Introduction to the Practice of Statistics

Create and evaluate data from real-world contexts as Introduction to the Practice of Statistics gets you practicing data gathering and analysis in the same way real statisticians do.

David S. Moore is Shanti S. Gupta Distinguished Professor of Statistics, Emeritus, at Purdue University and was 1998 president of the American Statistical Association. He received his A.B. from Princeton and his Ph.D. from Cornell, both in mathematics. He has written many research papers in statistical theory and served on the editorial boards of several major journals. Professor Moore is an elected fellow of the American Statistical Association and of the Institute of Mathematical Statistics and an elected member of the International Statistical Institute. He has served as program director for statistics and probability at the National Science Foundation.  In recent years, Professor Moore has devoted his attention to the teaching of statistics. He was the content developer for the Annenberg/Corporation for Public Broadcasting college-level telecourse Against All Odds: Inside Statistics and for the series of video modules Statistics: Decisions through Data, intended to aid the teaching of statistics in schools. He is the author of influential articles on statistics education and of several leading texts. Professor Moore has served as president of the International Association for Statistical Education and has received the Mathematical Association of America’s national award for distinguished college or university teaching of mathematics.

George P. McCabe is the Associate Dean for Academic Affairs in the College of Science and a Professor of Statistics at Purdue University. In 1966, he received a B.S. degree in mathematics from Providence College, and in 1970 a Ph.D. in mathematical statistics from Columbia University.  His entire professional career has been spent at Purdue with sabbaticals at Princeton, the Commonwealth Scientific and Industrial Research Organization in Melbourne (Australia); the University of Berne (Switzerland); the National Institute of Standards and Technology (Boulder, Colorado); and the National University of Ireland in Galway. Professor McCabe is an elected fellow of the American Association for the Advancement of Science and of the American Statistical Association; he was 1998 Chair of its section on Statistical Consulting. From 2008 to 2010, he served on the Institute of Medicine Committee on Nutrition Standards for the National School Lunch and Breakfast Programs.  He has served on the editorial boards of several statistics journals, has consulted with many major corporations, and has testified as an expert witness on the use of statistics.
 
Professor McCabe’s research has focused on applications of statistics.  Much of his recent work has been on problems of nutrition, including nutrient requirements, calcium metabolism, and bone health. He is author or coauthor of more than 160 publications in many different journals. Bruce A. Craig is Professor of Statistics and Director of the Statistical Consulting Service at Purdue University. He received his B.S. in mathematics and economics from Washington University in St. Louis and his PhD in statistics from the University of Wisconsin–Madison. He is an active member of the American Statistical Association and was chair of its section on Statistical Consulting in 2009. He also is an active member of the Eastern North American Region of the International Biometrics Society and aws elected by the voting membership to the Regional Committee from 2003 to 2006. Professor Craig has served on the editorial board of several statistical journals and has been a member of several data and safety monitoring boards, including Purdue's IRB. Professor Craig's research interests focus on the development of novel statistical methodology to address research questions in the life sciences. Areas of current interest are protein structure determination, diagnostic testing, and animal abundance estimation. In 2005, he was named Purdue University Faculty Scholar.

To Teachers: About This Book 
To Students: What Is Statistics? 
About the Authors   
Data Table Index   
Beyond the Basics Index  

Part I Looking at Data
CHAPTER 1
Looking at Data—Distributions
Introduction

1.1 Data
Key characteristics of a data set
Section 1.1 Summary
Section 1.1 Exercises

1.2 Displaying Distributions with Graphs
Categorical variables: bar graphs and pie charts
Quantitative variables: stemplots and histograms
Histograms
Data analysis in action: Don’t hang up on me
Examining distributions
Dealing with outliers
Time plots
Section 1.2 Summary
Section 1.2 Exercises

1.3 Describing Distributions with Numbers
Measuring center: the mean
Measuring center: the median
Mean versus median
Measuring spread: the quartiles
The five-number summary and boxplots
The 1.5 × IQR rule for suspected outliers
Measuring spread: the standard deviation
Properties of the standard deviation
Choosing measures of center and spread
Changing the unit of measurement
Section 1.3 Summary
Section 1.3 Exercises

1.4 Density Curves and Normal Distributions
Density curves
Measuring center and spread for density curves
Normal distributions
The 68–95–99.7 rule
Standardizing observations
Normal distribution calculations
Using the standard Normal table
Inverse Normal calculations
Normal quantile plots
Beyond the Basics: Density estimation
Section 1.4 Summary
Section 1.4 Exercises
Chapter 1 Exercises

