SGoFicance Trace: assessing significance in high dimensional testing problems

Abstract

Recently, an exact binomial test called SGoF (Sequential Goodness-of-Fit) has been introduced as a new method for handling high dimensional testing problems. SGoF looks for statistical significance when comparing the amount of null hypotheses individually rejected at level γ = 0.05 with the expected amount under the intersection null, and then proceeds to declare a number of effects accordingly. SGoF detects an increasing proportion of true effects with the number of tests, unlike other methods for which the opposite is true. It is worth mentioning that the choice γ = 0.05 is not essential to the SGoF procedure, and more power may be reached at other values of γ depending on the situation. In this paper we enhance the possibilities of SGoF by letting the γ vary on the whole interval (0,1). In this way, we introduce the ‘SGoFicance Trace’ (from SGoF's significance trace), a graphical complement to SGoF which can help to make decisions in multiple-testing problems. A script has been written for the computation in R of the SGoFicance Trace. This script is available from the web site http://webs.uvigo.es/acraaj/SGoFicance.htm.