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Variance of the number of false discoveries
Author(s) -
Owen Art B.
Publication year - 2005
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2005.00509.x
Subject(s) - variance (accounting) , statistics , mathematics , statistical hypothesis testing , null hypothesis , multiple comparisons problem , sampling (signal processing) , analysis of variance , econometrics , computer science , accounting , filter (signal processing) , business , computer vision
Summary. In high throughput genomic work, a very large number d of hypotheses are tested based on n ≪ d data samples. The large number of tests necessitates an adjustment for false discoveries in which a true null hypothesis was rejected. The expected number of false discoveries is easy to obtain. Dependences between the hypothesis tests greatly affect the variance of the number of false discoveries. Assuming that the tests are independent gives an inadequate variance formula. The paper presents a variance formula that takes account of the correlations between test statistics. That formula involves O ( d 2 ) correlations, and so a naïve implementation has cost O ( nd 2 ). A method based on sampling pairs of tests allows the variance to be approximated at a cost that is independent of d .