Reasoning with data : an introduction to traditional and Bayesian statistics using R / Jeffrey M. Stanton.

Format:

Book

Author/Creator:

Stanton, Jeffrey M., 1961- author.

Language:

English

Subjects (All):

Bayesian statistical decision theory--Problems, exercises, etc.

Bayesian statistical decision theory.

Bayesian statistical decision theory--Data processing.

Mathematical statistics--Problems, exercises, etc.

Mathematical statistics.

Mathematical statistics--Data processing.

R (Computer program language).

Genre:

Problems and exercises.

Physical Description:

x, 325 pages ; 26 cm

Place of Publication:

New York : The Guilford Press, [2017]

Summary:

Engaging and Accessible, This Book Teaches Readers How to Use Inferential Statistical Thinking To Check their assumptions, assess evidence about their beliefs, and avoid overinterpreting results that may look more promising than they really are. It provides step-by-step guidance for using both classical (frequentist) and Bayesian approaches to inference. Statistical techniques covered side by side from both frequentist and Bayesian approaches include hypothesis testing, replication, analysis of variance, calculation of effect sizes, regression, time series analysis, and more. Students also get a complete introduction to the open-source R programming language and its key packages. Throughout the text, simple commands in R demonstrate essential data analysis skills using real-data examples. The companion website (www.guilford.com/stanton2-materials) provides annotated R code for the book's examples, in-class exercises, supplemental reading lists, and links to online videos, interactive materials, and other resources. Pedagogical Features: Playful, conversational style and gradual approach; suitable for students without strong math backgrounds. End-of-chapter exercises based on real data supplied in the free R package. Technical explanation and equation/output boxes. Appendices on how to install R and work with the sample datasets. Book jacket.

Contents:

1 Statistical Vocabulary 7

Descriptive Statistics 7

Measures of Central Tendency 8

Measures of Dispersion 10

Box. Mean and Standard Deviation Formulas 14

Distributions and Their Shapes 15

Conclusion 19

Exercises 20

2 Reasoning with Probability 21

Outcome Tables 21

Contingency Tables 27

Box. Make Your Own Tables with R 30

Conclusion 34

Exercises 35

3 Probabilities in the Long Run 37

Sampling 38

Repetitious Sampling with R 40

Using Sampling Distributions and Quantiles to Think about Probabilities 45

Conclusion 49

Exercises 50

4 Introducing the Logic of Inference Using Confidence Intervals 52

Exploring the Variability of Sample Means with Repetitious Sampling 57

Our First Inferential Test: The Confidence Interval 60

Box. Formulas for the Confidence Interval 61

Conclusion 64

Exercises 65

5 Bayesian and Traditional Hypothesis Testing 67

Box. Notation, Formula, and Notes on Bayes' Theorem 69

Box. Markov-Chain Monte Carlo Overview 71

Box. Detailed Output from BESTmcmc() 74

The Null Hypothesis Significance Test 77

The Calculation of t 80

Replication and the NHST 83

Conclusion 84

Exercises 85

6 Comparing Groups and Analyzing Experiments 88

Box. Formulas for ANOVA 93

Frequentist Approach to ANOVA 95

Box. More Information about Degrees of Freedom 99

The Bayesian Approach to ANOVA 102

Box. Giving Some Thought to Priors 103

Box. Interpreting Bayes Factors 110

Finding an Effect 111

Conclusion 115

Exercises 117

7 Associations between Variables 119

Box. Formula for Pearson's Correlation 126

Inferential Reasoning about Correlation 127

Box. Reading a Correlation Matrix 129

Null Hypothesis Testing on the Correlation 132

Bayesian Tests on the Correlation Coefficient 135

Categorical Associations 138

Exploring the Cbi-Square Distribution with a Simulation 141

The Chi-Square Test with Real Data 146

The Bayesian Approach to the Chi-Square Test 147

Conclusion 154

Exercises 155

8 Linear Multiple Regression 157

Box. Making Sense of Adjusted R-Squared 169

The Bayesian Approach to Linear Regression 172

A Linear Regression Model with Real Data 176

Conclusion 179

Exercises 181

9 Interactions in ANOVA and Regression 183

Interactions in ANOVA 186

Box. Degrees of Freedom for interactions 187

Box. A Word about Standard Error 193

Interactions in Multiple Regression 195

Box. Diagnosing Residuals and Trying Alternative Models 200

Bayesian Analysis of Regression Interactions 204

Conclusion 208

Exercises 209

10 Logistic Regression 211

A Logistic Regression Model with Real Data 221

Box. Multinomial Logistic Regression 222

Bayesian Estimation of Logistic Regression 228

Conclusion 232

Exercises 234

11 Analyzing Change over Time 235

Repeated-Measures Analysis 237

Box. Using ezANOVA 244

Time-Series Analysis 246

Exploring a Time Series with Real Data 259

Finding Change Points in Time Series 263

Probabilities in Change-Point Analysis 266

Box. Quick View of ARIMA 268

Conclusion 270

Exercises 272

12 Dealing with Too Many Variables 274

Box. Mean Composites versus Factor Scores 281

Internal Consistency Reliability 282

Rotation 285

Conclusion 288

Exercises 289

13 All Together Now 291

The Big Picture 294.

Notes:

Includes bibliographical references and index.

ISBN:

9781462530267

1462530265

9781462530274

1462530273

OCLC:

960845674