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Gene set-based signal detection analyses are used to detect an association between a trait and a set of genes by accumulating signals across the genes in the gene set. Since signal detection is concerned with identifying whether any of the genes in the gene set are non-null, a goodness-of-fit (GOF) test can be used to compare whether the observed distribution of gene-level tests within the gene set agrees with the theoretical null distribution. Here, we present a flexible gene set-based signal detection framework based on tail-focused GOF statistics. We show that the power of the various statistics in this framework depends critically on two parameters: the proportion of genes within the gene set that are non-null and the degree of separation between the null and alternative distributions of the gene-level tests. We give guidance on which statistic to choose for a given situation and implement the methods in a fast and user-friendly R package, wHC (https://github.com/mqzhanglab/wHC). Finally, we apply these methods to a whole exome sequencing study of amyotrophic lateral sclerosis. [ABSTRACT FROM AUTHOR]