Teaching statistics : a bag of tricks / Andrew Gelman, Deborah Nolan.

Format:

Book

Author/Creator:

Gelman, Andrew

Contributor:

Nolan, Deborah Ann, 1955-

Class of 1932 Fund.

Language:

English

Subjects (All):

Statistics--Study and teaching (Higher).

Statistics.

Physical Description:

xv, 299 pages : illustrations ; 22 cm

Place of Publication:

Oxford ; New York : Oxford University Press, 2002.

Summary:

Students in the sciences, economics, psychology, social sciences and medicine take an introductory statistics course. And yet statistics can be notoriously difficult to teach as it is seen by many students as difficult and boring if not irrelevant to their subject of choice. To help dispel these misconceptions Gelman and Nolan have put together this fascinating and thought-provoking book. Based on years of teaching experience the book provides a wealth of demonstrations, examples and projects that involve active student participation. Part I of the book presents a large selection of activities for introductory statistics courses and has chapters such as 'First week of class' -- with exercises to break the ice and get students talking; then descriptive statistics, linear regression, data collection (sampling and experimentation), probability, inference, and statistical communication. Part II gives tips on what works and what doesn't, how to set up effective demonstrations and examples, how to encourage students to participate in class and to work effectively in group projects. A sample course plan is provided. Part III presents material for more advanced courses on topics such as decision theory, Bayesian statistics and sampling.

Contents:

1.1 The challenge of teaching introductory statistics 1

1.2 Fitting demonstrations, examples, and projects into a course 1

1.3 What makes a good example? 3

1.4 Why is statistics important? 3

Part I Introductory Probability and Statistics

2.1 Guessing ages 11

2.2 Where are the cancers? 13

2.3 Estimating a big number 14

2.4 What's in the news? 15

2.5 Collecting data from students 17

3 Descriptive statistics 19

3.1 Displaying graphs on the blackboard 19

3.2 Time series 19

3.2.1 World record times for the mile run 20

3.3 Numerical variables, distributions, and histograms 20

3.3.1 Categorical and continuous variables 20

3.3.2 Handedness 21

3.3.3 Soft drink consumption 22

3.4 Numerical summaries 22

3.4.1 Average soft drink consumption 22

3.4.2 The average student 24

3.5 Data in more than one dimension 24

3.5.1 Guessing exam scores 25

3.5.2 Who opposed the Vietnam War? 27

3.6 The normal distribution in one and two dimensions 28

3.6.1 Heights of men and women 29

3.6.2 Heights of conscripts 30

3.7 Linear transformations and linear combinations 31

3.7.1 College admissions 31

3.7.2 Social and economic indexes 31

3.7.3 Age adjustment 32

3.8 Logarithmic transformations 32

3.8.1 Simple examples: amoebas, squares, and cubes 33

3.8.2 Log-linear transformation: world population 33

3.8.3 Log-log transformation: metabolic rates 35

4 Linear regression and correlation 38

4.1 Fitting linear regressions 38

4.1.1 Simple examples of least squares 38

4.1.2 Tall people have higher incomes 39

4.1.3 Logarithm of world population 41

4.2 Correlation 43

4.2.1 Correlations of body measurements 43

4.2.2 Correlation and causation in observational data 44

4.3 Regression to the mean p45

4.3.2 Exam scores, heights, and the general principle 46

5 Data collection 48

5.1.1 Sampling from the telephone book 48

5.1.2 First digits and Benford's law 52

5.1.3 Wacky surveys 54

5.1.4 An election exit poll 55

5.1.5 Simple examples of bias 56

5.1.6 How large is your family? 56

5.2 Class projects in survey sampling 57

5.2.1 The steps of the project 58

5.2.2 Topics for student surveys 63

5.3 Experiments 66

5.3.1 An experiment that looks like a survey 66

5.3.2 Randomizing the order of exam questions 68

5.3.3 Taste tests 69

5.4 Observational studies 72

5.4.1 The Surgeon General's report on smoking 73

5.4.2 Large population studies 73

5.4.3 Coaching for the SAT 75

6 Statistical literacy and the news media 76

6.2 Assignment based on instructional packets 77

6.3 Assignment where students find their own articles 79

6.4 Guidelines for finding and evaluating sources 82

6.5 Discussion and student reactions 84

6.6 Examples of course packets 84

6.6.1 A controlled experiment: IV fluids for trauma victims 85

6.6.2 A sample survey: 1 in 4 youths abused, survey finds 90

6.6.3 An observational study: Monster in the crib 93

6.6.4 A model-based analysis: Illegal aliens put uneven load 98

7 Probability 103

7.1 Constructing probability examples 103

7.2 Random numbers via dice or handouts 103

7.2.1 Random digits via dice 103

7.2.2 Random digits via handouts 103

7.2.3 Normal distribution 104

7.2.4 Poisson distribution 104

7.3 Probabilities of compound events 104

7.3.1 Babies 104

7.3.2 Real vs. fake coin flips 105

7.3.3 Lotteries 107

7.4 Probability modeling 108

7.4.1 Lengths of baseball World Series 108

7.4.2 Voting and coalitions 110

7.4.3 Space shuttle failure and other rare events 110

7.5 Conditional probability 111

7.5.1 What's the color on the other side of the card? 111

7.5.2 Lie detectors and false positives 113

7.6 You can load a die but you can't bias a coin flip 114

7.6.1 Demonstration using plastic checkers and wooden dice 115

7.6.2 Sporting events and quantitative literacy 117

7.6.3 Physical explanation 118

8 Statistical inference 120

8.1 Weighing a "random" sample 120

8.2 From probability to inference: distributions of totals and averages 121

8.2.1 Where are the missing girls? 121

8.2.2 Real-time gambler's ruin 122

8.3 Confidence intervals: examples 123

8.3.1 Biases in age guessing 123

8.3.2 Comparing two groups 124

8.3.3 Land or water? 124

8.3.4 Poll differentials: a discrete distribution 125

8.3.5 Golf: can you putt like the pros? 126

8.4 Confidence intervals: theory 126

8.4.1 Coverage of confidence intervals 126

8.4.2 Noncoverage of confidence intervals 128

8.5 Hypothesis testing: z, t, and x[superscript 2] tests 128

8.5.1 Hypothesis tests from examples of confidence intervals 129

8.5.2 Binomial model: sampling from the phone book 130

8.5.3 Hypergeometric model: taste testing 131

8.5.4 Benford's law of first digits 131

8.5.5 Length of baseball World Series 131

8.6 Simple examples of applied inference 132

8.6.1 How good is your memory? 132

8.6.2 How common is your name? 133