CHAPTER 2
Looking at Data—Relationships
Introduction
2.1 Relationships
Examining relationships
Section 2.1 Summary
Section 2.1 Exercises

2.2 Scatterplots
Interpreting scatterplots
The log transformation
Adding categorical variables to scatterplots
Beyond the Basics: Scatterplot smoothers
Categorical explanatory variables
Section 2.2 Summary
Section 2.2 Exercises

2.3 Correlation
The correlation r
Properties of correlation
Section 2.3 Summary
Section 2.3 Exercises

2.4 Least-Squares Regression
Fitting a Line to Data
Prediction
Least-squares regression
Interpreting the regression line
Facts about least-squares regression
Correlation and regression
Another view of r2
Section 2.4 Summary
Section 2.4 Exercises

2.5 Cautions about Correlation and Regression
Residuals
Outliers and influential observations
Beware of the lurking variable
Beware of correlations based on averaged data
Beware of restricted ranges
Beyond the Basics: Data mining
Section 2.5 Summary
Section 2.5 Exercises

2.6 Data Analysis for Two-Way Tables
The two-way table
Joint distribution
Marginal distributions
Describing relations in two-way tables
Conditional distributions
Simpson’s paradox
Section 2.6 Summary
Section 2.6 Exercises

2.7 The Question of Causation
Explaining association
Establishing causation
Section 2.7 Summary
Section 2.7 Exercises
Chapter 2 Exercises

CHAPTER 3
Producing Data
Introduction
3.1 Sources of Data
Anecdotal data
Available data
Sample surveys and experiments
Section 3.1 Summary
Section 3.1 Exercises

3.2 Design of Experiments
Comparative experiments
Randomization
Randomized comparative experiments
How to randomize
Randomization using software
Randomization using random digits
Cautions about experimentation
Matched pairs designs
Block designs
Section 3.2 Summary
Section 3.2 Exercises

3.3 Sampling Design
Simple random samples
Selection of a simple random sample using software
Selection of a simple random sample using random digits
Stratified random samples
Multistage random samples
Cautions about sample surveys
Beyond the Basics: Capture-recapture sampling
Section 3.3 Summary
Section 3.3 Exercises

3.4 Ethics
Institutional review boards
Informed consent
Confidentiality
Clinical trials
Behavioral and social science experiments
Section 3.4 Summary
Section 3.4 Exercises
Chapter 3 Exercises

Part II Probability and Inference
CHAPTER 4
Probability: The Study of Randomness
Introduction
4.1 Randomness
The language of probability
Thinking about randomness
The uses of probability
Section 4.1 Summary
Section 4.1 Exercises

4.2 Probability Models
Sample spaces
Probability rules
Assigning probabilities: finite number of outcomes
Assigning probabilities: equally likely outcomes
Independence and the multiplication rule
Applying the probability rules
Section 4.2 Summary
Section 4.2 Exercises

4.3 Random Variables
Discrete random variables
Continuous random variables
Normal distributions as probability distributions
Section 4.3 Summary
Section 4.3 Exercises

4.4 Means and Variances of Random Variables
The mean of a random variable
Statistical estimation and the law of large numbers
Thinking about the law of large numbers
Beyond the Basics: More laws of large numbers
Rules for means
The variance of a random variable
Rules for variances and standard deviations
Section 4.4 Summary
Section 4.4 Exercises

4.5 General Probability Rules
General addition rules
Conditional probability
General multiplication rules
Tree diagrams
Bayes’s rule
Independence again
Section 4.5 Summary
Section 4.5 Exercises
Chapter 4 Exercises

CHAPTER 5
Sampling Distributions
Introduction
5.1 Toward Statistical Inference
Sampling variability
Sampling distributions
Bias and variability
Sampling from large populations
Why randomize?
Section 5.1 Summary
Section 5.1 Exercises

5.2 The Sampling Distribution of a Sample Mean
The mean and standard deviation of x ̅ 
The central limit theorem
A few more facts
Beyond the Basics: Weibull distributions
Section 5.2 Summary
Section 5.2 Exercises

5.3 Sampling Distributions for Counts and Proportions
The binomial distributions for sample counts
Binomial distributions in statistical sampling
Finding binomial probabilities
Binomial mean and standard deviation
Sample proportions
Normal approximation for counts and proportions
The continuity correction
Binomial formula
The Poisson distributions
Section 5.3 Summary
Section 5.3 Exercises
Chapter 5 Exercises

