1.  Probability

1. Basic Definitions and Axioms
2. Conditional Probability and Independence
3. Random Variables
4. Bayes Theorem (sensitivity, specificity)
5. Probability Distributions (discrete & continuous)
6. Mean and Variance of a Distribution
    

2.  Summarizing and Describing Data

1. Summary Statistics (sample mean, median, variance)
2. Graphical (histogram, box plots)
    

3.  Inferences for One Sample

   A. Inference for Means (and the Normal Distribution)

1. Confidence intervals

2. Central limit theorem

3. Hypothesis testing, significance levels, p-values, power

4. Sample size considerations

5. Transformations, QQ plots

   B.  Inference for Proportions (and the Binomial Distribution)

4.  The Two Sample Problem

1. Comparing 2 means (paired versus independent samples)
2. Comparing 2 proportions
3. Sample size considerations

5. Contingency Tables

1. 2 x 2 table: Fisher’s exact test and Chi-square test
2. r x c table

6. Statistical Methods in Epidemiology

1. Prospective, case–control and cross-sectional studies
2. Odds ratio and relative risk
3. Simpson’s Paradox and Mantel-Haenszel test
4. Matching and McNemar’s test

7. Introduction to Nonparametric Methods

1. Signed rank test, Wilcoxon rank sum test, Kruskal Wallis test
2. Advantages and disadvantages
3. Measures of agreement

8. The Analysis of Count Data

1. The Poisson distribution
2. Inference based on count data
3. Applications in epidemiology and bioassay

9. Issues and Controversies and Other Topics

1. p-values and confidence intervals
2. Frequentist, Bayesian & likelihood paradigms
3. Introduction to the delta method and bootstrapping
4. Multiple hypothesis testing
5. Elements of good data presentation and analysis