Author Profile

George Ross Ihaka is a New Zealand statistician, an Associate Professor of Statistics at the University of Auckland. Ihaka completed his undergraduate education at the University of Auckland, and obtained his PhD from the University of California, Berkeley. His thesis was titled Ruaumoko, after the Māori god of earthquakes, volcanoes and seasons. Along with Robert Gentleman, he is one of the originators of the R programming language. In 2008, he received the Pickering Medal, awarded by the Royal Society of New Zealand, for his work on R. As of 2010, he was working on a new statistical programming language based on Lisp. Many inventors seek fame and fortune, or at least recognition. This isn't the case for New Zealand statistician and associate professor George Ross Ihaka. Despite being the co-creator of R, an open-source programming language used by millions and loved by the likes of Google and the Bank of America, he remains modest and bighearted. Always resisting the pressure to commercialize his brainchild.

About The Book

Computational skills are kept to a minimum in the book by including R script programs. Students are not required to master the writing of R script programs, but explanations of how the programs work and program output are included in each chapter. R is a statistical package with an extensive library of functions that offers flexibility in writing customized statistical routines. The R script commands are run in the R Studio software which is a graphical user interface for Windows. The R Studio software makes accessing R programs, viewing output from the exercises, and graph displays easier for the student. This book is intended as a guide to data analysis with the R system for statistical computing. R is an environment incorporating an implementation of the S programming language, which is powerful, flexible and has excellent graphical facilities. In the book we aim to give relatively brief and straightforward descriptions of how to conduct a range of statistical analyses using R. Each chapter deals with the analysis appropriate for one or several data sets. A brief account of the relevant statistical background is included in each chapter along with appropriate references, but our prime focus is on how to use R and how to interpret results. We hope the book will provide students and researchers in many disciplines with a self-contained means of using R to analyse their data. R is an open-source project developed by dozens of volunteers for more than ten years now and is available from the Internet under the General Public Licence. R has become the lingua franca of statistical computing. Increasingly, implementations of new statistical methodology first appear as R add-on packages. In some communities, such as in bioinformatics, R already is the primary workhorse for statistical analyses. Because the sources of the R system are open and available to everyone without restrictions and because of its powerful language and graphical capabilities, R has started to become the main computing engine for reproducible statistical research. For a reproducible piece of research, the original observations, all data preprocessing steps, the statistical analysis as well as the scientific report form a unity and all need to be available for inspection, reproduction and modification by the readers. Reproducibility is a natural requirement for textbooks such as the book and therefore this book is fully reproducible using an R version greater or equal to 2.4.0. All analyses and results, including figures and tables, can be reproduced by the reader without having to retype a single line of R code.

Table of Contents

Preface..............................................................................................................v
Chapter 1. Introduction to Statistics and R.......................................................... 1
y What is Statistics? Types and Importance...............................................2
y Installing and Using R and RStudio........................................................11
y The R Console and Script Editor............................................................14
y Packages and Libraries (install.packages, library)................................ 17
y Data Types and Structures in R............................................................. 20
y Setting and Getting the Working Directory......................................... 29
Chapter 2. Organizing and Summarizing Data................................................. 34
y Types of Data: Categorical vs Numerical...............................................35
y Frequency Tables and Relative Frequencies........................................ 39
y Measures of Central Tendency (Mean, Median, Mode).......................55
y Measures of Dispersion (Range, Variance, SD).................................... 62
y Five-number Summary and Boxplots................................................... 65
Chapter 3. Data Visualization in R.......................................................................75
y Bar Charts and Pie Charts...................................................................... 76
y Histograms and Density Plots...............................................................86
y Boxplots and Violin Plots.......................................................................91
y Scatterplots and Line Graphs................................................................ 94
y Customizing Plots with ggplot2........................................................... 101
y Multi-panel Plots with par() and facet_wrap()...................................106
Chapter 4. Probability Basics............................................................................109
y Basic Probability Rules and Set Notation............................................ 110
y Conditional Probability and Bayes’ Theorem.......................................117
y Independent and Dependent Events.................................................. 129
y Permutations and Combinations......................................................... 135
Chapter 5. Probability Distributions................................................................. 155
y Discrete vs Continuous Distributions..................................................156
y Binomial Distribution in R (dbinom, rbinom)......................................168
Contents
y Normal Distribution (dnorm, rnorm, pnorm).......................................171
y Poisson and Exponential Distributions................................................ 175
y Visualizing Distributions in R................................................................185
Chapter 6. Sampling and Sampling Distributions...........................................189
y Populations vs Samples........................................................................190
y Random Sampling Methods................................................................199
y Sampling Distributions of the Mean................................................... 203
y Law of Large Numbers.........................................................................207
Chapter 7. Estimation and Confidence Intervals............................................. 213
y Point Estimation and Interval Estimation............................................ 214
y Confidence Intervals for Means...........................................................222
y Confidence Intervals for Proportions..................................................228
y Margin of Error and Sample Size........................................................ 236
Chapter 8. Hypothesis Testing Fundamentals.................................................245
y Null and Alternative Hypotheses........................................................ 246
y p-values and Significance Levels..........................................................257
y One-tailed vs Two-tailed Tests.............................................................275
Chapter 9. Comparing Two Groups................................................................. 280
y Independent Samples t-test................................................................ 281
y Paired Samples t-test.......................................................................... 285
y Mann-Whitney U Test (Non-parametric)............................................ 293
y Interpreting Test Outputs in R............................................................ 296
Bibliography............................................................................................... 299
Index........................................................................................................... 306