CHAPTER 6
Introduction to Inference
Introduction
Overview of inference
6.1 Estimating with Confidence
Statistical confidence
Confidence intervals
Confidence interval for a population mean
How confidence intervals behave
Choosing the sample size
Some cautions
Section 6.1 Summary
Section 6.1 Exercises

6.2 Tests of Significance
The reasoning of significance tests
Stating hypotheses
Test statistics
P-values
Statistical significance
Tests for a population mean
Two-sided significance tests and confidence intervals
The P-value versus a statement of significance
Section 6.2 Summary
Section 6.2 Exercises

6.3 Use and Abuse of Tests
Choosing a level of significance
What statistical significance does not mean
Don’t ignore lack of significance
Statistical inference is not valid for all sets of data
Beware of searching for significance
Section 6.3 Summary
Section 6.3 Exercises

6.4 Power and Inference as a Decision
Power
Increasing the power
Inference as decision
Two types of error
Error probabilities
The common practice of testing hypotheses
Section 6.4 Summary
Section 6.4 Exercises
Chapter 6 Exercises

CHAPTER 7
Inference for Means
Introduction
7.1 Inference for the Mean of a Population
The t distributions
The one-sample t confidence interval
The one-sample t test
Matched pairs t procedures
Robustness of the t procedures
Beyond the Basics: The bootstrap
Section 7.1 Summary
Section 7.1 Exercises

7.2 Comparing Two Means
The two-sample z statistic
The two-sample t procedures
The two-sample t confidence interval
The two-sample t significance test
Robustness of the two-sample procedures
Inference for small samples
Software approximation for the degrees of freedom
The pooled two-sample t procedures
Section 7.2 Summary
Section 7.2 Exercises

7.3 Additional Topics on Inference
Choosing the sample size
Inference for non-Normal populations
Transforming data
Use of a distribution-free procedure
Section 7.3 Summary
Section 7.3 Exercises
Chapter 7 Exercises

CHAPTER 8
Inference for Proportions
Introduction
8.1 Inference for a Single Proportion
Large-sample confidence interval for a single proportion
Beyond the Basics: The plus four confidence interval for a single proportion
Significance test for a single proportion
Choosing a sample size for a confidence interval
Choosing a sample size for a significance test
Section 8.1 Summary
Section 8.1 Exercises

8.2 Comparing Two Proportions
Large-sample confidence interval for a difference in proportions
Beyond the Basics: The plus four confidence interval for a difference in proportions
Significance test for a difference in proportions
Choosing a sample size for two sample proportions
Beyond the Basics: Relative risk
Section 8.2 Summary
Section 8.2 Exercises
Chapter 8 Exercises

Part III Topics in Inference

CHAPTER 9
Analysis of Two-Way Tables
Introduction
9.1 Inference for Two-Way Tables
The hypothesis: no association
Expected cell counts
The chi-square test
Computations
Computing conditional distributions
The chi-square test and the z test
Beyond the Basics: Meta-analysis
Section 9.1 Summary
Section 9.1 Exercises
9.2 Goodness of Fit
Section 9.2 Summary
Section 9.2 Exercises
Chapter 9 Exercises

CHAPTER 10
Inference for Regression
Introduction
10.1 Simple Linear Regression
Statistical model for linear regression
Preliminary data analysis and inference considerations
Estimating the regression parameters
Checking model assumptions
Confidence intervals and significance tests
Confidence intervals for mean response
Prediction intervals
Transforming variables
Beyond the Basics: Nonlinear regression
Section 10.1 Summary
Section 10.1 Exercises

10.2 More Detail about Simple Linear Regression
Analysis of variance for regression
The ANOVA F test
Calculations for regression inference
Inference for correlation
Section 10.2 Summary
Section 10.2 Exercises
Chapter 10 Exercises

CHAPTER 11
Multiple Regression
Introduction
11.1 Inference for Multiple Regression
Population multiple regression equation
Data for multiple regression
Multiple linear regression model
Estimation of the multiple regression parameters
Confidence intervals and significance tests for regression coefficients
ANOVA table for multiple regression
Squared multiple correlation R2
Section 11.1 Summary
Section 11.1 Exercises
11.2 A Case Study
Preliminary analysis
Relationships between pairs of variables
Regression on high school grades
Interpretation of results
Examining the residuals
Refining the model
Regression on SAT scores
Regression using all variables
Test for a collection of regression coefficients
Beyond the Basics: Multiple logistic regression
Section 11.2 Summary
Section 11.2 Exercises
Chapter 11 Exercises

