Multiple—test Procedures and Smile Plots

Abstract

multproc carries out multiple-test procedures, taking as input a list of p-values and an uncorrected critical p-value, and calculating a corrected overall critical p-value for rejection of null hypotheses. These procedures define a confidence region for a set-valued parameter, namely the set of null hypotheses that are true. They aim to control either the family-wise error rate (FWER) or the false discovery rate (FDR) at a level no greater than the uncorrected critical p-value. smileplot calls multproc and then creates a smile plot, with data points corresponding to estimated parameters, the p-values (on a reverse log scale) on the y-axis, and the parameter estimates (or another variable) on the x-axis. There are y-axis reference lines at the uncorrected and corrected overall critical p-values. The reference line for the corrected overall critical p-value, known as the parapet line, is an informal “upper confidence limit” for the set of null hypotheses that are true and defines a boundary between data mining and data dredging. A smile plot summarizes a set of multiple analyses just as a Cochrane forest plot summarizes a meta-analysis.