Summary of Topics Covered in STAT 535

1. Probability (needed to understand the statistical methods)
   • random variables & distributions (incl. commonly used normal and binomial distributions)
   • moments (mean, variance, skewness, kurtosis)
   • independence
   • law of large numbers & central limit theorem
2. Basics of Statistics
   • point estimators, confidence intervals, and test statistics
   • standard errors & sampling distributions
   • size, power, & p-values
3. Inferences from One or Two Samples
   • Student's t test and confidence interval for one sample, paired data, and two independent samples
   • effect of nonnormality and heteroscedasticity
   • diagnostic methods for checking assumptions
   • Welch's procedures for handling unequal variances
   • nonparametric methods (sign test, Wilcoxon signed-rank test, Wilcoxon rank sum test (Mann-Whitney test))
4. Inferences from Three or More Samples
   • one-way ANOVA F test and multiple comparison procedures
   • methods for dealing with unequal variances
   • nonparametric methods
5. Considerations for Experimental Designs and Modeling
   • observational units & the roles of randomization, replication, and blocking
   • controls & blinding
   • confounding & spurious associations
   • extraneous variables & modeling
6. Two-way ANOVA and Methods for Other Designs
   • crossed and nested (hierarchical) designs
   • interactions
   • analysis of covariance
7. Correlation and Regression
   • correlation and measures of association
   • simple linear regression
   • multiple regression modeling (polynomial regression, interactions)
   • checking assumptions and making transformations
8. Categorical Data Analysis
   • Pearson's goodness-of-fit tests
   • contingency tables & tests for lack of independence
   • brief coverage of logistic regreession