on to list some innovations in pedagogy. Perhaps the most important thing to say here is that the book really requires you to buy into the authors’ pedagogical approach. This is not the sort of book in which both students and instructor can largely ignore the exposition and concentrate on the practice exercises.

This review is written with an MAA audience in mind, which will include teachers who are not highly trained in statistics or cognizant of current thinking in statistics education, but still need to teach statistics. There can be a great benefit in using a book that spells out the approach of some leading thinkers in that area.

The one possible concern about the approach in this textbook is that it contains some very long and detailed verbal expositions. The quality is very high, but one wonders how many students will be able to follow them, or even how many will try. The instructor may need to read these passages very carefully and make sure that the points get covered in class and in the explorations and activities the students carry out.

This book is sufficiently different that it should be on every list of textbooks under consideration for a first course. It is especially recommended where none of the teaching team have been trained as statisticians. Just ask yourself how you would feel about a college-level mathematics course taught by a non-mathematician. Would you like them to listen to your thoughts on how to teach the course?

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.

P.  Preliminaries: Introduction to Statistical Investigations
                P.1 Introduction to the Six-Step Method
                P.2 Exploring Data
                P.3 Exploring Random Processes

Unit 1: Four Pillars of Inference: Strength, Size, Breadth, and Cause

1.  Chapter 1: Significance: How Strong Is the Evidence?
                1.1 Introduction to Chance Models
                1.2 Measuring the Strength of Evidence
                1.3 Alternative Measure of Strength of Evidence
                1.4 What Impacts Strength of Evidence?
                1.5 Inference for a Single Proportion: Theory-Based Approach
2. Chapter 2: Generalization: How Broadly Do the Results Apply?
                2.1 Sampling from a Finite Population
                2.2 Inference for a Single Quantitative Variable
                2.3 Errors and Significance
3. Chapter 3: Estimation: How Large is the Effect?
                3.1 Statistical Inference: Confidence Intervals
                3.2 2SD and Theory-Based Confidence Intervals for a Single Proportion
                3.3 2SD and Theory-Based Confidence Intervals for a Single Mean
                3.4 Factors that Affect the Width of a Confidence Interval
                3.5 Cautions When Conducting Inference
4. Chapter 4: Causation: Can We Say What Caused the Effect
                4.1 Association and Confounding
                4.2 Observational Studies versus Experiments

Unit 2: Comparing Groups

5. Chapter 5: Comparing Two Groups
                5.1 Comparing Two Groups: Categorical Response
                5.2 Comparing Two Proportions: Simulation-Based Approach
                5.3 Comparing Two Proportions: Theory-Based Approach
6. Chapter 6: Comparing Two Means
                6.1 Comparing Two Groups: Quantitative Response
                6.2 Comparing two Means: Simulation-Based Approach
                6.3 Comparing Two Means: Theory-Based Approach
7. Chapter 7: Paired Data: One Quantitative Variable
                7.1 Paired Designs
                7.2 Analyzing Paired Data: Simulation-Based Approach
                7.3 Analyzing Paired Data: Theory-Based Approach

Unit 3: Analyzing More General Situations

8. Chapter 8: Comparing More Than Two Proportions
                8.1 Comparing Multiple Proportions: Simulation-Based Approach
                8.2 Comparing Multiple Proportions: Theory-Based Approach
9. Chapter 9: Comparing More Than Two Means
                9.1 Comparing Multiple Means: Simulation-Based Approach
                9.2 Comparing Multiple Means: Theory-Based Approach
10.  Chapter 10: Two Quantitative Variables
                10.1 Two Quantitative Variables: Scatterplots and Correlation
                10.2 Inference for the Correlation Coefficient: Simulation-Based Approach
                10.3 Least Squares Regression
                10.4 Inference for the Regression Slope: Simulation-Based Approach
                10.5 Inference for the Regression Slope: Theory-Based Approach

Appendix A: Calculation Details

Appendix B: Stratified and Cluster Samples

Solutions to Selected Exercises