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Teaching StatisticsA Bag of Tricks$

Andrew Gelman and Deborah Nolan

Print publication date: 2017

Print ISBN-13: 9780198785699

Published to Oxford Scholarship Online: September 2017

DOI: 10.1093/oso/9780198785699.001.0001

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Introduction

Introduction

Chapter:
(p.1) 1 Introduction
Source:
Teaching Statistics
Author(s):

Andrew Gelman

Deborah Nolan

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198785699.003.0001

Abstract and Keywords

This introduction to Teaching Statistics describes how an instructor might use this book, the general philosophy behind incorporating demonstrations, examples, and projects into a course, and what makes a good example. This chapter also provides a list of the most popular activities and a table that maps statistical concepts to activities that can be found throughout the book.

Keywords:   Activities, instructor guide, teaching statistics

1.1 The challenge of teaching introductory statistics

We have taught introductory statistics to college students for several years. There are a variety of good textbooks at this level, all of which cover the material pretty well. However, we found it a challenge to keep students motivated in class. Statistics is problem-solving. Watching the instructor solve a problem on the blackboard is not as effective or satisfying for students as actively involving themselves in problems. To improve participation, we and our colleagues have been collecting and developing tools, tricks, and examples for statistics teaching.

Many teachers have their own special teaching methods but they are not always disseminated widely; as a result, some of the best ideas (for example, the survey of family sizes presented here on page 66 and the coin-flipping demonstration on page 119) have been rediscovered several times. We put together this book to collect all the good ideas that we have heard about or developed in our own courses.

By collecting many demonstrations and examples in one place and focusing on the techniques used to involve students as active participants, we intend this book to be a convenient resource for instructors of introductory probability and statistics at the high school and college level. Where possible, we give references to earlier descriptions of these demonstrations, but we recognize that many of them have been used by teachers long before they appeared in any of these cited publications.

This book contains a range of teaching tools. What we find most important about a teaching tool is the basic idea, along with details about how to implement it in class. This can often be explained in a few paragraphs. We try to do this where possible but without skimping on the little details that keep the students involved.

1.2 Fitting demonstrations and examples into a course

The demonstrations, examples, and project ideas presented here are most effective for relatively small classes (fewer than 60 students); with a large lecture course, some of the demonstrations can be done in the discussion sections. These materials are not intended to stand alone. We use them along with a traditional statistics text, lectures, homeworks, quizzes, and exams.

(p.2) The chapters in Part I of the book cover the topics roughly in order of when they occur during the semester, with enough so that there can be a class-participation activity of some sort during every lecture. Many of the activities are relevant to multiple statistical concepts, and so for convenience we have listed them on pages 6–8 by subject. Part III presents some demonstrations and activities for more advanced courses in statistics. In between, we discuss issues of implementing the class-participation activities, along with a detailed schedule of how they fit in to a course. Finally, background information on many of the examples is given in the Notes at the end of the book.

We have found student-participation demonstrations to be effective in dramatizing concepts that students often find difficult (for example, numeracy, conditional probability, the difference between an experiment and a survey, statistical and practical significance, the sampling distribution of confidence intervals). Students are made aware that they and others are subject to cognitive illusions (see, for example, the United Nations demonstration on page 78, the coin-flipping demonstration on page 119, and the lie detection example on page 127). In addition, the experiments that involve data-gathering illustrate general concerns of bias and variance (for example, in the age-guessing example on page 11 and the candy weighing on page 134) and also involve important practical issues such as time trends (shooting baskets on page 148), displaying data (guessing exam scores on page 25), experimental protocol (weighted coins on page 129 and helicopter design on page 337), and the relation between models and data (average family size on page 66). One reason that we believe these demonstrations are important is that the active settings emphasize that statistics is, in reality, a participatory process with many actors (typically, different people design a study, collect data, are experimental subjects, analyze data, interpret results, and so forth).

Perhaps most important, the demonstrations get all the students involved and help to create an environment where students feel free to participate and ask questions in class.

