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5. Practicing Statistics: Guided Investigations for the Second Course

# Practicing Statistics: Guided Investigations for the Second Course, 1st edition

• Shonda Kuiper
• Jeff Sklar

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## Overview

Building on the introductory course, Practicing Statistics: Guided Investigations for the Second Course presents a variety of compelling topics for a second course in statistics, such as multiple regression, nonparametric methods, and survival analysis. Every topic is introduced in the context of a real-world research question, asking students to explore the concepts firsthand with guided activities and research projects.

The number of students taking AP Statistics continues to rise, and the number of students taking an introductory statistics course has more than doubled since 1990. As a result, the goals of the second course have changed.  This course must engage students from multiple disciplines and demonstrate the broad applicability of statistics to their lives. To that end, this text takes an inquiry-based approach that teaches advanced statistical techniques through group work and hands-on exploration using real research questions.

The chapters are modular, so that instructors can select only the topics relevant to their course, and teach them in any order. The only prerequisite is an algebra-based introductory statistics or AP statistics course.

1. Nonparametric Methods: Schistosomiasis

1.1 Investigation: Can a New Drug Reduce the Spread of Schistosomiasis?

1.2 Statistical Inference Through a Randomization Test

1.3 Performing a Randomization Test Using a Computer Simulation

1.4 Two-Sided Tests

1.5 What Can We Conclude from the Schistosomiasis Study?

1.6 Permutation Tests versus Randomization Tests

1.7 Permutation and Randomization Tests for Matched Pairs Designs

1.8 The Bootstrap Distribution

1.9 Using Bootstrap Methods to Create Confidence Intervals

1.10 Relationship Between the Randomization Test and the Two-Sample t-Test

1.11 Wilcoxon Rank Sum Tests for Two Independent Samples

1.12 Kruskal-Wallis Test for Two or More Independent Samples

1.13 Multiple Comparisons

Research Project: Gender Discrimination Among University Faculty

2. Making Connections: The Two-Sample t-Test, Regression, and ANOVA

2.1 Investigation: Do Distracting Colors Influence the Time to Complete a Game?

2.2 The Two-Sample t-Test to Compare Population Means

2.3 The Regression Model to Compare Population Means

2.4 ANOVA to Compare Population Means

2.5 Comparing Planned Variability to Random Variability

2.6 Random Sampling and Random Allocation

2.7 What Can We Conclude from the Game Study?

2.8 Normal Probability Plots to Assess Normality

2.9 Transformations

2.10 Calculating Test Statistics

2.11 Confidence Intervals

Research Project: Building a Better Paper Helicopter

3. Multiple Regression: How Much Is Your Car Worth?

3.1 Investigation: How Can We Build a Model to Estimate Used Car Prices?

3.2 Goals of Multiple Regression

3.3 Variable Selection Techniques to Describe or Predict a Response

3.4 Checking Model Assumptions

3.5 Interpreting Model Coefficients

3.6 Categorical Explanatory Variables

3.7 What Can We Conclude from the 2005 GM Car Study?

3.8 F-Tests for Multiple Regression

3.9 Developing a Model to Confirm a Theory

3.10 Interaction and Terms for Curvature

3.11 A Closer Look at Variable Selection Criteria

Research Project: Economic Growth in Third World Countries

4. The Design and Analysis of Factorial Experiments: Microwave Popcorn

4.1 Investigation: Which Microwave Popcorn Is the Best?

4.2 Elements of a Well-Designed Experiment

4.3 Analyzing a Two-Way Factorial Design

4.4 Analyzing a Three-Way Factorial Design

4.5 What Can We Conclude from the Popcorn Study?

4.6 Paper Towels: Developing a Statistical Model for a Two-Way Factorial Design

4.7 Paper Towels: The Relationship Between Effects and ANOVA

4.8 Contrasts and Multiple Comparisons

Research Project: Testing for the Effect of Distracters

5. Block, Split-Plot, and Repeated Measures Designs: What Influences Memory?

5.1 Investigation: What Influences Memory?

5.2 Elements of a Well-Designed Experiment

5.3 Statistical Analysis Based on the Experimental Design

5.4 Three Commonly Used Design Structures

5.5 Crossed and Nested Factors

5.6 Fixed and Random Factors

5.7 Model Assumptions

5.8 What Can We Conclude from the Memory Study?

5.9 Calculating Crossed and Nested Effects

5.10 Mathematical Calculations for ANOVA

5.11 Hasse Diagrams

5.12 Wash Your Hands: Analysis of Covariance (ANCOVA)

Research Project: What Impacts Memory?

