Multiple testing

Consider the problem of assessing which variables in a GLM have nonzero coefficients. In the preceding chapters, we have described a variety of tests for obtaining \(p\)-values for each coefficient. Given this set of \(p\)-values (call them \(p_1\), , \(p_m\)), we must determine which variables to deem significant. As it turns out, this task is a nontrivial one for several reasons. In this chapter, we formalize this task as a multiple testing problem, discuss the challenges that arise, and describe some common methods for addressing these challenges.