University of Central FloridaUnited States of America
We discuss statistical methods suitable for comparing multiple populations versus one reference population and consider two common problems: (1) detecting all significant mean differences and (2) demonstrating that all mean differences are significant. Discussed methods include the Bonferroni approach (both problems), Min test (problem 2), and Strassburger-Bretz-Hochberg (SBH) confidence interval for estimating the smallest mean difference (problem 2). They illustrate the methods using the pooled 2010–2015 Tobacco Use Supplement to the Current Population Survey (TUS-CPS) data on the cigarette purchase price (per pack) reported by adult daily smokers (n = 34,728). The goal was to show that among seven considered racial/ethnic groups of daily smokers, non-Hispanic (NH) Whites paid least for cigarettes (on average). We used the design-based multiple linear regression to derive the estimates and raw p-values. The Min test supported the study goal. Likewise, SBH lower 95% confidence interval bound was $0.08, indicating that the other racial/ethnic groups of daily smokers paid at least eight cents more for a pack of cigarettes (on average) than did non-Hispanic Whites. However, Bonferroni method (that was originally proposed for problem 1) failed to support the study goal. The study highlights the importance of choosing the right statistical method for a given problem.
Part of the book: Recent Advances in Numerical Simulations