Teaching Statistics: A Bag of Tricks

Cover
Preface
Contents
1 Introduction
1.1 The challenge of teaching introductory statistics
1.2 Fitting demonstrations and examples into a course
1.3 What makes a good example?
1.4 Why is statistics important?
1.5 The best of the best
1.6 Our motivation for writing this book
Part I Introductory probability and statistics
2 First week of class
2.1 Guessing ages
2.2 Where are the cancers?
2.3 Estimating a big number
2.4 What’s in the news?
2.5 Collecting data from students
3 Descriptive statistics
3.1 Displaying graphs on the blackboard
3.2 Time series
3.2.1 World record times for the mile run
3.3 Numerical variables, distributions, and histograms
3.3.1 Categorical and continuous variables
3.3.2 Handedness
3.3.3 Soft drink consumption
3.4 Numerical summaries
3.4.1 Average soft drink consumption
3.4.2 The average student
3.5 Data in more than one dimension
3.5.1 Guessing exam scores
3.5.2 Who opposed the Vietnam War?
3.6 The normal distribution in one and two dimensions
3.6.1 Heights of men and women
3.6.2 Heights of conscripts
3.6.3 Scores on two exams
3.7 Linear transformations and linear combinations
3.7.1 College admissions
3.7.2 Social and economic indexes
3.7.3 Age adjustment
3.8 Logarithmic transformations
3.8.1 Simple examples: amoebas, squares, and cubes
3.8.2 Log-linear transformation: world population
3.8.3 Log-log transformation: metabolic rates
4 Statistical graphics
4.1 Guiding principles
4.2 Lecture topics
4.3 Assignments
4.4 Deconstruct and reconstruct a plot
4.5 One-minute revelation
4.6 Turning tables
5 Linear regression and correlation
5.1 Fitting linear regressions
5.1.1 Simple examples of least squares
5.1.2 Tall people have higher incomes
5.1.3 Logarithm of world population
5.2 Correlation
5.2.1 Correlations of body measurements
5.2.2 Correlation and causation in observational data
5.3 Regression to the mean
5.3.1 Mini-quizzes
5.3.2 Exam scores, heights, and the general principle
6 Data collection
6.1 Sample surveys
6.1.1 Sampling from the telephone book
6.1.2 First digits and Benford’s law
6.1.3 Wacky surveys
6.1.4 An election exit poll
6.1.5 Simple examples of bias
6.1.6 How large is your family?
6.2 Class projects in survey sampling
6.2.1 The steps of the project
6.2.2 Topics for student surveys
6.3 How big was the crowd?
6.4 Experiments
6.4.1 An experiment that looks like a survey
6.4.2 Randomizing the order of exam questions
6.4.3 Taste tests
6.4.4 Can they taste the difference?
6.5 Observational studies
6.5.1 The Surgeon General’s report on smoking
6.5.2 Large population studies
6.5.3 Coaching for the SAT
7 Statistical literacy and the news media
7.1 Introduction
7.2 Assignment based on instructional packets
7.3 Assignment where students find their own articles
7.4 Guidelines for finding and evaluating sources
7.5 Discussion and student reactions
7.6 Examples of course packets
7.6.1 A controlled experiment: Fluids for trauma victims
7.6.2 A sample survey: 1 in 4 youths abused, survey finds
7.6.3 An observational study: Monster in the crib
7.6.4 A model-based analysis: Illegal aliens
8 Probability
8.1 Constructing probability examples
8.2 Random numbers via dice or handouts
8.2.1 Random digits via dice
8.2.2 Random digits via handouts
8.2.3 Normal distribution
8.2.4 Poisson distribution
8.3 Probabilities of compound events
8.3.1 Babies
8.3.2 Real vs. fake coin flips
8.3.3 Lotteries
8.4 Probability modeling
8.4.1 Lengths of baseball World Series
8.4.2 Voting and coalitions
8.4.3 Space shuttle failure and other rare events
8.5 Conditional probability
8.5.1 What’s the color on the other side of the card?
8.5.2 Lie detectors and false positives
8.6 You can load a die but you can’t bias a coin flip
8.6.1 Demonstration using wooden dice
8.6.2 Sporting events and quantitative literacy
8.6.3 Physical explanation
9 Statistical inference
9.1 Weighing a “random” sample
9.2 From probability to inference: totals and averages
9.2.1 Where are the missing girls?
9.2.2 Real-time gambler’s ruin
9.3 Confidence intervals: examples
9.3.1 Biases in age guessing
9.3.2 Comparing two groups
9.3.3 Land or water?
9.3.4 Poll differentials: a discrete distribution
9.3.5 Golf: can you putt like the pros?
9.4 Confidence intervals: theory
9.4.1 Coverage of confidence intervals
9.4.2 Noncoverage of confidence intervals
9.5 Hypothesis testing: z, t, and χ2 tests
9.5.1 Hypothesis tests from confidence intervals
9.5.2 Binomial model: sampling from the phone book
9.5.3 Hypergeometric model: taste testing
9.5.4 Benford’s law of first digits
9.5.5 Length of baseball World Series
9.6 Simple examples of applied inference
9.6.1 How good is your memory?
9.6.2 How common is your name?
9.7 Advanced concepts of inference
9.7.1 Shooting baskets and statistical power
9.7.2 Do-it-yourself data dredging
9.7.3 Praying for your health
10 Multiple regression and nonlinear models
10.1 Regression of income on height and sex
10.1.1 Inference for regression coefficients
10.1.2 Multiple regression
10.1.3 Regression with interactions
10.1.4 Transformations
10.2 Exam scores
10.2.1 Studying the fairness of random exams
10.2.2 Measuring the reliability of exam questions
