Teaching Statistics A Bag of Tricks

by Gelman, Andrew; Nolan, Deborah

• ISBN13: 9780198572244
• ISBN10: 0198572247
• Format: Paperback
• Copyright: 2002-10-03
• Publisher: Oxford University Press

Summary

All students in the sciences, economics, psychology, social sciences andmedicine take an introductory statistics course. However, statistics can benotoriously difficult to teach as it is seen by many students as difficult andboring, if not irrelevant to their subject of choice. To help dispel thesemisconceptions, Gelman and Nolan have put together this fascinating andthought-provoking book. Based on years of teaching experience the book providesa wealth of demonstrations, examples and projects that involve active studentparticipation.Part I of the book presents a large selection of activities for introductorystatistics courses and combines chapters such as, 'First week of class', withexercises to break the ice and get students talking; then 'Descriptivestatistics' , collecting and displaying data; then follows the traditionaltopics - linear regression, data collection, probability and inference. Part IIgives tips on what does and what doesn't work in class: how to set up effectivedemonstrations and examples, how to encourage students to participate in classand work effectively in group projects. A sample course plan is provided. PartIII presents material for more advanced courses on topics such as decisiontheory, Bayesian statistics and sampling.

Author Biography

Andrew Gelman is a Professor in the Department of Statistics, Columbia University, New York.

