Introduction to Statistical Investigations

Introduction to Statistical Investigations, Binder Ready Version 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. This is an unbound, binder-ready version. 

Nathan Tintle attained his Ph.D. in Statistics in 2005 from Stony Brook University and has been the primary mentor for over 95 undergraduate students in extended summer and/or academic year research projects in statistics, with the bulk of these students conducting research in statistical genetics and biostatistics.

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

Index

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