Introduction to Statistical Thinking (With R, Without Calculus)

Preface......Page 5
I Introduction to Statistics......Page 11
Why Learn Statistics?......Page 13
Statistics......Page 14
Probability......Page 15
Key Terms......Page 16
Some Basic R Commands......Page 17
Solved Exercises......Page 20
Summary......Page 23
Variation in Data......Page 25
Frequency......Page 26
Critical Evaluation......Page 28
Saving the File and Setting the Working Directory......Page 29
Reading a CSV File into R......Page 33
Data Types......Page 34
Solved Exercises......Page 35
Summary......Page 37
Displaying Data......Page 39
Histograms......Page 40
Box Plots......Page 42
Measures of the Center of Data......Page 45
Skewness, the Mean and the Median......Page 46
Measures of the Spread of Data......Page 48
Solved Exercises......Page 50
Summary......Page 55
Different Forms of Variability......Page 57
A Population......Page 59
Random Variables......Page 63
Sample Space and Distribution......Page 64
Expectation and Standard Deviation......Page 66
Probability and Statistics......Page 69
Solved Exercises......Page 70
Summary......Page 72
Discrete Random Variables......Page 75
The Binomial Random Variable......Page 76
The Poisson Random Variable......Page 81
Continuous Random Variable......Page 84
The Uniform Random Variable......Page 85
The Exponential Random Variable......Page 89
Solved Exercises......Page 92
Summary......Page 94
The Normal Random Variable......Page 97
The Normal Distribution......Page 98
The Standard Normal Distribution......Page 100
Computing Percentiles......Page 102
Outliers and the Normal Distribution......Page 104
Approximate Binomial Probabilities and Percentiles......Page 106
Continuity Corrections......Page 107
Solved Exercises......Page 110
Summary......Page 112
The Sampling Distribution......Page 115
A Random Sample......Page 116
Sampling From a Population......Page 117
Theoretical Models......Page 122
The Law of Large Numbers......Page 125
The Central Limit Theorem (CLT)......Page 126
Applying the Central Limit Theorem......Page 129
Solved Exercises......Page 130
Summary......Page 133
An Overview......Page 135
Example 1......Page 137
Example 2......Page 139
Example 3......Page 140
Example 4......Page 141
Example 5......Page 144
II Statistical Inference......Page 147
Key Terms......Page 149
The Cars Data Set......Page 151
Statistics......Page 154
The Sampling Distribution......Page 155
Theoretical Distributions of Observations......Page 156
Sampling Distribution of Statistics......Page 157
The Normal Approximation......Page 158
Simulations......Page 159
Solved Exercises......Page 162
Summary......Page 167
Estimating Parameters......Page 169
Estimation of the Expectation......Page 170
The Accuracy of the Sample Average......Page 171
Comparing Estimators......Page 174
Variance and Standard Deviation......Page 176
Estimation of Other Parameters......Page 181
Solved Exercises......Page 183
Summary......Page 188
Intervals for Mean and Proportion......Page 191
Examples of Confidence Intervals......Page 192
Confidence Intervals for the Mean......Page 193
Confidence Intervals for a Proportion......Page 197
Intervals for Normal Measurements......Page 198
Confidence Intervals for a Normal Mean......Page 200
Confidence Intervals for a Normal Variance......Page 202
Choosing the Sample Size......Page 205
Solved Exercises......Page 206
Summary......Page 211
The Theory of Hypothesis Testing......Page 213
An Example of Hypothesis Testing......Page 214
The Structure of a Statistical Test of Hypotheses......Page 215
Error Types and Error Probabilities......Page 218
p-Values......Page 220
Testing Hypothesis on Expectation......Page 221
Testing Hypothesis on Proportion......Page 228
Solved Exercises......Page 231
Summary......Page 234
Comparing Two Distributions......Page 237
An Example of a Comparison of Means......Page 239
Confidence Interval for the Difference......Page 242
The t-Test for Two Means......Page 245
Comparing Sample Variances......Page 247
Solved Exercises......Page 250
Summary......Page 255
Points and Lines......Page 257
The Scatter Plot......Page 258
Linear Equation......Page 261
Fitting the Regression Line......Page 263
Inference......Page 266
R-squared and the Variance of Residuals......Page 270
Solved Exercises......Page 276
Summary......Page 288
Student Learning Objectives......Page 291
Comparing Sample Proportions......Page 292
Logistic Regression......Page 295
Solved Exercises......Page 299
A Review......Page 309
Physicians\' Reactions to the Size of a Patient......Page 310
Physical Strength and Job Performance......Page 316
Concluding Remarks......Page 323
Discussion in the Forum......Page 324