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