By Martina Bremer, Department of Mathematics, San Jose State University, California; Rebecca W. Doerge, Departments of Statistics and Agronomy, Purdue University, Indiana

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Using R at the Bench: Step-by-Step Data Analytics for Biologists is a convenient bench-side handbook for biologists, designed as a handy reference guide for elementary and intermediate statistical analyses using the free/public software package known as “R.” The expectations for biologists to have a more complete understanding of statistics are growing rapidly. New technologies and new areas of science, such as microarrays, next-generation sequencing, and proteomics, have dramatically increased the need for quantitative reasoning among biologists when designing experiments and interpreting results. Even the most routine informatics tools rely on statistical assumptions and methods that need to be appreciated if the scientific results are to be correct, understood, and exploited fully.

Although the original Statistics at the Bench is still available for sale and has all examples in Excel, this new book uses the same text and examples in R. A new chapter introduces the basics of R: where to download, how to get started, and some basic commands and resources. There is also a new chapter that explains how to analyze next-generation sequencing data using R (specifically, RNA-Seq). R is powerful statistical software with many specialized packages for biological applications and Using R at the Bench: Step-by-Step Data Analytics for Biologists is an excellent resource for those biologists who want to learn R. This handbook for working scientists provides a simple refresher for those who have forgotten what they once knew and an overview for those wishing to use more quantitative reasoning in their research. Statistical methods, as well as guidelines for the interpretation of results, are explained using simple examples. Throughout the book, examples are accompanied by detailed R commands for easy reference.

Contents

Acknowledgments

1 Introduction

2 Common Pitfalls

2.1 Examples of Common Mistakes

2.2 Defining Your Question

2.3 Working with and Talking to a Statistician

2.4 Exploratory versus Inferential Statistics

2.5 Different Sources of Variation

2.6 The Importance of Checking Assumptions and the Ramifications of Ignoring the Obvious

2.7 Statistical Software Packages

2.8 Installing and Using R and R Commander

2.8.1 Loading Data

2.8.2 Variable Types

2.8.3 Handling Graphics

2.8.4 Saving Your Work

2.8.5 Getting Help

3 Descriptive Statistics

3.1 Definitions

3.2 Numerical Ways to Describe Data

3.2.1 Categorical Data

3.2.2 Quantitative Data

3.2.3 Determining Outliers

3.2.4 How to Choose a Descriptive Measure

3.3 Graphical Methods to Display Data

3.3.1 How to Choose the Appropriate Graphical Display for Your Data

3.4 Probability Distributions

3.4.1 The Binomial Distribution

3.4.2 The Normal Distribution

3.4.3 Assessing Normality in Your Data

3.4.4 Data Transformations

3.5 The Central Limit Theorem

3.5.1 The Central Limit Theorem for Sample Proportions

3.5.2 The Central Limit Theorem for Sample Means

3.6 Standard Deviation versus Standard Error

3.7 Error Bars

3.8 Correlation

3.8.1 Correlation and Causation

4 Design of Experiments

4.1 Mathematical and Statistical Models

4.1.1 Biological Models

4.2 Describing Relationships between Variables

4.3 Choosing a Sample

4.3.1 Problems in Sampling: Bias

4.3.2 Problems in Sampling: Accuracy and Precision

4.4 Choosing a Model

4.5 Sample Size

4.6 Resampling and Replication

5 Confidence Intervals

5.1 Interpretation of Confidence Intervals

5.1.1 Confidence Levels

5.1.2 Precision

5.2 Computing Confidence Intervals

5.2.1 Confidence Intervals for Large Sample Mean

5.2.2 Confidence Interval for Small Sample Mean

5.2.3 Confidence Interval for Population Proportion

5.3 Sample Size Calculations

6 Hypothesis Testing

6.1 The Basic Principle

6.1.1 p-values

6.1.2 Errors in Hypothesis Testing

6.1.3 Power of a Test

6.1.4 Interpreting Statistical Significance

6.2 Common Hypothesis Tests

6.2.1 t-test

6.2.2 z-test

6.2.3 F-test

6.2.4 Tukey’s Test and Scheffé’s Test

6.2.5 χ^{2}-test: Goodness-of-Fit or Test of Independence

6.2.6 Likelihood Ratio Test

6.3 Non-parametric Tests

6.3.1 Wilcoxon-Mann-Whitney Rank Sum Test

6.3.2 Fisher’s Exact Test

6.3.3 Permutation Tests

6.4 E-values

7 Regression and ANOVA

7.1 Regression

7.1.1 Correlation and Regression

7.1.2 Parameter Estimation

7.1.3 Hypothesis Testing

7.1.4 Logistic Regression

7.1.5 Multiple Linear Regression

7.1.6 Model Building in Regression: Which Variables to Use?

7.1.7 Verification of Assumptions

7.1.8 Outliers in Regression

7.1.9 A Case Study

7.2 ANOVA

7.2.1 One-Way ANOVA Model

7.2.2 Two-Way ANOVA Model

7.2.3 ANOVA Assumptions

7.2.4 ANOVA Model for Microarray Data

7.3 What ANOVA and Regression Models Have in Common

8 Special Topics

8.1 Classification

8.2 Clustering

8.2.1 Hierarchical Clustering

8.2.2 Partitional Clustering

8.3 Principal Component Analysis

8.4 Microarray Data Analysis

8.4.1 The Data

8.4.2 Normalization

8.4.3 Statistical Analysis

8.4.4 The ANOVA Model

8.4.5 Variance Assumptions

8.4.6 Multiple Testing Issues

8.5 Next-Generation Sequencing Analysis

8.5.1 Experimental Overview

8.5.2 Statistical Issues in Next-Generation Sequencing Experiments