Statistics

There are books on statistical theory and books on statistical methods. This is neither. It is a book on statistical ideas and statistical reasoning and on their relevance to public policy and to the human sciences from medicine to sociology. We have included many elementary graphical and numerical techniques to give flesh to the ideas and muscle to the reasoning. Students learn to think about data by working with data. We have not, however, allowed technique to dominate concepts. Our intention is to teach verbally rather than algebraically, to invite discussion and even argument rather than mere computation, though some computation remains essential. The coverage is considerably broader than one might traditionally cover in a one-term course, as the table of contents reveals. In the spirit of general education, we have preferred breadth to detail.

Despite its informal nature, SCC is a textbook. It is organized for systematic study and has abundant exercises, many of which ask students to offer a discussion or make a judgment. Even those admirable individuals who seek pleasure in uncompelled reading should look at the exercises as well as the text. Teachers should be aware that the book is more serious than its low mathematical level suggests. The emphasis on ideas and reasoning asks more of the reader than many recipe-laden methods texts.

For the first time, SCC is now publish with SaplingPlus as it’s full course digital solution. We have a well developed library of both error specific feedback and generic feedback tutorial assessment, aligned to the main learning goals of the chapter and largely taken directly from the end-of-chapter exercises in the book. SaplingPlus also hosts our robust suite of teaching and learning resources: Concept and Controversy videos, statistical applets, Learning Curve, data sets, and many more teaching and learning focused tools.

Contents

To the Teacher: Statistics as a Liberal Discipline
SaplingPlus for Statistics
Acknowledgments
Prelude: Making Sense of Statistics
Statistics and You: What Lies ahead in This Book
About the Authors

PART I Producing Data
1 Where Do Data Come From?
Case Study: An Online Poll
Talking about Data: Individuals and Variables
Observational Studies
Sample Surveys
Census
Experiments
Chapter 1: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 1 Exercises

2 Samples, Good and Bad
Case Study: Assessing Polls
How to Sample Badly
Simple Random Samples
Can You Trust a Sample?
Chapter 2: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 2 Exercises

3 What Do Samples Tell Us?
Case Study: Childhood Vaccinations
From Sample to Population
Sampling Variability
Margin of Error and All That
Confidence Statements
Sampling from Large Populations
Statistical Controversies: Should Election Polls Be Banned?
Chapter 3: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 3 Exercises

4 Sample Surveys in the Real World
Case Study: Obtaining a Sample for a Survey
How Sample Surveys Go Wrong
Sampling Errors
Nonsampling Errors
Wording Questions
How to Live with Nonsampling Errors
Sample Design in the Real World
The Challenge of Internet Surveys
Statistical Controversies: The Harris Online Poll
Probability Samples
Questions to Ask Before You Believe a Poll
Chapter 4: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 4 Exercises
What’s the Verdict?

5 Experiments, Good and Bad
Case Study: Online vs. Traditional Courses
Talking about Experiments
How to Experiment Badly
Randomized Comparative Experiments
The Logic of Experimental Design
Statistical Significance
How to Live with Observational Studies
Chapter 5: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 5 Exercises
What’s the Verdict?

6 Experiments in the Real World
Case Study: Caffeine Dependence
Equal Treatment for All
Double-Blind Experiments
Refusals, Nonadherers, and Dropouts
Can We Generalize?
Experimental Design in the Real World
Matched Pairs and Block Designs
Statistical Controversies: Is It or Isn’t It a Placebo?
Chapter 6: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 6 Exercises
What’s the Verdict?

7 Data Ethics
Case Study: Marijuana and Driving Performance
First Principles
Institutional Review Boards
Informed Consent
Confidentiality
Clinical Trials
Statistical Controversies: Hope for Sale?
Behavioral and Social Science Experiments
Chapter 7: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 7 Exercises
What’s the Verdict?

8 Measuring
Case Study: Measuring Intelligence
Measurement Basics
Know Your Variables
Measurements, Valid and Invalid
Statistical Controversies: Six-Year Graduation Rates, High School GPA, and Standardized Tests
Measurements, Accurate and Inaccurate
Improving Reliability, Reducing Bias
Measuring Psychological and Social Factors
Chapter 8: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 8 Exercises

9 Do the Numbers Make Sense?
Case Study: Estimating Crowd Size
What Didn’t They Tell Us?
Are the Numbers Consistent with Each Other?
Are the Numbers Plausible?
Are the Numbers Too Good to Be True?
Is the Arithmetic Right?
Is There a Hidden Agenda?
Chapter 9: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 9 Exercises

Part I Review
Part I Summary
Part I Review Exercises

PART II Organizing Data
10 Graphs, Good and Bad
Case Study: Leading Causes of Death
Data Tables
Types of Variables
Pie Charts and Bar Graphs
Beware the Pictogram
Change over Time: Line Graphs
Watch those Scales!
Making Good Graphs
Chapter 10: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 10 Exercises
What’s the Verdict?

