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