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Statistical Analysis with R for Dummies


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Table of Contents

Introduction 1 About This Book 1 Similarity with This Other For Dummies Book 2 What You Can Safely Skip 2 Foolish Assumptions 2 How This Book Is Organized 3 Part 1: Getting Started with Statistical Analysis with R 3 Part 2: Describing Data 3 Part 3: Drawing Conclusions from Data 3 Part 4: Working with Probability 3 Part 5: The Part of Tens 4 Online Appendix A: More on Probability 4 Online Appendix B: Non-Parametric Statistics 4 Online Appendix C: Ten Topics That Just Didn't Fit in Any Other Chapter 4 Icons Used in This Book 4 Where to Go from Here 5 Part 1: Getting Started With Statistical Analysis with R 7 Chapter 1: Data, Statistics, and Decisions 9 The Statistical (and Related) Notions You Just Have to Know 10 Samples and populations 10 Variables: Dependent and independent 11 Types of data 12 A little probability 13 Inferential Statistics: Testing Hypotheses 14 Null and alternative hypotheses 14 Two types of error 15 Chapter 2: R: What It Does and How It Does It 17 Downloading R and RStudio 18 A Session with R 21 The working directory 21 So let's get started, already 22 Missing data 26 R Functions 26 User-Defined Functions 28 Comments 29 R Structures 29 Vectors 30 Numerical vectors 30 Matrices 31 Factors 33 Lists 34 Lists and statistics 35 Data frames 36 Packages 39 More Packages 42 R Formulas 43 Reading and Writing 44 Spreadsheets 44 CSV files 46 Text files 47 Part 2: Describing Data 49 Chapter 3: Getting Graphic 51 Finding Patterns 51 Graphing a distribution 52 Bar-hopping 53 Slicing the pie 54 The plot of scatter 55 Of boxes and whiskers 56 Base R Graphics 57 Histograms 57 Adding graph features 59 Bar plots 60 Pie graphs 62 Dot charts 62 Bar plots revisited 64 Scatter plots 67 Box plots 71 Graduating to ggplot2 71 Histograms 72 Bar plots 74 Dot charts 75 Bar plots re-revisited 78 Scatter plots 82 Box plots 86 Wrapping Up 89 Chapter 4: Finding Your Center 91 Means: The Lure of Averages 91 The Average in R: mean() 93 What's your condition? 93 Eliminate $-signs forth with() 94 Exploring the data 95 Outliers: The flaw of averages 96 Other means to an end 97 Medians: Caught in the Middle 99 The Median in R: median() 100 Statistics a la Mode 101 The Mode in R 101 Chapter 5: Deviating from the Average 103 Measuring Variation 104 Averaging squared deviations: Variance and how to calculate it 104 Sample variance 107 Variance in R 107 Back to the Roots: Standard Deviation 108 Population standard deviation 108 Sample standard deviation 109 Standard Deviation in R 109 Conditions, Conditions, Conditions 110 Chapter 6: Meeting Standards and Standings 111 Catching Some Z's 112 Characteristics of z-scores 112 Bonds versus the Bambino 113 Exam scores 114 Standard Scores in R 114 Where Do You Stand? 117 Ranking in R 117 Tied scores 117 Nth smallest, Nth largest 118 Percentiles 118 Percent ranks 120 Summarizing 121 Chapter 7: Summarizing It All 123 How Many? 123 The High and the Low 125 Living in the Moments 125 A teachable moment 126 Back to descriptives 126 Skewness 127 Kurtosis 130 Tuning in the Frequency 131 Nominal variables: table() et al 131 Numerical variables: hist() 132 Numerical variables: stem() 138 Summarizing a Data Frame 139 Chapter 8: What's Normal? 143 Hitting the Curve 143 Digging deeper 144 Parameters of a normal distribution 145 Working with Normal Distributions 147 Distributions in R 147 Normal density function 147 Cumulative density function 152 Quantiles of normal distributions 155 Random sampling 156 A Distinguished Member of the Family 158 Part 3: Drawing Conclusions from Data 161 Chapter 9: The Confidence Game: Estimation 163 Understanding Sampling Distributions 164 An EXTREMELY Important Idea: The Central Limit Theorem 165 (Approximately) Simulating the central limit theorem 167 Predictions of the central limit theorem 171 Confidence: It Has Its Limits! 173 Finding confidence limits for a mean 173 Fit to a t 175 Chapter 10: One-Sample Hypothesis Testing 179 Hypotheses, Tests, and Errors 179 Hypothesis Tests and Sampling Distributions 181 Catching Some Z's Again 183 Z Testing in R 185 t for One 187 t Testing in R 188 Working with t-Distributions 189 Visualizing t-Distributions 190 Plotting t in base R graphics 191 Plotting t in ggplot2 192 One more thing about ggplot2 197 Testing a Variance 198 Testing in R 199 Working with Chi-Square Distributions 201 Visualizing Chi-Square Distributions 201 Plotting chi-square in base R graphics 202 Plotting chi-square in ggplot2 203 Chapter 11: Two-Sample Hypothesis Testing 205 Hypotheses Built for Two 205 Sampling Distributions Revisited 206 Applying the central limit theorem 207 Z's once more 208 Z-testing for two samples in R 210 t for Two 212 Like Peas in a Pod: Equal Variances 212 t-Testing in R 214 Working with two vectors 214 Working with a data frame and a formula 215 Visualizing the results 216 Like p's and q's: Unequal variances 219 A Matched Set: Hypothesis Testing for Paired Samples 220 Paired Sample t-testing in R 222 Testing Two Variances 222 F-testing in