Introduction to Statistical Investigations leads students to learn about the process of conducting statistical investigations from data collection, to exploring data, to statistical inference, to drawing appropriate conclusions. The text is designed for a one-semester introductory statistics course.
It focuses on genuine research studies, active learning, and effective use of technology. Simulations and randomization tests introduce statistical inference, yielding a strong conceptual foundation that bridges students to theory-based inference approaches. Repetition allows students to see the logic and scope of inference. This implementation follows the GAISE recommendations endorsed by the American Statistical Association.
P. Preliminaries: Introduction to Statistical Investigations
P.1 Introduction to the Six-Step Method
P.2 Exploring Data
P.3 Exploring Random Processes
Unit 1: Four Pillars of Inference: Strength, Size, Breadth, and Cause
1.0 Significance: How Strong Is the Evidence?
1.1 Introduction to Chance Models
1.2 Measuring the Strength of Evidence
1.3 Alternative Measure of Strength of Evidence
1.4 What Impacts Strength of Evidence?
1.5 Inference for a Single Proportion: Theory-Based Approach
2.0 Generalization: How Broadly Do the Results Apply?
2.1 Sampling from a Finite Population
2.2 Inference for a Single Quantitative Variable
2.3 Errors and Significance
3.0 Estimation: How Large is the Effect?
3.1 Statistical Inference: Confidence Intervals
3.2 2SD and Theory-Based Confidence Intervals for a Single Proportion
3.3 2SD and Theory-Based Confidence Intervals for a Single Mean
3.4 Factors that Affect the Width of a Confidence Interval
3.5 Cautions When Conducting Inference
4.0 Causation: Can We Say What Caused the Effect
4.1 Association and Confounding
4.2 Observational Studies versus Experiments
Unit 2: Comparing Groups
5.0 Comparing Two Groups
5.1 Comparing Two Groups: Categorical Response
5.2 Comparing Two Proportions: Simulation-Based Approach
5.3 Comparing Two Proportions: Theory-Based Approach
6.0 Comparing Two Means
6.1 Comparing Two Groups: Quantitative Response
6.2 Comparing two Means: Simulation-Based Approach
6.3 Comparing Two Means: Theory-Based Approach
7.0 Paired Data: One Quantitative Variable
7.1 Paired Designs
7.2 Analyzing Paired Data: Simulation-Based Approach
7.3 Analyzing Paired Data: Theory-Based Approach
Unit 3: Analyzing More General Situations
8.0 Comparing More Than Two Proportions
8.1 Comparing Multiple Proportions: Simulation-Based Approach
8.2 Comparing Multiple Proportions: Theory-Based Approach
9.0 Comparing More Than Two Means
9.1 Comparing Multiple Means: Simulation-Based Approach
9.2 Comparing Multiple Means: Theory-Based Approach
Two Quantitative Variables
10.1 Two Quantitative Variables: Scatterplots and Correlation
10.2 Inference for the Correlation Coefficient: Simulation-Based Approach
10.3 Least Squares Regression
10.4 Inference for the Regression Slope: Simulation-Based Approach
10.5 Inference for the Regression Slope: Theory-Based Approach
A: Calculation Details
B: Stratified and Cluster Samples
Solutions to Selected Exercises
- Spiral approach to statistical process. A six-step process for conducting statistical investigations introduces students to the fundamental concept of statistical significance, along with collecting data and drawing conclusions.
- Active learning approach. Explorations in each chapter incorporate a variety of learning experiences such as shuffling cards, flipping coins, collecting data, running experiments, and using simulations. Explorations are flexible for individual students use or small to large groups, in and outside class.
- Randomization-based introduction to statistical inference. Makes use of modern computing and puts the logic of statistical inference at the center of the curriculum.
- Easy-to-use technology integrated throughout. Easy-to-use web applets enable students to conduct simulations and perform analyses. (Instructors may still use statistical software packages, if desired.)
- Real data from genuine studies. Uses real data from genuine research studies throughout the book, taken from a variety of fields of application.
- Focus on logic and scope of inference. Students are asked to consider questions of logic and scope of inference for every study encountered in the text.
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