8.7 Advanced concepts of inference 134

8.7.1 Shooting baskets and statistical power 134

8.7.2 Do-it-yourself data dredging 134

8.7.3 Praying for your health 135

9 Multiple regression and nonlinear models 137

9.1 Regression of income on height and sex 137

9.1.1 Inference for regression coefficients 137

9.1.2 Multiple regression 137

9.1.3 Regression with interactions 139

9.1.4 Transformations 140

9.2.1 Studying the fairness of random exams 141

9.2.2 Measuring the reliability of exam questions 141

9.3 A nonlinear model for golf putting 142

9.3.1 Looking at data 143

9.3.2 Constructing a probability model 143

9.3.3 Checking the fit of the model to the data 144

9.4 Pythagoras goes linear 145

10 Lying with statistics 147

10.1 Examples of misleading presentations of numbers 147

10.1.1 Fabricated or meaningless numbers 147

10.1.2 Misinformation 147

10.1.3 Ignoring the baseline 149

10.1.4 Arbitrary comparisons or data dredging 149

10.1.5 Misleading comparisons 151

10.2 Selection bias 153

10.2.1 Distinguishing from other sorts of bias 153

10.2.2 Some examples presented as puzzles 154

10.2.3 Avoiding over-skepticism 155

10.3 Reviewing the semester's material 155

10.3.1 Classroom discussion 155

10.3.2 Assignments: find the lie or create the lie 156

10.4 1 in 2 marriages end in divorce? 156

10.5 Ethics and statistics 158

10.5.1 Cutting corners in a medical study 158

10.5.2 Searching for statistical significance 159

10.5.3 Controversies about randomized experiments 159

10.5.4 How important is blindness? 160

10.5.5 Use of information in statistical inferences 161

11.1.1 Multitasking 167

11.1.2 Advance planning 167

11.1.3 Fitting an activity to your class 168

11.1.4 Common mistakes 168

11.2 In-class activities 171

11.2.1 Setting up effective demonstrations 171

11.2.2 Promoting discussion 172

11.2.3 Getting to know the students 173

11.2.4 Fostering group work 173

11.3 Using exams to teach statistical concepts 175

11.4.1 Monitoring progress 177

11.4.2 Organizing independent projects 178

11.4.3 Topics for projects 181

11.4.4 Statistical design and analysis 183

12 Structuring an introductory statistics course 189

12.2 Finding time for student activities in class 190

12.3 A detailed schedule for a semester-long course 190

12.4 Outline for an alternative schedule of activities 198

Part III More Advanced Courses

13 Decision theory and Bayesian statistics 203

13.1 Decision analysis 204

13.1.1 How many quarters are in the jar? 204

13.1.2 Utility of money 207

13.1.3 Risk aversion 209

13.1.4 What is the value of a life? 210

13.1.5 Probabilistic answers to true-false questions 211

13.1.6 Homework project: evaluating real-life forecasts 212

13.1.7 Real decision

problems 213

13.2 Bayesian statistics 215

13.2.1 Where are the cancers? 215

13.2.2 Subjective probability intervals and calibration 216

13.2.3 Drawing parameters out of a hat 219

13.2.4 Where are the cancers? A simulation 219

13.2.5 Hierarchical modeling and shrinkage 220

14 Student activities in survey sampling 222

14.1 First week of class 222

14.1.1 News clippings 222

14.1.2 Class survey 223

14.2 Random number generation 224

14.2.1 What do random numbers look like? 224

14.2.2 Random numbers from coin flips 224

14.3 Estimation and confidence intervals 225

14.4 A visit to Clusterville 226

14.5 Statistical literacy and discussion topics 228

14.6.1 Research papers on complex surveys 231

14.6.2 Sampling and inference in StatCity 232

14.6.3 A special topic in sampling 236

15.1 Setting up a probability course as a seminar 237

15.2.1 Probabilities of compound events 239

15.2.2 Introducing the concept of expectation 240

15.3 Challenging problems 241

15.4 Does the Poisson distribution fit real data? 243

15.5 Organizing student projects 244

15.6 Examples of structured projects 244

15.6.1 Fluctuations in coin tossing

arcsine laws 245

15.6.2 Recurrence and transience in Markov chains 247

15.7 Examples of unstructured projects 249

15.7.1 Martingales 249

15.7.2 Generating functions and branching processes 250

15.7.3 Limit distributions of Markov chains 250

15.7.4 Permutations 251

15.8 Research papers as projects 252

16 Directed projects in a mathematical statistics course 254

16.1 Organization of a case study 255

16.2 Fitting the cases into a course 255

16.2.1 Covering the cases in lectures 256

16.2.2 Group work in class 256

16.2.3 Cases as reports 257

16.2.4 Independent projects in a seminar course 257

16.3 A case study: quality control 258

16.4 A directed project: helicopter design 259

16.4.2 Designing the study and fitting a response surface 261.

Notes:

Includes bibliographical references and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1932 Fund.

ISBN:

0198572255

0198572247

OCLC:

50017627