Beginning R: An Introduction to Statistical Programming

Title Page......Page 1
Copyright Page......Page 2
Contents at a Glance......Page 4
Table of Contents......Page 6
About the Author......Page 15
About the Technical Reviewer......Page 16
Acknowledgments......Page 17
Conventions......Page 18
Contacting the Author......Page 19
Getting and Using R......Page 20
A First R Session......Page 22
Moving Around in R......Page 25
Creating a Vector......Page 27
Performing Vector Arithmetic......Page 28
Adding Elements to a Vector......Page 29
Creating a Matrix......Page 31
Referring to Matrix Rows and Columns......Page 32
Matrix Manipulation......Page 33
Creating a Data Frame from Vectors......Page 37
Creating a Data Frame Using the R Data Editor......Page 39
Reading a Table into a Data Frame......Page 40
Conclusion......Page 42
What is Programming?......Page 43
Getting Ready to Program......Page 44
The Requirements for Learning to Program......Page 45
Looping......Page 46
Essentials of R Programming......Page 47
Comparison Operators......Page 48
Logical Operators......Page 49
Input and Output in R......Page 50
Understanding the R Environment......Page 52
For Loops......Page 53
The Repeat Loop......Page 55
Avoiding Explicit Loops: The Apply Function Family......Page 56
A First R Program......Page 58
Another Example—Finding Pythagorean Triples......Page 59
Using R to Solve Quadratic Equations......Page 60
The S3 and S4 Classes......Page 61
Conclusion......Page 64
Examining an R Function from the Base R Code......Page 65
Creating a Function......Page 66
Calculating a Confidence Interval for a Mean......Page 67
Avoiding Loops with Vectorized Operations......Page 70
Vectorizing If-Else Statements Using ifelse()......Page 72
Making More Powerful Functions......Page 73
Any, All, and Which......Page 75
Making Functions More Useful......Page 76
Confidence Intervals Revisited......Page 78
Conclusion......Page 81
The Mean......Page 82
The Mode......Page 84
Measuring Variability......Page 86
Range......Page 87
Median and Mean Absolute Deviation......Page 88
Covariance and Correlation......Page 89
Measuring Symmetry (or Lack Thereof)......Page 91
Conclusion......Page 93
Frequency Distributions and Tables......Page 94
Pie Charts......Page 96
Bar Charts......Page 100
Boxplots......Page 102
Histograms......Page 104
Line Graphs......Page 105
Scatterplots......Page 106
Saving and Using Graphics......Page 108
Conclusion......Page 109
Discrete Probability Distributions......Page 110
The Binomial Distribution: The Number of Successes as a Random Variable......Page 112
The Poisson Distribution......Page 115
Relating Discrete Probability to Normal Probability......Page 116
Conclusion......Page 118
Characteristics of the Normal Distribution......Page 119
Finding Normal Densities Using the dnorm Function......Page 120
Converting a Normal Distribution to the Standard Normal Distribution......Page 121
Finding a Right-tailed Probability......Page 122
Using rnorm to Generate Random Samples......Page 123
The Sampling Distribution of Means......Page 125
A One-sample z Test......Page 126
Conclusion......Page 127
Confidence Intervals for Means......Page 128
Confidence Intervals for the Mean Using the Normal Distribution......Page 129
Confidence Intervals for the Mean Using the t Distribution......Page 130
Confidence Intervals for Proportions......Page 132
Understanding the Chi-square Distribution......Page 133
Confidence Intervals for Variances and Standard Deviations......Page 134
Confidence Intervals for Differences between Means......Page 136
Confidence Intervals Using the stats Package......Page 137
Conclusion......Page 138
A Brief Introduction to Hypothesis Testing......Page 139
Understanding the t Distribution......Page 140
The One-sample t Test......Page 142
The Paired-samples t Test......Page 143
The Welch t Test......Page 146
Welch t Test for “Side-by-side” Data......Page 148
Doing the Welch t test with “Stacked” Data and Indicator Coding......Page 149