The goal of class-participation tools is to improve learning within class and also to encourage more learning outside of class. Our demonstrations are intended to involve students in traditional lecture material and are not intended as a substitute for more detailed student-involved investigations or group projects. In Section 6.2 we include step-by-step instructions on how to run a class survey project, and in Section 6.4.3 we provide directions for running a simple taste-testing experiment. Chapter 12 gives advice on coordinating projects in which groups of students work on projects of their own design.

At the center of any course on introductory statistics are worked examples illustrating the important concepts and methods in real-data situations that are interesting to students. Good statistics texts are full of such examples, and a good lecture course will introduce new examples rather than simply working out material already in the textbook. Interesting examples can often be found directly from newspapers, magazines, and scientific articles; Chapter 7 presents some examples that have worked well in our classes.

(p.3) There are many other excellent examples in statistics textbooks and other sources. We discuss various places to find additional material in Section 12.6.

1.3 What makes a good example?

We enjoy discussing in class the issue of what makes a good example, opening up some of our teaching strategies to the students.

When a topic is introduced, we like the first example to be simple so that the mechanics of the method are transparent. It is also good to prepare a handout showing the steps of the procedure so that the students can follow along without having to scribble everything down from the blackboard. You can put some fill-in-the-blanks on the handout so the students have to pay attention during the exposition.

It can be good to use fake data for a first example and to discuss how you set up the fake data and why you did it the way you did. For example, we first introduce the log-log transformation with the simple example of the relation between the area of a square and its circumference (page 33). Once students are familiar with the log-log transformation, we use it to model real data and to introduce some realistic complexity (for example, the data on metabolic rates on page 35).

1.4 Why is statistics important?

Finally, it is useful before studying these demonstrations and examples to remind ourselves why we think it is important for students to learn statistics. We use statistics when we make decisions, both at an individual and a public level, and we use statistics to understand the world. Many of the major decisions affecting the lives of everything on this planet have some statistical justification or basis, and the methods we teach are relevant to understanding these decisions. These points are well illustrated by the kinds of studies reported in the press that students chose to read about for a course project (see page 93). For example, a pre-med student who ate fish frequently was interested in the observational study described in “Study finds fish-heavy diet offers no heart protection,” New York Times, April 13, 1995. Another student who commuted to school wanted to learn more about a commuter survey reported on in the article entitled, “For MUNI riders, familiarity breeds contempt, study says,” San Francisco Examiner, August 27, 1998, and yet another chose to follow up on the article, “Audit finds stockbrokers treat women differently,” San Francisco Chronicle, March 22, 1995, because of her political convictions. Of course, studies of college students, such as “More students drinking to get drunk, study finds,” San Francisco Examiner, September 11, 1998, generate interest among most students.

Studies reported in the newspaper typically use statistics to analyze data collected by survey, experiment, or observationally (examples of each of these appear in Chapter 6). But in some cases, the simple act of collecting and reporting numerical data has a positive effect. For example, around 1990, Texas began requiring every school and school district in the state to report average test (p.4) scores for all grades in each of several ethnic groups. This provides an incentive for schools to improve performance across these sub-populations.

Another example of the value of public statistics is the Toxics Release Inventory, the result of laws in 1984 and 1990 that require industrial plants to release information on pollutants released and recycled each year. Both the Texas schools and the environmental releases improved after these innovations. Although one cannot be sure of causal links in these observational settings (see page 85), our point is that gathering and disseminating information can stimulate understanding and action.

1.5 The best of the best

This book collects our favorite demonstrations, activities, and examples. But among these we have some particular favorites that get the students thinking hard about problems from unexpected angles. If you only want to use a few of our activities, we suggest you try these first.