Table of Contents

Introduction	1	(10)
The challenge of teaching introductory statistics	1	(1)
Fitting demonstrations, examples, and projects into a course	1	(2)
What makes a good example?	3	(1)
Why is statistics important?	3	(1)
The best of the best	4	(1)
Our motivation for writing this book	4	(7)
PART I INTRODUCTORY PROBABILITY AND STATISTICS
First week of class	11	(8)
Guessing ages	11	(2)
Where are the cancers	13	(1)
Estimating a big number	14	(1)
What's in the new-s?	15	(2)
Collecting data from students	17	(2)
Descriptive statistics	19	(19)
Displaying graphs on the blackboard	19	(1)
Time series	19	(1)
World record times for the mile run	20	(1)
Numerical variables distributions, and histograms	20	(2)
Categorical and continuous variables	20	(1)
Handedness	21	(1)
Soft, drink consumption	22	(1)
Numerical summaries	22	(2)
Average soft drink consumption	22	(2)
The average student	24	(1)
Data in more than one dimension	24	(4)
Guessing exam scores	25	(2)
Who opposed the Vietnam War?	27	(1)
The normal distribution in one and two dimensions	28	(3)
Heights of men and women	29	(1)
Heights of conscripts	30	(1)
Scores on two exams	30	(1)
Linear transformations and linear combinations	31	(1)
College admissions	31	(1)
Social and economic indexes	31	(1)
Age adjustment	32	(1)
Logarithmic transformations	32	(6)
Simple examples: amoebas, squares, and cubs	33	(1)
Log-linear transformation: world population	33	(2)
Log-log transformation: metabolic rates	35	(3)
Linear regression and correlation	38	(10)
Fitting linear regressions	38	(5)
Simple examples of least squares	38	(1)
Tall people have higher incomes	39	(2)
Logarithm of world population	41	(2)
Correlation	43	(2)
Correlations of body measurements	43	(1)
Correlation and causation in observational data	44	(1)
Regression to the mean	45	(3)
Mini-quizzes	45	(1)
Exam scores, heights, and the general principle	46	(2)
Data collection	48	(28)
Sample surveys	48	(9)
Sampling from the telephone book	48	(4)
First digits and Benford's law	52	(2)
Wacky surveys	54	(1)
An election exit poll	55	(1)
Simple examples of bias	56	(1)
How large is your family?	56	(1)
Class projects in survey sampling	57	(9)
The steps of the project	58	(5)
Topics for student surveys	63	(3)
Experiments	66	(6)
An experiment that looks like a survey	66	(2)
Randomizing the order of exam questions	68	(1)
Taste tests	69	(3)
Observational studies	72	(4)
The Surgeon General's report on smoking	73	(1)
Large population studies	73	(2)
Coaching for the SAT	75	(1)
Statistical literacy and the news media	76	(27)
Introduction	76	(1)
Assignment based on instructional packets	77	(2)
Assignment where students find their own articles	79	(3)
Guidelines for finding and evaluating sources	82	(2)
Discussion and student reactions	84	(1)
Examples of course packets	84	(19)
A controlled experiment: IV fluids for trauma victims	85	(5)
A sample survey: 1 in 4 youths abused, survey finds	90	(3)
An observational study: Monster in the crib	93	(5)
A model-based analysis: Illegal aliens put uneven load	98	(5)
Probability	103	(17)
Constructing probability examples	103	(1)
Random numbers via dice or handouts	103	(1)
Random digits via dice	103	(1)
Random digits via handouts	103	(1)
Normal distribution	104	(1)
Poisson distribution	104	(1)
Probabilities of compound events	104	(4)
Babies	104	(1)
Real vs. fake coin flips	105	(2)
Lotteries	107	(1)
Probability modeling	108	(3)
Lengths of baseball World Series	108	(2)
Voting and coalitions	110	(1)
Space shuttle failure and other rare events	110	(1)
Conditional probability	111	(3)
What's the color on the other side of the card?	111	(2)
Lie detectors and false positives	113	(1)
You can load a die but you can't bias a coin flip	114	(6)
Demonstration using plastic checkers and wooden dice	115	(2)
Sporting events and quantitative literacy	117	(1)
Physical explanation	118	(2)
Statistical inference	120	(17)
Weighing a ``random'' sample	120	(1)
From probability to inference: distributions of totals and averages	121	(2)
Where are the missing girls?	121	(1)
Real-time gambler's ruin	122	(1)
Confidence intervals: examples	123	(3)
Biases in age guessing	123	(1)
Comparing two groups	124	(1)
Land or water?	124	(1)
Poll differentials: a discrete distribution	125	(1)
Golf: can you putt like the pros?	126	(1)
Confidence intervals: theory	126	(2)
Coverage of confidence intervals	126	(2)
Noncoverage of confidence intervals	128	(1)
Hypothesis testing: z, t, and χ2 tests	128	(4)
Hypothesis tests from examples of confidence intervals	129	(1)
Binomial model: sampling from the phone book	130	(1)
Hypergeometric model: taste testing	131	(1)
Benford's law of first digits	131	(1)
Length of baseball World Series	131	(1)
Simple examples of applied inference	132	(2)
How good is your memory?	132	(1)
How common is your name?	133	(1)
Advanced concepts of inference	134	(3)
