This document discusses methods for calculating sample sizes for different study designs. It provides formulas and examples for calculating sample sizes needed to estimate a prevalence or mean, compare two proportions or means, and detect a specified difference between groups. The key factors that determine sample size are the expected values in each group, desired level of precision or minimum detectable difference, and desired power and confidence level. Precise sample size calculations are necessary to avoid underpowered studies and ensure appropriate resources are allocated.