This chapter first focuses on goodness-of-fit tests. A simple case is testing for normality (e.g., the Shapiro–Wilks test). We generally recommend against this because large sample sizes can find statistically significant differences even if those differences are not important, and vice versa. We show Q-Q plots to graphically check for the largeness of departures from normality. We discuss the Kolmogorov–Smirnoff test for any difference between two distributions. We review goodness-of-fit tests for contingency tables (Pearson’s chi-squared test and Fisher’s exact test) and for logistic regression (the Hosmer–Lemeshow test). The rest of the chapter is devoted to equivalence or noninferiority tests. The margin of equivalence or noninferiority must be prespecified, and for noninferiority tests of a new drug against a standard, the margin should be larger than the difference between the placebo and the standard. We discuss the constancy assumption and biocreep. We note that while poor design (poor compliance, poor study population choice, poor measurement) generally decreases power in superiority design, these can lead to high Type I error rates in noninferiority designs.