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Advanced High School Statistics
Third Edition
David M Diez, Mine Çetinkaya-Rundel, Leah Dorazio, Christopher D Barr
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Front Matter
Preface
1
Data collection
1.1
Case study: using stents to prevent strokes
1.1.1
Case study
1.1.2
Section summary
1.1.3
Exercises
1.2
Data basics
1.2.1
Observations, variables, and data matrices
1.2.2
Types of variables
1.2.3
Relationships between variables
1.2.4
Section summary
1.2.5
Exercises
1.3
Overview of data collection principles
1.3.1
Populations and samples
1.3.2
Anecdotal evidence
1.3.3
Explanatory and response variables
1.3.4
Observational studies versus experiments
1.3.5
Section summary
1.3.6
Exercises
1.4
Observational studies and sampling strategies
1.4.1
Observational studies
1.4.2
Sampling from a population
1.4.3
Simple, systematic, stratified, cluster, and multistage sampling
1.4.4
Section summary
1.4.5
Exercises
1.5
Experiments
1.5.1
Reducing bias in human experiments
1.5.2
Principles of experimental design
1.5.3
Completely randomized, blocked, and matched pairs design
1.5.4
Testing more than one variable at a time
1.5.5
Section summary
1.5.6
Exercises
1.6
Chapter exercises
1.6
Exercises
2
Summarizing data
2.1
Examining numerical data
2.1.1
Scatterplots for paired data
2.1.2
Stem-and-leaf plots and dot plots
2.1.3
Histograms
2.1.4
Describing Shape
2.1.5
Descriptive versus inferential statistics
2.1.6
Section summary
2.1.7
Exercises
2.2
Numerical summaries and box plots
2.2.1
Measures of center
2.2.2
Standard deviation as a measure of spread
2.2.3
Z-scores
2.2.4
Box plots and quartiles
2.2.5
Technology: summarizing 1-variable statistics
2.2.6
Outliers and robust statistics
2.2.7
Linear transformations of data
2.2.8
Comparing numerical data across groups
2.2.9
Mapping data (special topic)
2.2.10
Section summary
2.2.11
Exercises
2.3
Normal distribution
2.3.1
Normal distribution model
2.3.2
Using the normal distribution to approximate empirical distributions
2.3.3
Finding areas under the normal curve
2.3.4
Normal probability examples
2.3.5
68-95-99.7 rule
2.3.6
Evaluating the normal approximation (special topic)
2.3.7
Technology: finding normal probabilities
2.3.8
Section summary
2.3.9
Exercises
2.4
Considering categorical data
2.4.1
Contingency tables and bar charts
2.4.2
Row and column proportions
2.4.3
Using a bar chart with two variables
2.4.4
Mosaic plots
2.4.5
The only pie chart you will see in this book
2.4.6
Section summary
2.4.7
Exercises
2.5
Case study: malaria vaccine (special topic)
2.5.1
Variability within data
2.5.2
Simulating the study
2.5.3
Checking for independence
2.5.4
Exercises
2.5.5
Chapter Highlights
2.6
Chapter exercises
2.6
Exercises
3
Probability and probability distributions
3.1
Defining probability
3.1.1
Introductory examples
3.1.2
Probability
3.1.3
Disjoint or mutually exclusive outcomes
3.1.4
Probabilities when events are not disjoint
3.1.5
Complement of an event
3.1.6
Independence
3.1.7
Section summary
3.1.8
Exercises
3.2
Conditional probability
3.2.1
Exploring probabilities with a contingency table
3.2.2
Marginal and joint probabilities
3.2.3
Defining conditional probability
3.2.4
Smallpox in Boston, 1721
3.2.5
General multiplication rule
3.2.6
Sampling without replacement
3.2.7
Independence considerations in conditional probability
3.2.8
Checking for independent and mutually exclusive events
3.2.9
Tree diagrams
3.2.10
Bayes’ Theorem
3.2.11
Section summary
3.2.12
Exercises
3.3
Simulations
3.3.1
Setting up and carrying out simulations
3.3.2
Section summary
3.3.3
Exercises
3.4
Random variables
3.4.1
Introduction to expected value
3.4.2
Probability distributions
3.4.3
Expectation
3.4.4
Variability in random variables
3.4.5
Linear transformations of a random variable
3.4.6
Linear combinations of random variables
3.4.7
Variability in linear combinations of random variables
3.4.8