Shooting baskets and statistical power	134	(1)
Do-it-yourself data dredging	134	(1)
Praying for your health	135	(2)
Multiple regression and nonlinear models	137	(10)
Regression of income on height and sex	137	(4)
Inference for regression coefficients	137	(1)
Multiple regression	137	(2)
Regression with interactions	139	(1)
Transformations	140	(1)
Exam scores	141	(1)
Studying the fairness of random exams	141	(1)
Measuring the reliability of exam questions	141	(1)
A nonlinear model for golf putting	142	(3)
Looking at data	143	(1)
Constructing a probability model	143	(1)
Checking the fit of the model to the data	144	(1)
Pythagoras goes linear	145	(2)
Lying with statistics	147	(20)
Examples of misleading presentations of numbers	147	(6)
Fabricated or meaningless numbers	147	(1)
Misinformation	147	(2)
Ignoring the baseline	149	(1)
Arbitrary comparisons or data dredging	149	(2)
Misleading comparisons	151	(2)
Selection bias	153	(2)
Distinguishing from other sorts of bias	153	(1)
Some examples presented as puzzles	154	(1)
Avoiding over-skepticism	155	(1)
Reviewing the semester's material	155	(1)
Classroom discussion	155	(1)
Assignments: find the lie or create the lie	156	(1)
1 in 2 marriages end in divorce?	156	(2)
Ethics and statistics	158	(9)
Cutting corners in a medical study	158	(1)
Searching for statistical significance	159	(1)
Controversies about randomized experiments	159	(1)
How important is blindness?	160	(1)
Use of information in statistical inferences	161	(6)
PART II PUTTING IT ALL TOGETHER
How to do it	167	(22)
Getting started	167	(4)
Multitasking	167	(1)
Advance planning	167	(1)
Fitting an activity to your class	168	(1)
Common mistakes	168	(3)
In-class activities	171	(4)
Setting lip effective demonstrations	171	(1)
Promoting discussion	172	(1)
Getting to know the students	173	(1)
Fostering group work	173	(2)
Using exams to teach statistical concepts	175	(1)
Projects	175	(10)
Monitoring progress	177	(1)
Organizing independent projects	178	(3)
Topics for projects	181	(2)
Statistical design and analysis	183	(2)
Resources	185	(4)
What's in a spaghetti box? Cooking up activities from scratch	185	(1)
Books	186	(1)
Periodicals	187	(1)
Web sites	187	(1)
People	188	(1)
Structuring an introductory statistics course	189	(14)
Before the semester begins	189	(1)
Finding time for student activities in class	190	(1)
A detailed schedule for a semester-long course	190	(8)
Outline for an alternative schedule of activities	198	(5)
PART III MORE ADVANCED COURSES
Decision theory and Bayesian statistics	203	(19)
Decision analysis	204	(11)
How many quarters are in the jar?	204	(3)
Utility of money	207	(2)
Risk aversion	209	(1)
What is the value of a life?	210	(1)
Probabilistic answers to true-false questions	211	(1)
Homework project: evaluating real-life forecasts	212	(1)
Real decision problems	213	(2)
Bayesian statistics	215	(7)
Where are the cancers?	215	(1)
Subjective probability intervals and calibration	216	(3)
Drawing parameters out of hat	219	(1)
Where are the cancers? A simulation	219	(1)
Hierarchical modeling and shrinkage	220	(2)
Student activities in survey sampling	222	(15)
First week of class	222	(2)
News clippings	222	(1)
Class survey	223	(1)
Random number generation	224	(1)
What do random numbers look like?	224	(1)
Random numbers from coin flips	224	(1)
Estimation arid confidence intervals	225	(1)
A visit to Clusterville	226	(2)
Statistical literacy and discussion topics	228	(2)
Projects	230	(7)
Research papers on complex surveys	231	(1)
Sampling and inference in StatCity	232	(4)
A special topic in sampling	236	(1)
Problems and projects in probability	237	(17)
Setting a probability course as a, seminar	237	(1)
Introductory problems	238	(3)
Probabilities of compound events	239	(1)
Introducing the concept of expectation	240	(1)
Challenging problems	241	(2)
Does the Poisson distribution fit, real data	243	(1)
Organizing student projects	244	(1)
Examples of structured projects	244	(5)
Fluctuations in coin tossing---arcsine laws	245	(2)
Recurrence and transience in Markov chains	247	(2)
Examples of unstructured projects	249	(3)
Martingales	249	(1)
Generating functions and branching processes	250	(1)
Limit distributions of Markov chains	250	(1)
Permutations	251	(1)
Research papers as projects	252	(2)
Directed projects in a mathematical statistics course	254	(11)
Organization of a case study	255	(1)
Fitting the cases into a course	255	(3)
Covering the cases in lectures	256	(1)
Group work in class	256	(1)
Cases as reports	257	(1)
Independent projects in a seminar course	257	(1)
A case study: quality control	258	(1)
A directed project: helicopter design	259	(6)
General instructions	259	(2)
Designing the study and fitting a response surface	261	(4)
Notes	265	(12)
References	277	(11)
Author Index	288	(4)
Subject Index	292