CHAPTER 12
One-Way Analysis of Variance
Introduction
12.1 Inference for One-Way Analysis of Variance
Data for one-way ANOVA
Comparing means
The two-sample t statistic
An overview of ANOVA
The ANOVA model
Estimates of population parameters
Testing hypotheses in one-way ANOVA
The ANOVA table
The F test
Software
Beyond the Basics: Testing the Equality of Spread
Section 12.1 Summary
Section 12.1 Exercises

12.2 Comparing the Means
Contrasts
Multiple comparisons
Power
Section 12.2 Summary
Section 12.2 Exercises
Chapter 12 Exercises

CHAPTER 13
Two-Way Analysis of Variance
Introduction
13.1 The Two-Way ANOVA Model
Advantages of two-way ANOVA
The two-way ANOVA model
Main effects and interactions
13.2 Inference for Two-Way ANOVA
The ANOVA table for two-way ANOVA
Chapter 13 Summary
Chapter 13 Exercises

Companion Chapters
(on the IPS website www.macmillanhighered.com/ips9e and in LaunchPad)
CHAPTER 14
Logistic Regression
Introduction
14.1 The Logistic Regression Model
Binomial distributions and odds
Odds for two groups
Model for logistic regression
Fitting and interpreting the logistic regression model

14.2 Inference for Logistic Regression
Confidence intervals and significance tests
Multiple logistic regression
Chapter 14 Summary
Chapter 14 Exercises
Chapter 14 Notes and Data Sources

CHAPTER 15
Nonparametric Tests
Introduction
15.1 The Wilcoxon Rank Sum Test
The rank transformation
The Wilcoxon rank sum test
The Normal approximation
What hypotheses does Wilcoxon test?
Ties
Rank, t, and permutation tests
Section 15.1 Summary
Section 15.1 Exercises

15.2 The Wilcoxon Signed Rank Test
The Normal approximation
Ties
Testing a hypothesis about the median of a distribution
Section 15.2 Summary
Section 15.2 Exercises

15.3 The Kruskal-Wallis Test
Hypotheses and assumptions
The Kruskal-Wallis test
Section 15.3 Summary
Section 15.3 Exercises
Chapter 15 Exercises
Chapter 15 Notes and Data Sources

CHAPTER 16
Bootstrap Methods and Permutation Tests
Introduction
Software
16.1 The Bootstrap Idea
The big idea: resampling and the bootstrap distribution
Thinking about the bootstrap idea
Using software
Section 16.1 Summary
Section 16.1 Exercises

16.2 First Steps in Using the Bootstrap
Bootstrap t confidence intervals
Bootstrapping to compare two groups
Beyond the Basics: The bootstrap for a scatterplot smoother
Section 16.2 Summary
Section 16.2 Exercises

16.3 How Accurate Is a Bootstrap Distribution?
Bootstrapping small samples
Bootstrapping a sample median
Section 16.3 Summary
Section 16.3 Exercises

16.4 Bootstrap Confidence Intervals
Bootstrap percentile confidence intervals
A more accurate bootstrap confidence interval: BCa
Confidence intervals for the correlation
Section 16.4 Summary
Section 16.4 Exercises

16.5 Significance Testing Using Permutation Tests
Using software
Permutation tests in practice
Permutation tests in other settings
Section 16.5 Summary
Section 16.5 Exercises
Chapter 16 Exercises
Chapter 16 Notes and Data Sources

CHAPTER 17
Statistics for Quality: Control and Capability
Introduction
Use of data to assess quality
17.1 Processes and Statistical Process Control
Describing processes
Statistical process control
x ̅ charts for process monitoring
s charts for process monitoring
Section 17.1 Summary
Section 17.1 Exercises

17.2 Using Control Charts
x ̅ and R charts
Additional out-of-control rules
Setting up control charts
Comments on statistical control
Don’t confuse control with capability!
Section 17.2 Summary
Section 17.2 Exercises

17.3 Process Capability Indexes
The capability indexes Cp and Cpk
Cautions about capability indexes
Section 17.3 Summary
Section 17.3 Exercises

17.4 Control Charts for Sample Proportions
Control limits for p charts
Section 17.4 Summary
Section 17.4 Exercises
Chapter 17 Exercises
Chapter 17 Notes and Data Sources

Tables 
Answers to Odd-Numbered Exercises 
Notes and Data Sources 
Index 

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