Using R for Introductory Statistics

413 Pages·2004·3.205 MB·English

by  John Verzani

Using R for Introductory Statistics

Using R for Introductory Statistics
John Verzani

CHAPMAN & HALL/CRC
A CRC Press Company
Boca Raton London New York Washington, D.C.
This edition published in the Taylor & Francis e-Library, 2005.
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Library of Congress Cataloging-in-Publication Data Verzani, John. Using R for introductiory
statistics/John Verzani. p. cm. Includes index. ISBN 1-58488-4509 (alk. paper) 1. Statistics—
Data processing. 2. R (Computer program language) I. Title QA276.4.V47 2004 519.5—dc22
2004058244
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Contents

1 Data 1
2 Univariate data 31
3 Bivariate data 67
4 Multivariate Data 102
5 Describing populations 138
6 Simulation 161
7 Confidence intervals 178
8 Significance tests 207
9 Goodness of fit 239
10 Linear regression 264
11 Analysis of variance 298
12 Two extensions of the linear model 327

A Getting, installing, and running R 343
B Graphical user interfaces and R 348
C Teaching with R 354
D More on graphics with R 356
E Programming in R 369
Index 392

Preface
What is R?
R is a computer language for statistical computing similar to the S language developed at
Bell Laboratories. The R software was initially written by Ross Ihaka and Robert
Gentleman in the mid 1990s. Since 1997, the R project has been organized by the R
Development Core Team. R is open-source software and is part of the GNU project. R is
being developed for the Unix, Macintosh, and Windows families of operating systems.
The R home page (http://www.r-project.org/) contains more information about R and
instructions for downloading a copy.
R is excellent software to use while first learning statistics. It provides a coherent,
flexible system for data analysis that can be extended as needed. The open-source nature
of R ensures its availability. R’s similarity to S allows you to migrate to the commercially
supported S-Plus software if desired. Finally, despite its reputation, R is as suitable for
students learning statistics as it is for researchers using statistics.
The purpose of this book
This book started as a set of notes, titled “simpleR,” that were written to fill a gap in
documentation for using R in an introductory statistics class. The College of Staten Island
had been paying a per-seat fee to use a commercial statistics program. The cost of the
program precluded widespread installation and curtailed accessibility. It was determined
that the students would be better served if they could learn statistics with a software
package that taught them good computer skills at the outset, could be installed all over
campus and at home with relative ease, and was free to use. However, no suitable
materials were available to accompany the class text. Hence, the basis for “simpleR”—a
set of notes to accompany an in-class text.
Now, as R gains wider acceptance, for pedagogic, style, and economic rea-sons, there
is an increase, but no abundance, in available documentation. The adoption of R as the
statistical software of choice when learning statistics depends on introductory materials.
This book aims to serve the needs of students in introductory applied-statistics classes
that are based on precalculus skills. An emphasis is put on finding simple-looking
solutions, rather than clever ones. Certainly, this material could be covered more quickly
(and is in other books such as those by Dalgaard, Fox, and Venables and Ripley). The
goal here is to make it as accessible to student-learners as possible.
This book aims to serve a hybrid purpose: to cover both statistical topics and the R
software. Though the material stands alone, this book is also intended to be useful as an
accompaniment to a standard introductory statistics book.
Description of this book
The pacing and content of this book are a bit different from those in most introductory
texts. More time is spent with exploratory data analysis (EDA) than is typical, a chapter
on simulation is included, and a unified approach to linear models is given. If this book is
being used in a semester-long sequence, keep in mind that the early material is
conceptually easier but requires that the student learn more on the computer. The pacing
is not as might be expected, as time must be spent learning the software and its
idiosyncrasies.
Chapters 1 through 4 take a rather leisurely approach to the material, developing the
tools of data manipulation and exploration. The material is broken up so that users who
wish only to analyze univariate data can safely avoid the details of data frames, lists, and
model formulas covered in Chapter 4. Those wishing to cover all the topics in the book
can work straight through these first four chapters.
Chapter 5 covers populations, random samples, sampling distributions, and the central
limit theorem. There is no attempt to cover the background probability concepts
thoroughly. We go over only what is needed in the sequel to make statistical inference.
Chapter 6 introduces simulation and the basics of defining functions. Since R is a
programming language, simulations are a strong selling point for R’s use in the
classroom.
Traditional topics in statistical inference are covered in chapters 7–11. Chapters 7, 8,
and 9 cover confidence intervals, significance tests, and goodness of fit. Chapters 10 and
11 cover linear models. Although this material is broken up into chapters on linear
regression and analysis of variance, for the most part we use a common approach to both.
Chapter 12 covers a few extensions to the linear model to illustrate how R is used in a
consistent manner with many different statistical models. The necessary background to
appreciate the models is left for the reader to find.
The appendices cover some background material and have information on writing
functions and producing graphics that goes beyond the scope of the rest of the text.
Typographic conventions
The book uses a few quirky typographic conventions. Variables and commands are
typeset with a data typeface; functions as a. function() (with accompanying parentheses);
and arguments to functions as col= (with a trailing equal sign). Help-page references have
a leading question mark: ?par. Data sets are typeset like faithful. Those that require a
package to be loaded prior to usage also have the package name, such as Animals
(MASS). Large blocks of commands are set off with a vertical bar:
> hist(rnorm(100)) # draw histogram
Often the commands include a comment, as does the one above. The output is formatted
to have 4 digits and 65 characters per column, and the type size is smaller, in order to get
more information in a single line. This may cause minor differences if the examples are
tried with different settings.
Web accompaniments
The home page for this book is
http://www.math.csi.cuny.edu/UsingR
On this page you will find solutions to selected homework problems (a full solutions
manual for instructors is available from the publisher), a list of errata, and an
accompanying package containing data sets and a few functions used in the text. The
UsingR package contains data sets collected from various places. Consult the help page
of a data set for proper attribution. The package needs to be installed on your computer
prior to usage. If your computer has an internet connection, the command
> install.packages("UsingR")
will fetch the package from CRAN, R’s warehouse of add-on packages, and install it. The
command library (UsingR) will load the package for use.
If for some reason this fails, the package can be retrieved from this book’s home page
with the commands
> where="http://www.math.csi.cuny.edu/UsingR"
> install.packages("UsingR",contriburl=where)
Finally, if that fails, the package can be downloaded from the home page and installed
manually as described in Chapter 1.
Using R
The R software is obtained from the Comprehensive R Archive Network (CRAN), which
may be reached from the main R web site http://www.r-project/. org. Some basic details
for installation appear in Appendix A and more detail is on the CRAN website. This book
was written to reflect the changes introduced by version 2.0.0 of R. R has approximately
two new major releases per year (the second number in the version number). Despite the
addition of numerous improvements with each new version, the maintainers of R do a
very careful job with the upgrades to R. Minor bug fixes appear in maintenance versions
(the third number). It is recommended that you upgrade your installation to keep pace
with these changes to R, although these new releases may affect some of the details given
in this text.
Acknowledgments
The author has many people to thank for this project. First, the numerous contributors to
the R software and especially the core members for their seemingly tireless efforts in
producing this excellent software. Next, the editorial staff at Chapman Hall/CRC was