Normal approximation for sums of random variables
3.4.9
Section summary
3.4.10
Exercises
3.5
Geometric distribution
3.5.1
Bernoulli distribution
3.5.2
Geometric distribution
3.5.3
Technology: geometric probablities
3.5.4
Section summary
3.5.5
Exercises
3.6
Binomial Distribution
3.6.1
Introducing the binomial formula
3.6.2
When and how to apply the formula
3.6.3
Technology: binomial probabilities
3.6.4
An example of a binomial distribution
3.6.5
The mean and standard deviation of a binomial distribution
3.6.6
Normal approximation to the binomial distribution
3.6.7
Normal approximation breaks down on small intervals (special topic)
3.6.8
Section summary
3.6.9
Exercises
3.6.10
Chapter Highlights
3.7
Chapter exercises
3.7
Exercises
4
Sampling Distributions
4.1
Sampling distribution of a sample proportion
4.1.1
The mean and standard deviation of
p
^
4.1.2
The Central Limit Theorem
4.1.3
Normal approximation for the distribution of
p
^
4.1.4
Section summary
4.1.5
Exercises
4.2
Sampling distribution of a sample mean
4.2.1
The mean and standard deviation of
x
¯
4.2.2
The Central Limit Theorem Revisted
4.2.3
Normal approximation for the sampling distribution of
x
¯
4.2.4
Section summary
4.2.5
Exercises
4.3
Sampling distribution for a difference
4.3.1
The mean and SD for a difference of two random variables (review)
4.3.2
Differenece of Sample Proportions
4.3.3
Difference of sample means
4.3.4
Section Summary
4.3.5
Exercises
4.3.6
Chapter Highlights
4.4
Chapter exercises
4.4
Exercises
5
Foundations for inference
5.1
Estimating unknown parameters
5.1.1
Point estimates
5.1.2
Understanding the variability of a point estimate
5.1.3
Introducing the standard error
5.1.4
Basic properties of point estimates
5.1.5
Section summary
5.1.6
Exercises
5.2
Confidence intervals
5.2.1
Capturing the population parameter
5.2.2
Constructing a 95% confidence interval
5.2.3
Changing the confidence level
5.2.4
Margin of error
5.2.5
Interpreting confidence intervals
5.2.6
Confidence interval procedures: a five step process
5.2.7
Section summary
5.2.8
Exercises
5.3
Introducing hypothesis testing
5.3.1
Case study: medical consultant
5.3.2
Setting up the null and alternate hypothesis
5.3.3
Evaluating the hypotheses with a p-value
5.3.4
Calculating the p-value by simulation (special topic)
5.3.5
Hypothesis testing: a five step process
5.3.6
Decision errors
5.3.7
Choosing a significance level
5.3.8
Statistical power of a hypothesis test
5.3.9
Statistical significance versus practical significance
5.3.10
Statistical significance versus a real difference
5.3.11
When to retreat
5.3.12
Section summary
5.3.13
Exercises
5.3.14
Chapter Highlights
5.4
Chapter exercises
5.4
Exercises
6
Inference for categorical data
6.1
Inference for a single proportion
6.1.1
Distribution of a sample proportion (review)
6.1.2
Checking conditions for inference using a normal distribution
6.1.3
Confidence intervals for a proportion
6.1.4
Calculator: the 1-proportion Z-interval
6.1.5
Choosing a sample size when estimating a proportion
6.1.6
Hypothesis testing for a proportion
6.1.7
Calculator: the 1-proportion Z-test
6.1.8
Section summary
6.1.9
Exercises
6.2
Difference of two proportions
6.2.1
6.2.2
Sampling distribution for the difference of two proportions (review)
6.2.3
Checking conditions for inference using a normal distribution
6.2.4
Confidence interval for the difference of two proportions
6.2.5
Calculator: the 2-proportion Z-interval
6.2.6
Hypothesis testing when
:
H
0
:
p
1
=
p
2
6.2.7
Calculator: the 2-proportion Z-test
6.2.8
Section summary
6.2.9
Exercises
6.3
Testing for goodness of fit using chi-square
6.3.1
Creating a test statistic for one-way tables
6.3.2
The chi-square test statistic
6.3.3
The chi-square distribution and finding areas
6.3.4
Finding a p-value for a chi-square distribution
6.3.5
Evaluating goodness of fit for a distribution
6.3.6
Calculator: chi-square goodness of fit test
6.3.7
