Designed for a two-semester, introductory course for graduate students in the social sciences, this text introduces three major advances in the field: 1) sample size estimation needed to justify normality via the central limit theorem, 2) the impact of outliers and heavy-tailed distributions on power and our ability to obtain an accurate assessment of how groups differ and variables are related, and 3) the deleterious effects of heteroscedasticity on conventional ANOVA and regression methods. Focusing on conceptual issues rather than complex computational details, it also provides a library of R functions.