  • Where are the cancers? (page 13)

  • World record times for the mile run (page 20)

  • Handedness of students (page 21)

  • Guessing exam scores (page 25)

  • Who opposed the Vietnam War? (page 27)

  • Metabolic rates of animals (page 35)

  • Tall people have higher incomes (pages 49 and 151)

  • Sampling from the telephone book (page 58)

  • How large is your family? (page 66)

  • An experiment that looks like a survey (page 78)

  • Randomizing the order of exam questions (page 81)

  • Real vs. fake coin flips (page 119)

  • What color is the card? (page 125)

  • Weighing a “random” sample (page 134)

  • Where are the missing girls? (page 135)

  • Coverage and noncoverage of confidence intervals (pages 140–142)

  • Shooting baskets (page 148)

  • Examples of lying with statistics (page 162)

  • How many quarters are in the jar? (page 278)

  • What is the value of a life? (page 284)

  • Subjective probability intervals (page 290)

  • Helicopter design project (page 337)

1.6 Our motivation for writing this book

This book grew out of our shared interest in teaching. We describe three events in our teaching career that influenced its creation.

(p.5) The first time that one of us taught a statistics course, we took ten minutes halfway through the course and asked the students for anonymous written comments. As we feared, most of comments were negative; the course was in fact a disaster, largely because we did not follow the textbook closely, and the homeworks were a mix of too easy and too hard. Our lectures were focused too much on concepts and not enough on skills, with the result that the students learned little of either. This experience inspired us, in the immediate time frame, to organize our courses better (and, indeed, our courses were much more successful after that). We were also inspired to begin gathering the demonstrations, examples, and teaching tools that ultimately were collected in this book, as a means of getting the students more actively involved in their own learning.

Another time, one of us was asked to teach a special seminar in probability for a small number of advanced undergraduate students who showed promise for graduate study. We were asked to break from the traditional lecture style and have students read original research papers even though they had no probability background before starting the seminar. This was a tall order, but the students did not disappoint us. The experience opened our eyes to the variety and level of work that students could tackle with the right kind of guidance, and as a result, we started to experiment with projects and advanced work in our regular courses.

Then in 1994, we jointly led an undergraduate research project in statistical literacy. The students’ enthusiasm for the project surprised and inspired us, and led to the design of our course packets in statistical literacy (Chapter 7). This project further sparked discussions on ideas for making classroom lectures more fun for students and on ways to design meaningful course projects, and after years of sharing ideas and techniques, we decided to write this book to provide a resource for other instructors of statistics. We hope you find it useful.

(p.6)

Table 1.1 Demonstrations, examples, and projects that can be used in the first part of an introductory statistics course. See also Tables 1.21.3 and Chapter 13. Some activities are listed more than once because we return to them throughout the course.

Concept

Activities

Introducing data collection

2.1:

Guessing ages

2.5:

Collecting handedness data

Numeracy

2.3:

Estimating a big number

Relevance of statistics

1.4:

Why is statistics important?

2.2:

Where are the cancers?

2.4:

What’s in the news?

Time plots, interpolation and extrapolation

3.2.1:

World record times for the mile run

3.8.2:

World population

Histograms

3.3.2:

Handedness of students

3.3.3:

Soft drink consumption

Means and medians

3.4.1:

Average soft drink consumption

3.4.2:

The average student

Scatterplots

3.5.1:

Guessing exam scores

10.2:

Psychometric analysis of exam scores

Two-way tables

3.5.2:

Who opposed the Vietnam War?

Normal distribution

3.6.1:

Heights of men and women

3.6.2:

Heights of conscripts

3.6.3:

Scores on two exams

Linear transformations

3.7.1:

College admissions

3.7.2:

Social and economic indexes

3.7.3:

Age adjustment

Logarithmic transformations

3.8.1:

Amoebas, squares, and cubes

3.8.2:

World population

3.8.3:

Metabolic rates

6.1.2:

First digits and Benford’s law

Linear regression with one predictor

5.1.2:

Tall people have higher incomes

5.1.3:

World population

Correlation

5.2.1:

Correlations of body measurements

5.2.2:

Exam scores and number of pages written

10.2:

Psychometric analysis of exam scores

Regression to the mean

5.3.1:

Memory quizzes

5.3.2:

Scores on two exams

5.3.2:

Heights of mothers and daughters

(p.7)

Table 1.2 Demonstrations, examples, and projects that can be used in the middle part of an introductory statistics course. See also Tables 1.11.3 and Chapter 13. Some activities are listed more than once because we return to them throughout the course.