Section summary
6.3.8
Exercises
6.4
Chi-square tests for two-way tables
6.4.1
Introduction
6.4.2
Expected counts in two-way tables
6.4.3
The chi-square test for homogeneity for two-way tables
6.4.4
The chi-square test of independence for two-way tables
6.4.5
Technology: chi-square test for two-way tables
6.4.6
Section summary
6.4.7
Exercises
6.4.8
Chapter Highlights
6.5
Chapter exercises
6.5
Exercises
7
Inference for numerical data
7.1
Inference for a mean with the
t
-distribution
7.1.1
Using a normal distribution for inference when
σ
is known
7.1.2
Introducing the
t
-distribution
7.1.3
Technology: finding area under the
t
-distribution
7.1.4
Checking conditions for inference on a mean using the
t
-distribution
7.1.5
One sample
t
-interval for a mean
7.1.6
Technologu: the 1-sample
t
-interval
7.1.7
Choosing a sample size when estimating a mean
7.1.8
Hypothesis testing for a mean
7.1.9
Technology: 1-sample
t
-test
7.1.10
Section summary
7.1.11
Exercises
7.2
Inference for paired data
7.2.1
Paired observations and samples
7.2.2
Hypothesis tests for paired data
7.2.3
Technology: The 1-Sample
t
-Test With Paired Data
7.2.4
Confidence intervals for the mean of a difference
7.2.5
Technology: the 1-sample
t
-interval with paired data
7.2.6
Section summary
7.2.7
Exercises
7.3
Inference for the difference of two means
7.3.1
Sampling distribution for the difference of two means (review)
7.3.2
Checking conditions for inference on a difference of means
7.3.3
Confidence intervals for a difference of means
7.3.4
Technology: the 2-sample
t
-interval
7.3.5
Hypothesis testing for the difference of two means
7.3.6
Technology: the 2-sample
t
-test
7.3.7
Section summary
7.3.8
Exercises
7.3.9
Chapter Highlights
7.4
Chapter exercises
7.4
Exercises
8
Introduction to linear regression
8.1
Line fitting, residuals, and correlation
8.1.1
Fitting a line to data
8.1.2
Using linear regression to predict possum head lengths
8.1.3
Residuals
8.1.4
Describing linear relationships with correlation
8.1.5
Section summary
8.1.6
Exercises
8.2
Fitting a line by least squares regression
8.2.1
An objective measure for finding the best line
8.2.2
Finding the least squares line
8.2.3
Interpreting the coefficients of a regression line
8.2.4
Extrapolation is treacherous
8.2.5
Using
R
2
to describe the strength of a fit
8.2.6
Technology: linear correlation and regression
8.2.7
Types of outliers in linear regression
8.2.8
Categorical predictors with two levels (special topic)
8.2.9
Section summary
8.2.10
Exercises
8.3
Transformations for skewed data
8.3.1
Introduction to transformations
8.3.2
Transformations to achieve linearity
8.3.3
Section summary
8.3.4
Exercises
8.4
Inference for the slope of a regression line
8.4.1
The role of inference for regression parameters
8.4.2
Conditions for the least squares line
8.4.3
Constructing a confidence interval for the slope of a regression line
8.4.4
Midterm elections and unemployment
8.4.5
Understanding regression output from software
8.4.6
Technology: the
t
-test for the slope
8.4.7
Which inference procedure to use for paired data?
8.4.8
Section summary
8.4.9
Exercises
8.4.10
Chapter Highlights
8.5
Chapter exercises
8.5
Exercises
Appendices
A
Data sets within the text
A.1
Data sets within the text
A.1.1
Chapter 1: Data Collection
A.1.2
Chapter 2: Summarizing Data
A.1.3
Chapter 3: Probability
A.1.4
Chapter 4: Distributions of random variables
A.1.5
Chapter 5: Foundations for inference
A.1.6
Chapter 6: Inference for categorical data
A.1.7
Chapter 7: Inference for numerical data
A.1.8
Chapter 8: Introduction to linear regression
B
Distribution Tables
B.1
Random Number Table
B.2
Normal Probability Table
B.3
t
Probability Table
B.4
Chi-Square Probability Table
C
Calculator reference, Formulas, and Inference guide
C.1
Calculator reference
C.2
Inference guide
Appendix
C
Calculator reference, Formulas, and Inference guide
C.1
Calculator reference
C.2
Inference guide
