Introduction to Statistical Data Analysis for the Life Sciences

Claus Thorn Ekstrøm is an associate professor of statistics in the Department of Basic Sciences and Environment and leader of the Center for Applied Bioinformatics in the Faculty of Life Sciences at the University of Copenhagen. His research interests include genetic marker error detection, simulation-based inference, image analysis, and the analysis of microarray DNA chips, metabolic profiles, and quantitative traits for complex human families. Helle Sørensen is an associate professor of statistics and probability theory in the Department of Mathematical Sciences in the Faculty of Science at the University of Copenhagen. Her research interests include statistical applications in eco-toxicology and animal science as well as statistical methods for stochastic processes.

Description of Samples and Populations
Data types
Visualizing categorical data
Visualizing quantitative data
Statistical summaries
What is a probability?

Linear Regression
Fitting a regression line
When is linear regression appropriate?
The correlation coefficient
Perspective


Comparison of Groups
Graphical and simple numerical comparison
Between-group variation and within-group variation
Populations, samples, and expected values
Least squares estimation and residuals
Paired and unpaired samples
Perspective

The Normal Distribution
Properties
One sample
Are the data (approximately) normally distributed?
The central limit theorem


Statistical Models, Estimation, and Confidence Intervals
Statistical models
Estimation
Confidence intervals
Unpaired samples with different standard deviations

Hypothesis Tests
Null hypotheses
t-tests
Tests in a one-way ANOVA
Hypothesis tests as comparison of nested models
Type I and type II errors

Model Validation and Prediction
Model validation
Prediction

Linear Normal Models
Multiple linear regression
Additive two-way analysis of variance
Linear models
Interactions between variables

Probabilities
Outcomes, events, and probabilities
Conditional probabilities
Independence

The Binomial Distribution
The independent trials model
The binomial distribution
Estimation, confidence intervals, and hypothesis tests
Differences between proportions

Analysis of Count Data
The chi-square test for goodness-of-fit
2 × 2 contingency table
Two-sided contingency tables

Logistic Regression
Odds and odds ratios
Logistic regression models
Estimation and confidence intervals
Hypothesis tests
Model validation and prediction

Case Exercises
Case 1: Linear modeling
Case 2: Data transformations
Case 3: Two sample comparisons
Case 4: Linear regression with and without intercept
Case 5: Analysis of variance and test for linear trend
Case 6: Regression modeling and transformations
Case 7: Linear models
Case 8: Binary variables
Case 9: Agreement
Case 10: Logistic regression


Appendix A: Summary of Inference Methods
Statistical concepts
Statistical analysis
Model selection


Appendix B: Introduction to R
Working with R
Data frames and reading data into R
Manipulating data
Graphics with R
Reproducible research
Installing R
Exercises


Appendix C: Statistical Tables
The x2 distribution
The normal distribution
The t distribution
The F distribution





Bibliography


Index


R Commands and Output and Exercises appear at the end of each chapter.