Applied Statistics with Resampling Methods and R
Applied Statistics with Resampling Methods and R
About the Book
Applied Statistics with Resampling Methods and R is intended to support an introductory undergraduate statistics or data science course, particularly those that emphasize data analysis and statistical computing. It covers statistics for doing univariate and bivariate descriptive analysis, including robust descriptive statistics. The book uses resampling methods (randomization and bootstrapping) for statistical inference, including methods for hypothesis testing and parameter estimation in several type of study designs. Data analytic examples are used to teach statistical concepts throughout, and students are introduced to the R packages and functions needed for basic data analysis. Each chapter includes data analytic problems for practice or assessment. R script, data, and metadata files are available by chapter at github.com/bblaine6.
About the Author
Table of Contents
Contents
1 Preface Using this book 1
2 Descriptive Statistics with a Numeric Variable 4
2.1 Goals of descriptive analysis 4
2.2 Location statistics 6
2.3 Variability statistics 8
2.4 Shape statistics 10
2.5 Influential values 17
2.6 Writing up a descriptive analysis 19
2.7 Problems 21
3 Bivariate Descriptive Statistics I: Categorical Predictor and Numeric Outcome 22
3.1 Goals of bivariate analysis 22
3.2 Study design 22
3.3 Summarizing the difference between groups with location and variability statistics 24
3.4 Creating a 2-level categorical variable 33
3.5 Interpreting group differences 34
3.6 Writing up a descriptive analysis with categorical predictor and numeric outcome 35
3.7 Problems 37
4 Bivariate Descriptive Statistics II: Categorical Predictor and Categorical Outcome 39
4.1 Proportions and probabilities 39
4.2 Contingency tables 40
4.3 Risk difference, risk ratio, and odds ratio 42
4.4 Grouped barplots 47
4.5 Interpreting group differences 48
4.6 Writing up a descriptive analysis with categorical predictor and categorical outcome 49
4.7 Problems 51
5 Bivariate Descriptive Statistics III: Numeric Predictor and Numeric Outcome 52
5.1 Correlational statistics 52
5.2 Logic of linear regression 52
5.3 Least squares regression and the regression coefficient 54
5.4 Least squares regression example 59
5.5. Correlation coefficients 62
5.6 Influential observations 65
5.7 Scatterplots 67
5.8 Correlation and causation in correlational data 68
5.9 Writing up a descriptive analysis with numeric predictor and numeric outcome 69
5.10 Problems 71
6 Bivariate Descriptive Statistics IV: Numeric Predictor and Categorical Outcome 73
6.1 Introduction to logistic regression 73
6.2 Logic of logistic regression: the logit function 74
6.3 Logistic regression analysis 78
6.4 Logistic regression example 81
6.5 Influential observations 85
6.6 Plots in logistic regression 86
6.7 Interpreting the results of logistic regression 89
6.8 Writing up a descriptive analysis with numeric predictor and categorical outcome 91
6.9 Problems 92
7 Randomization Methods for Hypothesis Testing 94
7.1 Introduction to statistical inference 94
7.2 Dimensions of statistical inference 95
7.3 Randomization test 96
7.4 Interpreting the results of a randomization test 99
7.5 Subtypes of the randomization test 101
7.6 Randomization tests in R 102
7.7 Writing up the results of a randomization test 109
7.8 Problems 111
8 Bootstrapping Methods for Parameter Estimation 112
8.1 Introduction to estimation 112
8.2 The logic of bootstrapping 112
8.3 Parameter estimation 114
8.4 Bootstrapped confidence intervals 119
8.5 Example of bootstrapped interval estimation 123
8.7 Factors that affect a confidence interval 125
8.8 Writing up a parameter estimation study 129
8.9 Problems 131
9 Using Resampling Methods for Statistical Inference 132
9.1 Introduction 132
9.2 Statistical inference framework 132
9.3 Statistical models 134
9.4 Resampling for inference in an ANOVA model 137
9.5 Resampling for inference in a proportions model 142
9.6 Resampling for inference in a regression model 147
9.7 Resampling for inference in a logistic model 151
9.8 Conclusion 154
9.9 Problems 156
10 About the Author 132
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