Introduction to Statistical Data Analysis for the Life Sciences

Any practical introduction to statistics in the life sciences requires a focus on applications and computational statistics combined with a reasonable level of mathematical rigor. It must offer the right combination of data examples, statistical theory, and computing required for analysis today. And it should involve R software, the lingua franca of statistical computing. Introduction to Statistical Data Analysis for the Life Sciences covers all the usual material but goes further than other texts to emphasize: Both data analysis and the mathematics underlying classical statistical analysis Modeling aspects of statistical analysis with added focus on biological interpretations Applications of statistical software in analyzing real-world problems and data sets Developed from their courses at the University of Copenhagen, the authors imbue readers with the ability to model and analyze data early in the text and then gradually fill in the blanks with needed probability and statistics theory. While the main text can be used with any statistical software, the authors encourage a reliance on R. They provide a short tutorial for those new to the software and include R commands and output at the end of each chapter. Data sets used in the book are available on a supporting website. Each chapter contains a number of exercises, half of which can be done by hand. The text also contains ten case exercises where readers are encouraged to apply their knowledge to larger data sets and learn more about approaches specific to the life sciences. Ultimately, readers come away with a computational toolbox that enables them to perform actual analysis for real data sets as well as the confidence and skills to undertake more sophisticated analyses as their careers progress.

Table of Contents:
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.