The t Test Assuming Equality of Variance......Page 150
Conclusion......Page 152
Understanding the F Distribution......Page 153
Using the F Distribution to Test Variances......Page 154
Compounding Alpha and Post Hoc Comparisons......Page 155
The Variance Partition in the One-Way ANOVA......Page 156
An Example of the One-Way ANOVA......Page 157
Tukey HSD Test......Page 159
Bonferroni-Corrected Post Hoc Comparisons......Page 160
Conclusion......Page 161
Two-Way ANOVA......Page 162
Sums of Squares in Two-Way ANOVA......Page 163
An Example of a Two-Way ANOVA......Page 164
Examining Interactions......Page 166
Effect Size in the Two-Way ANOVA......Page 168
The Variance Partition in Repeated-Measures ANOVA......Page 169
Example of a Repeated-Measures ANOVA......Page 170
Mixed-Factorial ANOVA......Page 173
Example of a Mixed-Factorial ANOVA......Page 174
Conclusion......Page 177
Covariance and Correlation......Page 178
Regression......Page 181
An Example: Predicting the Price of Gasoline......Page 187
Examining the Linear Relationship......Page 188
Fitting a Quadratic Model......Page 189
Determining Confidence and Prediction Intervals......Page 194
Conclusion......Page 196
The Multiple Regression Equation......Page 197
Multiple Regression Example: Predicting Job Satisfaction......Page 198
Using Matrix Algebra to Solve a Regression Equation......Page 204
The t Test as a Special Case of Correlation......Page 206
ANOVA as a Special Case of Multiple Regression......Page 208
Dealing with Collinearity......Page 210
Conclusion......Page 211
What Is Logistic Regression?......Page 212
Logistic Regression with One Dichotomous Predictor......Page 213
Logistic Regression with One Continuous Predictor......Page 216
Logistic Regression with Multiple Predictors......Page 218
Comparing Logistic and Multiple Regression......Page 225
Conclusion......Page 227
Chi-Square Tests of Goodness of Fit......Page 228
Goodness-of-Fit Tests with Equal Expected Frequencies......Page 229
Goodness-of-Fit Tests with Unequal Expected Frequencies......Page 230
Chi-Square Tests of Independence......Page 231
Relating the Standard Normal Distribution to Chi-Square......Page 233
Effect Size for Chi-Square Tests......Page 235
Demonstrating the Relationship of Phi to the Correlation Coefficient......Page 236
Conclusion......Page 239
The Mann-Whitney U Test......Page 240
The Mann-Whitney Test with Small Samples......Page 241
The Mann-Whitney Test with Larger Samples......Page 243
The Wilcoxon Signed-Ranks Test for Small Samples......Page 246
Nonparametric Alternatives to ANOVA......Page 248
The Kruskal-Wallis Test......Page 249
The Friedman Test for Repeated Measures or Randomized Blocks......Page 251
Spearman Rank Correlation......Page 253
The Kendall Tau Coefficient......Page 256
Conclusion......Page 257
Defining Statistical Simulation......Page 258
Random Numbers......Page 259
A Confidence Interval Simulation......Page 260
A t Test Simulation......Page 263
A Uniform Distribution Simulation......Page 264
A Binomial Distribution Simulation......Page 265
Conclusion......Page 267
The Pitfalls of Hypothesis Testing......Page 268
The Bootstrap......Page 269
Bootstrapping the Mean......Page 270
Bootstrapping the Median......Page 271
Jackknifing......Page 272
Permutation Tests......Page 274
Conclusion......Page 279
The Concept of a Package......Page 280
Some Windows Considerations......Page 281
Establishing the Skeleton of an R Package......Page 283
Editing the R Documentation......Page 287
Building and Checking the Package......Page 290
Installing the Package......Page 291
Making Sure the Package Works Correctly......Page 292
Adding a New Function......Page 296
Building the Package Again......Page 297
Conclusion......Page 299
The R Commander Interface......Page 300
Confidence Intervals in R Commander......Page 306
Using R Commander for Hypothesis Testing......Page 309
Using R Commander for Regression......Page 311
Conclusion......Page 313
Index......Page 314