Statistics Using R with Biological Examples

Statistics Using R

with Biological Examples

Kim Seefeld, MS, M.Ed.*

Ernst Linder, Ph.D.

University of New Hampshire, Durham, NH

Department of Mathematics & Statistics

*Also affiliated with the Dept. of Nephrology and the

Biostatistics Research Center, Tufts-NEMC, Boston,MA.

Copyright May 2007, K Seefeld

Permission granted to reproduce for nonprofit, educational use.

1

Preface

This book is a manifestation of my desire to teach researchers in biology a bit

more about statistics than an ordinary introductory course covers and to

introduce the utilization of R as a tool for analyzing their data. My goal is to

reach those with little or no training in higher level statistics so that they can do

more of their own data analysis, communicate more with statisticians, and

appreciate the great potential statistics has to offer as a tool to answer biological

questions. This is necessary in light of the increasing use of higher level

statistics in biomedical research. I hope it accomplishes this mission and

encourage its free distribution and use as a course text or supplement.

I thank all the teachers, professors, and research colleagues who guided my own

learning �C especially those in the statistics and biological research departments

at the University of Michigan, Michigan State University, Dartmouth Medical

School, and the University of New Hampshire. I thank the Churchill group at the

Jackson labs to invite me to Bar Harbor while I was writing the original

manuscript of this book. I especially thank Ernst Linder for reviewing and

working with me on this manuscript, NHCTC for being a great place to teach,

and my current colleagues at Tufts-NEMC.

I dedicate this work to all my students �C past, present and future �C both those

that I teach in the classroom and the ones I am ��teaching�� through my writings.

I wish you success in your endeavors and encourage you never to quit your

quest for answers to the research questions that interest you most.

K Seefeld, May 2007

Copyright May 2007, K Seefeld

Permission granted to reproduce for nonprofit, educational use.

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1

Overview

The coverage in this book is very different from a traditional introductory

statistics book or course (of which both authors have taught numerous times).

The goal of this book is to serve as a primer to higher level statistics for

researchers in biological fields. We chose topics to cover from current

bioinformatics literature and from available syllabi from the small but growing

number of courses titled something like ��Statistics for Bioinformatics��. Many

of the topics we have chosen (Markov Chains, multivariate analysis) are

considered advanced level topics, typically taught only to graduate level

students in statistics. We felt the need to bring down the level that these topics

are taught to accommodate interested people with non-statistical background. In

doing so we, as much as possible, eliminated using complicated equations and

mathematical language. As a cautionary note, we are not hoping to replace a

graduate level background in statistics, but we do hope to convey a conceptual

understanding and ability to perform some basic data analysis using these

concepts as well as better understand the vocabulary and concepts frequently

appearing in bioinfomatic literature. We anticipate that this will inspire further

interest in statistical study as well as make the reader a more educated consumer

of the bioinformatics literature, able to understand and analyze the statistical

techniques being used. This should also help open communication lines

between statisticians and researchers.

We (the authors) are both teachers who believe in learning by doing and feel

there would be little use in presenting statistical concepts without providing

examples using these concepts. In order to present applied examples, the

complexity of data analysis needed for bioinformatics requires a sophisticated

computer data analysis system. It is not true, as often misperceived by

researchers, that computer programming languages (such as Java or Perl) or

office applications (such as spreadsheets or database applications) can replace a

Copyright May 2007, K Seefeld

Permission granted to reproduce for nonprofit, educational use.

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statistical applications package. The majority of functionality needed to perform

sophisticated data analysis is found only in specialized statistical software. We

feel very fortunate to be able to obtain the software application R for use in this

book. R has been in active, progressive development by a team of top-notch

statisticians for several years. It has matured into one of the best, if not the best,

sophisticated data analysis programs available. What is most amazing about R is

that it completely free, making it wonderfully accessible to students and

researchers.

The structure of the R software is a base program, providing basic program

functionality, which can be added onto with smaller specialized program

modules called packages. One of the biggest growth areas in contributed

packages in recent years has come from bioinformatics researchers, who have

contributed packages for QTL and microarray analysis, among other

applications. Another big advantage is that because R is so flexible and

extensible, R can unify most (if not all) bioinformatics data analysis tasks in one

program with add-on packages. Rather than learn multiple tools, students and

researchers can use one consistent environment for many tasks. It is because of

the price of R, extensibility, and the growing use of R in bioinformatics that R

was chosen as the software for this book.

The ��disadvantage�� of R is that there is a learning curve required to master its

use (however, this is the case with all statistical software). R is primarily a

command line environment and requires some minimal programming skills to

use. In the beginning of the book we cover enough ground to get one up and

running with R.. We are assuming the primary interest of the reader is to be an

applied user of this software and focus on introducing relevant packages and

how to use the available existing functionality effectively. However, R is a fully

extensible system and as an open source project, users are welcome to contribute

code. In addition, R is designed to interface well with other technologies,

including other programming languages and database systems. Therefore R will

appeal to computer scientists interested in applying their skills to statistical data

analysis applications.

Now, let��s present a conceptual overview of the organization of the book.

The Basics of R (Ch 2 �C 5)

This section presents an orientation to using R. Chapter 2 introduces the R

system and provides guidelines for downloading R and obtaining and installing

packages. Chapter 3 introduces how to work with data in R, including how to

manipulate data, how to save and import/export datasets, and how to get help.

Chapter 4 covers the rudimentary programming skills required to successfully

work with R and understand the code examples given in coming chapters.

Chapter 5 covers basic exploratory data analysis and summary functionality and

outliners the features of R��s graphics system.

Copyright May 2007, K Seefeld

Permission granted to reproduce for nonprofit, educational use.

4

Probability Theory and Modeling (Ch 6-9)

These chapters are probably the most ��theoretical�� in the book. They cover a lot

of basic background information on probability theory and modeling. Chapters

6-8 cover probability theory, univariate, and multivariate probability

distributions respectively. Although this material may seem more academic

than applied, this material is important background for understanding Markov

chains, which are a key application of statistics to bioinformatics as well as for a

lot of other sequence analysis applications. Chapter 9 introduces Bayesian data

analysis, which is a different theoretical perspective on probability that has vast

applications in bioinformatics.

Markov Chains (Ch 10-12)

Chapter 10 introduces the theory of Markov chains, which are a popular method

of modeling probability processes, and often used in biological sequence

analysis. Chapter 11 explains some popular algorithms �C the Gibbs sampler and

the Metropolis Hastings algorithm �C that use Markov chains and appear

extensively in bioinformatics literature. BRugs is introduced in Chapter 12

using applied genetics examples.

Inferential Statistics (Ch 13-15)

The topics in these chapters are the topics covered in traditional introductory

statistics courses and should be familiar to most biological researchers.

Therefore the theory presented for these topics is relatively brief. Chapter 13

covers the basics of statistical sampling theory and sampling distributions, but

added to these basics is some coverage of bootstrapping, a popular inference

technique in bioinformatics. Chapter 14 covers hypothesis testing and includes

instructions on how to do most popular test using R. Regression and ANOVA

are covered in Chapter 15 along with a brief introduction to general linear

models.

Advanced Topics (Ch 16-17)

Chapter 16 introduces techniques for working with multivariate datasets,

including clustering techniques. It is hoped that this book serves as a bridge to

enable biological researchers to understand the statistical techniques used in

these packages.

Copyright May 2007, K Seefeld

Permission granted to reproduce for nonprofit, educational use.

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