This book offers an introduction to applied statistics through data analysis, integrating statistical computing methods. It covers robust and non-robust descriptive statistics used in each of four bivariate statistical models that are commonly used in research: ANOVA, proportions, regression, and logistic. The text teaches statistical inference principles using resampling methods (such as randomization and bootstrapping), covering methods for hypothesis testing and parameter estimation. These methods are applied to each statistical model introduced in preceding chapters.
Data analytic examples are used to teach statistical concepts throughout, and students are introduced to the R packages and functions required for basic data analysis in each of the four models. The text also includes introductory guidance to the fundamentals of data wrangling, as well as examples of write-ups so that students can learn how to communicate findings. Each chapter includes problems for practice or assessment. Supplemental instructional videos are also available as an additional aid to instructors, or as a general resource to students.
This book is intended for an introductory or basic statistics course with an applied focus, or an introductory analytics course, at the undergraduate level in a two-year or four-year institution. This can be used for students with a variety of disciplinary backgrounds, from business, to the social sciences, to medicine. No sophisticated mathematical background is required.
Author(s): Bruce Blaine
Publisher: Springer
Year: 2023
Language: English
Pages: 196
City: Cham
Preface
Expectations for Student and Instructor
Chapter Teaching and Learning Goals
Contents
Chapter 1: Foundations I: Introductory Data Analysis with R
1.1 Goals of Data Analysis
1.2 Statistics to Summarize a Numeric Variable
1.2.1 Location Statistics
1.2.2 Variability Statistics
1.3 Data Analytic Example 1
1.4 Data Analysis with a Categorical Variable
1.5 Data Analytic Example 2
1.6 Problems
Chapter 2: Foundations II: Statistical Models and Study Design
2.1 Goals of Data Analysis with Bivariate Data
2.1.1 Summarizing Bivariate Data: Relationship Direction and Magnitude
2.1.2 Exploring Bivariate Data
2.2 Statistical Models and Data Analysis
2.2.1 ANOVA Model
2.2.2 Proportions Model
2.2.3 Regression Model
2.2.4 Logistic Model
2.3 Interpreting Bivariate Relationships: Generalizability and Causation
2.3.1 Generalizability
2.3.2 Causation
2.4 Summary
2.5 Exercises
Chapter 3: Statistics and Data Analysis in an ANOVA Model
3.1 Data Analysis in an ANOVA Model
3.2 Describing the X-Y Relationship in an ANOVA Model
3.2.1 Location-Based Effect Size Statistics
3.2.2 Other Effect Size Statistics
3.2.3 Plots
3.3 Data Analytic Example 1
3.4 Exploring Influential Values
3.5 Interpreting Group Differences from an ANOVA Model
3.6 Data Analytic Example 2
3.7 Writing a Data Analytic Report
3.8 Problems
Chapter 4: Statistics and Data Analysis in a Proportions Model
4.1 Introduction
4.2 Contingency Tables
4.3 Statistics for Describing the X-Y Relationship in a Proportions Model
4.4 Data Analytic Example 1
4.5 Plots for Describing the X-Y Relationship in a Proportions Model
4.6 Data Analytic Example 2
4.7 Writing Up a Descriptive Analysis
4.8 Problems
Chapter 5: Statistics and Data Analysis in a Regression Model
5.1 Data Analysis in a Regression Model
5.2 Logic of Linear Regression
5.3 Least Squares Regression
5.4 Data Analytic Example 1
5.5 Correlation
5.6 Influential Observations
5.7 Plots
5.8 Interpreting Correlations
5.9 Data Analytic Example 2
5.10 Writing Up a Regression Analysis
5.11 Problems
Chapter 6: Statistics and Data Analysis in a Logistic Model
6.1 Data Analysis in a Logistic Model
6.2 Logic of Logistic Regression
6.3 Logistic Regression Analysis
6.4 Data Analytic Example 1
6.5 Influential Observations
6.6 Plots
6.7 Interpreting the Results of Logistic Regression
6.8 Data Analytic Example 2
6.9 Writing Up a Descriptive Analysis
6.10 Problems
Chapter 7: Statistical Inference I: Randomization Methods for Hypothesis Testing
7.1 Introduction to Statistical Inference
7.2 Randomization Test
7.3 Interpreting the Results of a Randomization Test
7.3.1 p-Value
7.3.2 Exchangeability
7.3.3 Statistical Alternatives Under HA
7.4 Subtypes of the Randomization Test
7.4.1 Monte Carlo Test
7.4.2 Permutation Test
7.5 Doing Randomization Tests in R
7.5.1 Example 1: Randomization Test Using the Mean Difference
7.5.2 Example 2: Randomization Test Using the Median Difference
7.6 Writing Up the Results of a Randomization Test
7.7 Problems
Chapter 8: Statistical Inference II: Bootstrapping Methods for Parameter Estimation
8.1 Introduction to Parameter Estimation
8.2 The Logic of Bootstrapping
8.3 Parameter Estimation
8.4 Bootstrapped Confidence Intervals
8.5 Estimation with Effect Size Statistics
8.6 How to Interpret a Confidence Interval
8.7 Factors That Affect Confidence Intervals
8.8 Writing Up a Parameter Estimation Study
8.9 Problems
Chapter 9: Using Resampling Methods for Statistical Inference: Four Examples
9.1 Introduction
9.2 Doing Systematic Data Analysis: A Seven-Step Process
9.3 Data Analysis in an ANOVA Model: An Example
9.4 Data Analysis in a Proportions Model: An Example
9.5 Data Analysis in a Regression Model: An Example
9.6 Data Analysis in a Logistic Model: An Example
9.7 Statistical Significance and Practical Significance
9.8 Problems
Chapter 10: Statistics and Data Analysis in a Pre-Post Design
10.1 Introduction
10.2 Data Analysis in Pre-Post Data
10.3 Data Analytic Example 1
10.4 Internal Validity in Pre-Post Designs
10.5 Writing Up a Descriptive Analysis
10.6 Problems
