January 2012 semester

Biology 548b is a graduate course on quantitative methods for data analysis in ecology and evolution. The format is a mixture of lectures/discussions on methodological topics and practical workshops using the R package. Students are assumed to have taken an introductory undergraduate statistics course at some point in their careers. We will begin at a fairly basic level using a general linear model approach.

This page is under continuous construction, with new information added as the semester proceeds.

Lectures and workshops are held in Beaty Biodiversity 224.

See the workshops page for computer requirements.

Below is a list of lecture topics and contents.

Lecture topics

Links to the lecture slides will be added before each lecture time. Click the refresh button on your browser to make sure you are seeing the latest version of this page.

Introduction

Lecture overheads
About the course
Course objectives
About the instructor
Why we use R
Organizing data for use in R
Handout: Effective data management
Review of some basic concepts in statistics

Graphics

Lecture overheads
The purpose of graphs
Types of graphs
Examples of bad graphs and how to improve them
Using tables to show patterns in data
Principles of effective display

Design of experiments

Lecture overheads
What is an experiment
Why do experiments
Clinical trials
How to minimize bias in experiments
How to minimize effects of sampling error in experiments
Experiments with more than one factor
What if you can’t do experiments
Planning your sample size to maximize precision and power

Linear models

Lecture overheads
What is a linear model
Linear regression example
Single factor ANOVA example
Estimating parameters for categorical variables
Analyzing data from experiments: Analysis follows design
The lure of model simplification
Perils of correcting for covariates
Core assumptions of linear models
Options for handling certain violations of assumptions

Mixed effects models

Lecture overheads
Random vs fixed effects
Two-factor ANOVA example
Why the calculations are different with random effects
Problem of unbalanced designs with random effects
Examples of experiments with random effects
Linear mixed-effects models
Example: Estimating repeatability of a measurement
Assumptions of linear mixed-effects models
An example violating the assumptions, with solutions

Likelihood

Lecture overheads
Probability and likelihood
Maximum likelihood estimation
Example: estimate a proportion
Likelihood-based confidence intervals
Example: estimate speciation and extinction rates
Log-likelihood ratio test

Generalized linear models

Lecture overheads
What is a generalized linear model
Linear predictors and link functions
Example: estimate a proportion
Analysis of deviance
Example: fit dose-response data using logistic regression
Example: fit count data using a log-linear model
Advantages and assumptions of glm
Quasi-likelihood modeling when there is excessive variance

Model selection

Lecture overheads
The problem of model selection
How to find a parsimonious model
Criterion: Mallow’s C_p
Information-theoretic criterion: AIC
Search strategies: All subsets regression; stepAIC
Several models may fit about equally well
The science part: formulate a set of candidate models
Looking ahead: multimodel inference

Bayesian data analysis

Lecture overheads
What is probability
Two probability definitions
Bayes Theorem
Prior probability and posterior probability
How Bayesian inference is different from what we usually do
Example: one species or two? Example: estimate a proportion
Credible intervals
Quick notes on Bayesian model selection

Bootstrap and resampling

Lecture overheads
Estimation
The sampling distribution
Standard error of an estimate
The bootstrap standard error
The bootstrap confidence interval
Bootstrap estimate of phylogeny
Comparing two groups
Randomization test

Meta-analysis

Lecture overheads
Meta-analysis compared with traditional review article
Quantitative summaries compared with vote-counting
Defining the question and scope for a meta-analysis
Gathering the data and calculating effect size
Fixed and mixed-effects models to analyze effect sizes
Associating effect sizes with study quality, other variables
File-drawer problem and publication bias
Make your results accessible to meta-analysis

Programming

Lecture overheads
Programming & language
Program structure
Important concepts
Debugging
Guest lecture by Rich FitzJohn: packages & version control Lecture overheads Rich

Reproducibility

3- minute talks on reproducibility of scientific data

Multi-variate

Lecture overheads