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Review Enrichment or depletion of a GO category within a class of genes: which test?
"... Motivation: A number of available program packages determine the significant enrichments and/or depletions of GO categories among a class of genes of interest. Whereas a correct formulation of the problem leads to a single exact null distribution, these GO tools use a large variety of statistical te ..."
Abstract

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Motivation: A number of available program packages determine the significant enrichments and/or depletions of GO categories among a class of genes of interest. Whereas a correct formulation of the problem leads to a single exact null distribution, these GO tools use a large variety of statistical tests whose denominations often do not clarify the underlying pvalue computations. Summary: We review the different formulations of the problem and the tests they lead to: the binomial, chisquare, equality of two probabilities, Fisher’s exact, and hypergeometric tests. We clarify the relationships existing between these tests, in particular the equivalence between the hypergeometric test and Fisher’s exact test. We recall that the other tests are valid only for large samples, the test of equality of two probabilities and the chisquare test being equivalent. We discuss the appropriateness of one and twosided pvalues, as well as some discreteness and conservatism issues. 1
A Last Lecture 19492009: Quantiles are “Optimal” by
"... This paper discusses (1) our research to provide a framework for almost all statistical methods and philosophies, (2) need to plan the future of the “Science of Statistics ” in order to compete for leadership in the practice of the “Statistics of Science”, (3) grand unifying ideas of the Science of ..."
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This paper discusses (1) our research to provide a framework for almost all statistical methods and philosophies, (2) need to plan the future of the “Science of Statistics ” in order to compete for leadership in the practice of the “Statistics of Science”, (3) grand unifying ideas of the Science of Statistics, (4) an elegant rigorous proof when quantile function minimizes check loss function which is the basis of quantile regression, (5) exact and approximate confidence quantiles (confidence interval endpoint functions) for parameters p and logodds(p) given a sample of a 01 variable.