Preface v
1 Introduction to Data 1
1.1 Statistics and artificial intelligence 1
1.2 Data and variables 3
1.3 Populations, samples, and study design 5
2 Summarizing Data 9
2.1 Examining numerical data 9
2.2 Considering categorical data 19
3 Probability 25
3.1 Defining probability 25
3.2 Conditional probability 30
4 Random Variables 37
4.1 Defining random variables 37
4.2 Expectation and variance 43
4.3 Joint distributions 47
5 Distributions 55
5.1 Uniform distribution 55
5.2 Normal distribution 57
5.3 Binomial distribution 62
6 Foundations for Inference 69
6.1 Point estimates and sampling variability 69
6.2 Confidence intervals for a proportion 73
7 Sampling Distribution and Point Estimation 77
7.1 Sampling distribution 77
7.2 Point estimation 86
8 Inference for Means 91
8.1 Confidence interval for a population mean 92
8.2 Hypothesis test for a population mean 99
8.3 Power calculations for a population mean 107
8.4 Paired data 109
8.5 Difference of two means: unequal variances 113
8.6 Difference of two means: equal variances 117
8.7 Power calculations for a difference of means 120
8.8 Comparing many means: ANOVA 123
8.9 Summary of tests for means 128
9 Linear Regression 131
9.1 Line fitting, residuals, and correlation 132
9.2 Fitting a line by least squares 140
9.3 Inference for linear regression 146
9.4 Multiple linear regression 152
10 Logistic Regression 159
10.1 Modeling a binary outcome 160
10.2 Fitting and interpreting logistic regression 163
10.3 Making and evaluating decisions 166
10.4 From regression to machine learning 171
A R Basics 175
B Statistical Tables 179
C Solutions to Exercises 187
References 215
Index 217