6. Categorical Data Analysis: Is a Tumor Malignant or Benign?

6.1 Investigation: Is Cell Shape Associated with Malignancy?

6.2 Summarizing Categorical Data

6.3 A Simulation Study: How Likely Is It That the Observed Sample Would Occur by Chance?

6.4 Fisher’s Exact Test

6.5 Two-Sided Hypothesis Tests

6.6 The Chi-Square Test

6.7 What Can We Conclude from the Cancer Study?

6.8 Relative Risk and the Odds Ratio

6.9 Sampling Designs

6.10 Comparing Tests of Homogeneity and Independence

6.11 Chi-Square Goodness-of-Fit Tests

Research Project: Infant Handling in Female Baboons

7. Logistic Regression: The Space Shuttle Challenger

7.1 Investigation: Did Temperature Influence the Likelihood of an O-Ring Failure?

7.2 Review of the Least Squares Regression Model

7.3 The Logistic Regression Model

7.4 The Logistic Regression Model Using Maximum Likelihood Estimates

7.5 Interpreting the Logistic Regression Model

7.6 Inference for the Logistic Regression Model

7.7 What Can We Conclude from the Space Shuttle Study?

7.8 Logistic Regression with Multiple Explanatory Variables

7.9 The Drop-in-Deviance Test

7.10 Measures of Association

7.11 Review of Means and Variances of Binary and Binomial Data

7.12 Calculating Logistic Regression Models for Binomial Counts

7.13 Calculating Residuals for Logistic Models with Binomial Counts

7.14 Assessing the Fit of a Logistic Regression Model with Binomial Counts

7.15 Diagnostic Plots

7.16 Maximum Likelihood Estimation in Logistic Regression

Research Project: Substance Abuse Among Youth

8. Poisson Log-Linear Regression: Detecting Cancer Clusters

8.1 Investigation: Are Cancer Rates Higher for People Living near a Toxic Waste Area?

8.2 Comparing Count Data for Groups

8.3 Building Models for Count Data

8.4 The Binomial Model for Count Data

8.5 The Poisson Model for Count Data

8.6 Adding a Covariate to the Poisson Count Model

8.7 Interpreting Poisson Regression Model Parameters

8.8 Poisson Regression Models with More Than One Covariate

8.9 Inference for Poisson Regression Models

8.10 Assessing the Fit of the Poisson Regression Model

8.11 What Can We Conclude from the Cancer Rate Study?

8.12 Estimation Methods for Generalized Linear Models

8.13 Do No-Smoking-at-Work Policies Keep Smoking at Home?

8.14 Is the Number of Species on Archipelago Islands Related to Island Area, Elevation, and Neighboring Islands?

Research Project: Hitting a Grand Slam in Baseball

9. Survival Analysis: Melting Chocolate Chips

9.1 Investigation: How Long Does It Take for Chocolate Chips to Melt?

9.2 Overview of Survival Analysis Studies and Data

9.3 The Survival Function

9.4 Descriptive Statistics for Survival Data

9.5 Confidence Intervals for Survival Probabilities

9.6 Comparing Survival Functions

9.7 What Can We Conclude About Melting Chocolate Chips?

9.8 The Hazard Function

9.9 The Cumulative Hazard Function

9.10 Additional Types of Incomplete Data

Research Project: Shapesplosion: A Study of Reaction Time

10. Principal Component Analysis: Stock Market Values

10.1 Investigation: Can a Single Variable Explain Patterns in the Stock Market?

10.2 A Visual Interpretation of PCA

10.3 Calculating Principal Components for Two Variables

10.4 Understanding Eigenvalues

10.5 A Three-Dimensional Example

10.6 What Can We Conclude from the Stock Market Investigation?

10.7 The Impact of Standardizing Each Variable

10.8 Determining the Number of Components to Retain

10.9 Interpreting Principal Components

10.10 Comparing Regression and Principal Components

10.11 Incorporating Principal Components into Other Statistical Methods

10.12 Calculating Eigenvectors and Eigenvalues Using Matrix Algebra

Research Project: The Global Warming Hockey Stick Controversy

11. Bayesian Data Analysis: What Colors Come in Your M&M’s Candy Bag?

11.1 Investigation: Do Prior Beliefs Improve Your Estimate of the Proportion of Brown or Orange M&M’s?

11.2 Combining Prior Information About π with Data

11.3 Prior Distributions for π

11.4 Calculating the Posterior Distribution for π

11.5 The Posterior Mean

11.6 What Can We Conclude About Colors of M&M’s?

11.7 Screening for the HIV Virus in the U.S. Blood Bank Supply: Applications of Bayes’ Rule

11.8 Ganzfeld Experiments: Continuous Prior Distributions for π

Research Project: Do You Believe in ESP?

Appendix of Tables

Index

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