Multiple comparison adjustments have a long history, yet confusion remains about which procedures control type 1 error rate in a strong sense and how to show this. Part of the confusion stems from a powerful technique called the closed testing principle, whose statement is deceptively simple, but is sometimes misinterpreted. This primer presents a straightforward way to think about multiplicity adjustment.
Keywords: closed testing principle; familywise error rate; sequentially rejective Bonferroni; strong vs weak control of the FWER.
Published 2020. This article is a U.S. Government work and is in the public domain in the USA.