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Statistics with R
A Beginner's Guide

Second Edition

- Robert Stinerock - Universidade Nova de Lisboa, Portugal

Additional resources:

December 2022 | 448 pages | SAGE Publications Ltd

Statistics is made simple with this award-winning guide to using R and applied statistical methods.

With a clear step-by-step approach explained using real world examples, learn the practical skills you need to use statistical methods in your research from an expert with over 30 years of teaching experience. With a wealth of hands-on exercises and online resources created by the author, practice your skills using the data sets and R scripts from the book with detailed screencasts that accompany each script.

This book is ideal for anyone looking to:

• Complete an introductory course in statistics

• Prepare for more advanced statistical courses

• Gain the transferable analytical skills needed to interpret research from across the social sciences

• Learn the technical skills needed to present data visually

• Acquire a basic competence in the use of R and RStudio.

This edition also includes a gentle introduction to Bayesian methods integrated throughout.

The author has created a wide range of online resources, including: over 90 R scripts, 36 datasets, 37 screen casts, complete solutions for all exercises, and 130 multiple-choice questions to test your knowledge.

With a clear step-by-step approach explained using real world examples, learn the practical skills you need to use statistical methods in your research from an expert with over 30 years of teaching experience. With a wealth of hands-on exercises and online resources created by the author, practice your skills using the data sets and R scripts from the book with detailed screencasts that accompany each script.

This book is ideal for anyone looking to:

• Complete an introductory course in statistics

• Prepare for more advanced statistical courses

• Gain the transferable analytical skills needed to interpret research from across the social sciences

• Learn the technical skills needed to present data visually

• Acquire a basic competence in the use of R and RStudio.

This edition also includes a gentle introduction to Bayesian methods integrated throughout.

The author has created a wide range of online resources, including: over 90 R scripts, 36 datasets, 37 screen casts, complete solutions for all exercises, and 130 multiple-choice questions to test your knowledge.

Chapter 1: Introduction and R Instructions

Basic Terminology

Data: Qualitative or Quantitative

Data: Cross-Sectional or Longitudinal

Descriptive Statistics

Probability

Statistics: Estimation and Inference

Chapter 2: Descriptive Statistics: Tabular and Graphical Methods

Methods of Summarizing and Displaying Qualitative Data

Methods of Summarizing and Displaying Quantitative Data

Cross Tabulations and Scatter Plots

Chapter 3: Descriptive Statistics: Numerical Methods

Measures of Central Tendency

Measures of Location

Exploratory Data Analysis: The Box Plot Display

Measures of Variability

The z-Score: A Measure of Relative Location

Measures of Association: The Bivariate Case

The Geometric Mean

Chapter 4: Introduction to Probability

Some Important Definitions

Counting Rules

Assigning Probabilities

Events and Probabilities

Probabilities of Unions and Intersections of Events

Conditional Probability

Bayes' Theorem and Events

Chapter 5: Discrete Probability Distributions

The Discrete Uniform Probability Distribution

The Expected Value and Standard Deviation of a Discrete Random Variable

The Binomial Probability Distribution

The Poisson Probability Distribution

The Hypergeometric Probability Distribution

The Hypergeometric Probability Distribution: The General Case

Bayes' Theorem and Discrete Random Variables

Chapter 6: Continuous Probability Distributions

Continuous Uniform Probability Distribution

Normal Probability Distribution

Exponential Probability Distribution

Optional Material: Derivation of the Cumulative Exponential Probability Func- tion

Bayes' Theorem and Continuous Random Variables

Chapter 7: Point Estimation and Sampling Distributions

Populations and Samples

The Simple Random Sample

The Sample Statistic: x, s, and p

The Sampling Distribution of x

The Sampling Distribution of p

Some Other Commonly Used Sampling Methods

Bayes' Theorem: Approximate Bayesian Computation

Chapter 8: Confidence Interval Estimation

Interval Estimate of µ When σ Is Known

Interval Estimate of µ When σ Is Unknown

Sample Size Determination in the Case of µ

Interval Estimate of p

Sample Size Determination in the Case of p

Bayes’ Theorem: Confidence Intervals or Credible Intervals

Chapter 9: Hypothesis Tests: Introduction, Basic Concepts, and an Example

Chapter 10: Hypothesis Tests about Means and Proportions: Applications

The Lower-Tail Hypothesis Test about μ: σ Is Known

The Two-Tail Hypothesis Test about μ: σ Is Known

The Upper-Tail Hypothesis Test about μ: σ Is Unknown

The Two-Tail Hypothesis Test about μ: σ is Unknown

Hypothesis Tests about p

Calculating the Probability of a Type II Error: β

Adjusting the Sample Size to Control the Size of β

Bayes’ Theorem and an Inferential Approach to p

Chapter 11: Comparisons of Means and Proportions

The Difference between μ1 and μ2: Independent Samples

The Difference between μ1 and μ2: Paired Samples

The Difference between p1 and p2: Independent Samples

Bayes’ Theorem and the Difference between p1 and p2

Chapter 12: Simple Linear Regression

Simple Linear Regression: The Model

The Estimated Regression Equation

Goodness of Fit: The Coefficient of Determination, r2

The Hypothesis Test about β1

Alternative Approaches to Testing Significance

So Far, We Have Tested Only b1. Will We Also Test b0?

Assumptions: What Are They?

Assumptions: How Are They Validated?

Optional Material: Derivation of the Expressions for the Least-Squares Estimates of β0 and β1

Bayes’ Theorem: Using Stan to Estimate the Relationship between Two Variables

Chapter 13: Multiple Regression

Simple Linear Regression: A Reprise

Multiple Regression: The Model

Multiple Regression: The Multiple Regression Equation

The Estimated Multiple Regression Equation

Multiple Regression: The 2 Independent Variable Case

Assumptions: What Are They? Can We Validate Them?

Tests of Significance: The Overall Regression Model

Tests of Signicance: The Independent Variables

There Must Be An Easier Way Than This, Right?

Using the Estimated Regression Equation for Prediction

Independent Variable Selection: The Best-Subsets Method

Logistic Regression: The Zero-One Dependent Variable

Bayes' Theorem: Stan and Multiple Regression Analysis