Concept

Activities

Introduction to sampling

6.1.1:

Sampling from the telephone book

6.1.2:

First digits and Benford’s law

6.1.5:

Simple examples of sampling bias

6.1.6:

How large is your family?

9.1:

Weighing a “random” sample

Applied survey sampling

6.1.3:

Wacky surveys

6.1.4:

An election exit poll

6.2:

Class projects in survey sampling

7.6.2:

1 in 4 youths abused, survey finds

18:

Activities in survey sampling

Experiments

6.4.1:

An experiment that looks like a survey

6.4.2:

Randomizing the order of exam questions

6.4.3:

Soda and coffee tasting

7.6.1:

IV fluids for trauma victims

11.5:

Ethics and statistics

20.4:

Designing a paper “helicopter”

Observational studies

5.1.2:

Tall people have higher incomes

6.5.1:

The Surgeon General’s report on smoking

6.5.2:

Large population studies

6.5.3:

Coaching for the SAT

7.6.3:

Monster in the crib

10.1:

Regression of income on height and sex

Statistical literacy

7:

Statistical literacy and the news media

11:

Lying with statistics

Probability and randomness

8.2:

Random numbers via dice or handouts

8.3.1:

Probabilities of boy and girl births

8.3.2:

Real vs. fake coin flips

8.3.3:

Lotteries

Conditional probability

8.3.1:

Was Elvis an identical twin?

8.5.1:

What color is the other side of the card?

8.5.2:

Lie detectors and false positives

Applied probability modeling

8.4.1:

Lengths of baseball World Series

8.4.2:

Voting and coalitions

8.4.3:

Probability of space shuttle failure

8.6:

Crooked dice and biased coins

10.3:

Success rates of golf putts

17.1.1:

How many quarters?

17.1.2:

Utility of money

17.1.4:

What is the value of a life?

17.1.5:

Probabilistic answers to exam questions

19.4:

Does the Poisson distribution fit real data?

(p.8)

Table 1.3 Demonstrations, examples, and projects that can be used in the last part of an introductory statistics course. See also Tables 1.11.2 and Chapter 13. Some activities are listed more than once because we return to them throughout the course.

Concept

Activities

Distribution of the sample mean

9.2.1:

Where are the missing girls?

9.2.2:

Real-time gambler’s ruin

9.3.4:

Poll differentials

Bias and variance of an estimate

2.1:

Guessing ages

9.1:

Weighing a “random” sample

9.3.1:

Biases in age guessing

Confidence intervals

9.3.2:

An experiment that looks like a survey

9.3.3:

Land or water?

9.3.4:

Poll differentials

9.4.1:

Coverage of confidence intervals

9.4.2:

Noncoverage of confidence intervals

9.6.1:

How good is your memory?

9.6.2:

How common is your name?

17.2.2:

Subjective probability intervals

17.2.5:

Hierarchical modeling and shrinkage

Hypothesis testing

6.4.2:

Randomizing the order of exam questions

8.3.2:

Real vs. fake coin flips

9.3.5:

Golf: can you putt like the pros?

9.5.1:

Land or water?

9.5.1:

Evidence for the anchoring effect

9.5.2:

Detecting a flawed sampling method

9.5.3:

Taste testing projects

9.5.4:

Testing Benford’s law

9.5.5:

Lengths of baseball World Series

Statistical power

9.2.1:

Where are the missing girls?

9.7.1:

Shooting baskets

Multiple comparisons

9.7.2:

Do-it-yourself data dredging

9.7.3:

Praying for your health

Multiple regression

10.1:

Regression of income on height and sex

10.2:

Exam scores

20.3:

Quality control

Nonlinear regression

10.3:

Success rate of golf putts

10.4:

Pythagoras goes linear

20.4:

Designing a paper “helicopter”

Lying with statistics and statistical communication

11.1:

Many examples from the news media

11.2:

Selection bias

11.4:

1 in 2 marriages end in divorce?

11.5:

Ethics and statistics