10.3 A nonlinear model for golf putting
10.3.1 Looking at data
10.3.2 Constructing a probability model
10.3.3 Checking the fit of the model to the data
10.4 Pythagoras goes linear
11 Lying with statistics
11.1 Examples of misleading presentations of numbers
11.1.1 Fabricated or meaningless numbers
11.1.2 Misinformation
11.1.3 Ignoring the baseline
11.1.4 Arbitrary comparisons or data dredging
11.2 Selection bias
11.2.1 Distinguishing from other sorts of bias
11.2.2 Some examples presented as puzzles
11.2.3 Avoiding over-skepticism
11.3 Reviewing the semester’s material
11.3.1 Classroom discussion
11.3.2 Assignments: Find the lie or create the lie
11.4 1 in 2 marriages end in divorce?
11.5 Ethics and statistics
11.5.1 Cutting corners in a medical study
11.5.2 Searching for statistical significance
11.5.3 Controversies about randomized experiments
11.5.4 How important is blindness?
11.5.5 Use of information in statistical inferences
Part II Putting it all together
12 How to do it
12.1 Getting started
12.1.1 Multitasking
12.1.2 Advance planning
12.1.3 Fitting an activity to your class
12.1.4 Common mistakes
12.2 In-class activities
12.2.1 Setting up effective demonstrations
12.2.2 Promoting discussion
12.2.3 Getting to know the students
12.2.4 Fostering group work
12.3 Tricks for the large lecture
12.4 Using exams to teach statistical concepts
12.5 Projects
12.5.1 Monitoring progress
12.5.2 Organizing independent projects
12.5.3 Topics for projects
12.5.4 Statistical design and analysis
12.6 Resources
12.6.1 What’s in a spaghetti box?
12.6.2 Books
12.6.3 Periodicals
12.6.4 Web sites
12.6.5 People
13 Structuring an introductory statistics course
13.1 Before the semester begins
13.2 Finding time for student activities in class
13.3 A detailed schedule for a semester-long course
13.4 Outline for an alternative schedule of activities
14 Teaching statistics to social scientists
14.1 Starting with predictions, graphs, and deterministic models
14.2 Teaching style
14.3 A case study: the sampling distribution of the sample mean
14.4 Starting an applied regression course
14.5 How is there time to cover all the material?
15 Statistics diaries
15.1 Examples of student diaries
15.2 Using diaries in statistics classes
16 A course in statistical communication and graphics
16.1 Background
16.2 Plan for a 13-week course
Part III More advanced courses
17 Decision theory and Bayesian statistics
17.1 Decision analysis
17.1.1 How many quarters are in the jar?
17.1.2 Utility of money
17.1.3 Risk aversion
17.1.4 What is the value of a life?
17.1.5 Probabilistic answers to true–false questions
17.1.6 Homework project: evaluating real-life forecasts
17.1.7 Real decision problems
17.2 Bayesian statistics
17.2.1 Where are the cancers?
17.2.2 Subjective probability intervals and calibration
17.2.3 Drawing parameters out of a hat
17.2.4 Where are the cancers? A simulation
17.2.5 Hierarchical modeling and shrinkage
18 Student activities in survey sampling
18.1 First week of class
18.1.1 News clippings
18.1.2 Question bias
18.1.3 Class survey
18.2 Random number generation
18.2.1 What do random numbers look like?
18.2.2 Random numbers from coin flips
18.3 Estimation and confidence intervals
18.4 A visit to Clusterville
18.5 Statistical literacy and discussion topics
18.6 Projects
18.6.1 Analyzing data from a complex survey
18.6.2 Research papers on complex surveys
18.6.3 Sampling and inference in StatCity
18.6.4 A special topic in sampling
19 Problems and projects in probability
19.1 Setting up a probability course as a seminar
19.2 Introductory problems
19.2.1 Probabilities of compound events
19.2.2 Introducing the concept of expectation
19.3 Challenging problems
19.4 Does the Poisson distribution fit real data?
19.5 Organizing student projects
19.6 Examples of structured projects
19.6.1 Fluctuations in coin tossing—arcsine laws
19.6.2 Recurrence and transience in Markov chains
19.7 Examples of unstructured projects
19.7.1 Martingales
19.7.2 Generating functions and branching processes
19.7.3 Limit distributions of Markov chains
19.7.4 Permutations
19.8 Research papers as projects
20 Directed projects in a mathematical statistics course
20.1 Organization of a case study
20.2 Fitting the cases into a course
20.2.1 Covering the cases in lectures
20.2.2 Group work in class
20.2.3 Cases as reports
20.2.4 Independent projects in a seminar course
20.3 A case study: quality control
20.4 A directed project: helicopter design
20.4.1 General instructions
20.4.2 Designing the study and fitting a response surface
21 Statistical thinking in a data science course
21.1 Goals
21.1.1 Statistical thinking in a computational context
21.1.2 Core paradigms
21.1.3 Learn how to learn new technologies
21.1.4 Connect to real modern problems
21.2 Topics
21.2.1 Language basics
21.2.2 Graphics
21.2.3 Data structures
21.2.4 Programming concepts
21.2.5 Text manipulation
21.2.6 Information technologies
21.2.7 Statistical methods
21.3 Projects and student work
21.4 Copy the master
21.5 Spam filtering assignment
21.6 Interactive visualization assignment
Notes
References
Author Index
Subject Index