11 Displaying Distributions with Graphs
Case Study: Apartment Rental Prices
Histograms
Interpreting Histograms
Stemplots
Chapter 11: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 11 Exercises

12 Describing Distributions with Numbers
Case Study: Education and Income
Median and Quartiles
The Five-Number Summary and Boxplots
Statistical Controversies: Income Inequality
Mean and Standard Deviation
Choosing Numerical Descriptions
Chapter 12: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 12 Exercises

13 Normal Distributions
Case Study: Applying the Normal Distribution to Data
Density Curves
The Center and Variability of a Density Curve
Normal Distributions
The 68–95–99.7 Rule
Standard Scores
Percentiles of Normal Distributions*
Chapter 13: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 13 Exercises

14 Describing Relationships: Scatterplots and Correlation
Case Study: SAT Scores
Scatterplots
Interpreting Scatterplots
Multiple Variables
Correlation
Understanding Correlation
Chapter 14: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 14 Exercises
What’s the Verdict?

15 Describing Relationships: Regression, Prediction, and Causation
Case Study: Housing Prices
Regression Lines
Regression Equations
Understanding Prediction
Correlation and Regression
The Question of Causation
Statistical Controversies: Gun Control
Evidence for Causation
Correlation, Prediction, and Big Data
Chapter 15: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 15 Exercises
What’s the Verdict?

16 The Consumer Price Index and Government Statistics
Case Study: Who’s the Greatest Basketball Player of All Time?
Index Numbers
Fixed Market Basket Price Indexes
Using the CPI
Understanding the CPI
Statistical Controversies: Does the CPI Overstate Inflation?
The Place of Government Statistics
The Question of Social Statistics
Chapter 16: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 16 Exercises
What’s the Verdict?

Part II Review
Part II Summary
Part II Review Exercises

PART III Chance
17 Thinking about Chance
Case Study: Shared Birthdays
The Idea of Probability
The Ancient History of Chance
Myths about Chance Behavior
Personal Probabilities
Probability and Risk
Chapter 17: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 17 Exercises

18 Probability Models
Case Study: Super Bowl Probabilities
Probability Models
Probability Rules
Probability and Odds
Probability Models for Sampling
Chapter 18: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 18 Exercises
What’s the Verdict?

19 Simulation
Case Study: Luck or Cheating?
Where Do Probabilities Come From?
Simulation Basics
Thinking about Independence
More Elaborate Simulations
Chapter 19: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 19 Exercises

20 The House Edge: Expected Values
Case Study: Better Betting?
Expected Values
The Law of Large Numbers
Thinking about Expected Values
Statistical Controversies: The State of Legalized Gambling
Finding Expected Values by Simulation
Chapter 20: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 20 Exercises
What’s the Verdict?

Part III Review
Part III Summary
Part III Review Exercises

PART IV Inference
21 What Is a Confidence Interval?
Case Study: Social Media Use
Estimating
Estimating with Confidence
Understanding Confidence Intervals
More on Confidence Intervals for a Population Proportion*
The Sampling Distribution of a Sample Mean*
Confidence Intervals for a Population Mean*
Chapter 21: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 21 Exercises

22 What Is a Test of Significance?
Case Study: Political Views
The Reasoning of Statistical Tests of Significance
Hypotheses and P-values
Statistical Significance
Calculating P-values*
Tests for a Population Mean*
Chapter 22: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 22 Exercises

23 Use and Abuse of Statistical Inference
Case Study: Boys and Breakfast Ceral
Using Inference Wisely
The Woes of Significance Tests
The Advantages of Confidence Intervals
Significance at the 5% Level Isn’t Magical
Statistical Controversies: Should Hypothesis Tests Be Banned?
Beware of Searching for Significance
Inference as Decision*
Chapter 23: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 23 Exercises
What’s the Verdict?

24 Two-Way Tables and the Chi-Square Test*
Case Study: Freedom of Speech and Political Beliefs
Two-Way Tables
Inference for a Two-Way Table
The Chi-Square Test
Using the Chi-Square Test
Simpson’s Paradox
Chapter 24: Statistics in Summary
Link It
Case Study Evaluated
Macmillan Learning Online Resources
Check the Basics
Chapter 24 Exercises

Part IV Review
Part IV Summary
Part IV Review Exercises

Solutions to Now It’s Your Turn Exercises
Answers to Odd-Numbered Exercises
Resolving the Controversy
Index
Table A Random digits
Table B Percentiles of the Normal distributions

Available online at www.macmillanlearning.com/scc10e:
Notes and Data Sources