R 224 F in conjunction with t 225 Working with F-Distributions 226 Visualizing F-Distributions 226 Chapter 12: Testing More than Two Samples 231 Testing More Than Two 231 A thorny problem 232 A solution 233 Meaningful relationships 237 ANOVA in R 237 Visualizing the results 239 After the ANOVA 239 Contrasts in R 242 Unplanned comparisons 243 Another Kind of Hypothesis, Another Kind of Test 244 Working with repeated measures ANOVA 245 Repeated measures ANOVA in R 247 Visualizing the results 249 Getting Trendy 250 Trend Analysis in R 254 Chapter 13: More Complicated Testing 255 Cracking the Combinations 255 Interactions 257 The analysis 257 Two-Way ANOVA in R 259 Visualizing the two-way results 261 Two Kinds of Variables at Once 263 Mixed ANOVA in R 266 Visualizing the Mixed ANOVA results 268 After the Analysis 269 Multivariate Analysis of Variance 270 MANOVA in R 271 Visualizing the MANOVA results 273 After the analysis 275 Chapter 14: Regression: Linear, Multiple, and the General Linear Model 277 The Plot of Scatter 277 Graphing Lines 279 Regression: What a Line! 281 Using regression for forecasting 283 Variation around the regression line 283 Testing hypotheses about regression 285 Linear Regression in R 290 Features of the linear model 292 Making predictions 292 Visualizing the scatter plot and regression line 293 Plotting the residuals 294 Juggling Many Relationships at Once: Multiple Regression 295 Multiple regression in R 297 Making predictions 298 Visualizing the 3D scatter plot and regression plane 298 ANOVA: Another Look 301 Analysis of Covariance: The Final Component of the GLM 305 But wait - there's more 311 Chapter 15: Correlation: The Rise and Fall of Relationships 313 Scatter plots Again 313 Understanding Correlation 314 Correlation and Regression 316 Testing Hypotheses About Correlation 319 Is a correlation coefficient greater than zero? 319 Do two correlation coefficients differ? 320 Correlation in R 322 Calculating a correlation coefficient 322 Testing a correlation coefficient 322 Testing the difference between two correlation coefficients 323 Calculating a correlation matrix 324 Visualizing correlation matrices 324 Multiple Correlation 326 Multiple correlation in R 327 Adjusting R-squared 328 Partial Correlation 329 Partial Correlation in R 330 Semipartial Correlation 331 Semipartial Correlation in R 332 Chapter 16: Curvilinear Regression: When Relationships Get Complicated 335 What Is a Logarithm? 336 What Is e? 338 Power Regression 341 Exponential Regression 346 Logarithmic Regression 350 Polynomial Regression: A Higher Power 354 Which Model Should You Use? 358 Part 4: Working with Probability 359 Chapter 17: Introducing Probability 361 What Is Probability? 361 Experiments, trials, events, and sample spaces 362 Sample spaces and probability 362 Compound Events 363 Union and intersection 363 Intersection again 364 Conditional Probability 365 Working with the probabilities 366 The foundation of hypothesis testing 366 Large Sample Spaces 366 Permutations 367 Combinations 368 R Functions for Counting Rules 369 Random Variables: Discrete and Continuous 371 Probability Distributions and Density Functions 371 The Binomial Distribution 374 The Binomial and Negative Binomial in R 375 Binomial distribution 375 Negative binomial distribution 377 Hypothesis Testing with the Binomial Distribution 378 More on Hypothesis Testing: R versus Tradition 380 Chapter 18: Introducing Modeling 383 Modeling a Distribution 383 Plunging into the Poisson distribution 384 Modeling with the Poisson distribution 385 Testing the model's fit 388 A word about chisq.test() 391 Playing ball with a model 392 A Simulating Discussion 396 Taking a chance: The Monte Carlo method 396 Loading the dice 396 Simulating the central limit theorem 401 Part 5: The Part of Tens 405 Chapter 19: Ten Tips for Excel Emigres 407 Defining a Vector in R Is Like Naming a Range in Excel 407 Operating on Vectors Is Like Operating on Named Ranges 408 Sometimes Statistical Functions Work the Same Way 412 And Sometimes They Don't 412 Contrast: Excel and R Work with Different Data Formats 413 Distribution Functions Are (Somewhat) Similar 414 A Data Frame Is (Something) Like a Multicolumn Named Range 416 The sapply() Function Is Like Dragging 417 Using edit() Is (Almost) Like Editing a Spreadsheet 418 Use the Clipboard to Import a Table from Excel into R 419 Chapter 20: Ten Valuable Online R Resources 421 Websites for R Users 421 R-bloggers 421 Microsoft R Application Network 422 Quick-R 422 RStudio Online Learning 422 Stack Overflow 422 Online Books and Documentation 423 R manuals 423 R documentation 423 RDocumentation 423 YOU CANanalytics 423 The R Journal 424 Index 425

About the Author

Joseph Schmuller, PhD, has taught undergraduate and graduate statistics, and has 25 years of IT experience. The author of four editions of Statistical Analysis with Excel For Dummies and three editions of Teach Yourself UML in 24 Hours (SAMS), he has created online coursework for and is a former Editor in Chief of PC AI magazine. He is a Research Scholar at the University of North Florida.

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