Abstract
In this paper we present a new R package called sgof for multiple hypothesis testing. The principal aim of this package is to implement SGoF-type multiple testing methods, known to be more powerful than the classical false discovery rate (FDR) and family-wise error rate (FWER) based methods in certain situations, particularly when the number of tests is large. This package includes Binomial and Conservative SGoF and the Bayesian and Beta-Binomial SGoF multiple testing procedures, which are adaptations of the original SGoF method to the Bayesian setting and to possibly correlated tests, respectively. The sgof package also implements the Benjamini-Hochberg and Benjamini-Yekutieli FDR controlling procedures. For each method the package provides (among other things) the number of rejected null hypotheses, estimation of the corresponding FDR, and the set of adjusted p values. Some automatic plots of interest are implemented too. Two real data examples are used to illustrate how sgof works.
Highlights
IntroductionWe find many statistical inference problems in areas such as genomics and proteomics which involve the simultaneous testing of thousands of null hypotheses producing as a result a number of significant p values or effects (an increase in gene expression, or RNA/protein levels)
Multiple testing refers to any instance that involves the simultaneous testing of several null hypotheses, i.e., H01, H02, . . . , H0n.Nowadays, we find many statistical inference problems in areas such as genomics and proteomics which involve the simultaneous testing of thousands of null hypotheses producing as a result a number of significant p values or effects
We find many statistical inference problems in areas such as genomics and proteomics which involve the simultaneous testing of thousands of null hypotheses producing as a result a number of significant p values or effects
Summary
We find many statistical inference problems in areas such as genomics and proteomics which involve the simultaneous testing of thousands of null hypotheses producing as a result a number of significant p values or effects (an increase in gene expression, or RNA/protein levels). These hypotheses may have complex and unknown dependence structures. In the multiple testing setting, a specific procedure for deciding which null hypotheses should be rejected is needed In this sense, the family-wise error rate (FWER) and the false discovery rate (FDR) have been proposed as suitable significance criteria to perform the multiple testing adjustment. The FDR and FWER based methods have the drawback of a rapidly decreasing power as the number of tests grows, being unable to detect even one effect in particular situations such as when there is a small to moderate proportion of weak effects
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