The control of the false discovery rate in multiple testing under dependency
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Cites background from "The control of the false discovery ..."
...For Permissions, please email: journals.permissions@oupjournals.org BiNGO dependency of the test statistics (Benjamini and Yekutieli, 2001)....
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...dependency of the test statistics (Benjamini and Yekutieli, 2001)....
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Cites background from "The control of the false discovery ..."
...Which procedure is more appropriate? The first procedure requires that the tests be based on behavioral endpoints that are either statistically independent or positively dependent [6]....
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Cites background from "The control of the false discovery ..."
...The work cannot be used commercially without permission from the journal....
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Cites methods from "The control of the false discovery ..."
...0, we add two more popular FDR correction methods: Benjamini-Hochberg (40) and Benjamini-Yekutieli (41)....
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...In KOBAS 2.0, we add two more popular FDR correction methods: Benjamini-Hochberg (40) and Benjamini-Yekutieli (41)....
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References
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"The control of the false discovery ..." refers background or methods in this paper
...The false discovery rate (FDR), suggested by Benjamini and Hochberg (1995) is a new and different point of view for how the errors in multiple testing could be considered. The FDR is the expected proportion of erroneous rejections among all rejections. If all tested hypotheses are true, controlling the FDR controls the traditional FWE. But when many of the tested hypotheses are rejected, indicating that many hypotheses are not true, the error from a single erroneous rejection is not always as crucial for drawing conclusions from the family tested, and the proportion of errors is controlled instead. Thus we are ready to bear with more errors when many hypotheses are rejected, but with less when fewer are rejected. (This frequentist goal has a Bayesian flavor.) In many applied problems it has been argued that the control of the FDR at some specified level is the more appropriate response to the multiplicity concern: examples are given in Section 2.1 and discussed in Section 4. The practical difference between the two approaches is neither trivial nor small and the larger the problem the more dramatic the difference is. Let us demonstrate this point by comparing two specific procedures, as applied to Example 1.1. To fix notation, let us assume that of the m hypotheses tested H0 1 H0 2 H0 m m0 are true null hypotheses, the number and identity of which are unknown. The other m−m0 hypotheses are false. Denote the corresponding random vector of test statistics X1 X2 Xm , and the corresponding p-values (observed significance levels) by P1 P2 Pm where Pi = 1−FH0 i Xi . Benjamini and Hochberg (1995) showed that when the test statistics are independent the following procedure controls the FDR at level q ·m0/m ≤ q....
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...Otherwise, when some of the hypotheses are true and some are false, the FDR is smaller [Benjamini and Hochberg (1995)]....
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...The FDR controlling multiple testing procedure [Benjamini and Hochberg (1995)], given by (1), is a step-up procedure that involves a linear set of constants on the p-value scale (step-up in terms of test statistics, not p-values). The FDR controlling procedure is related to the global test for the intersection hypothesis, which is defined in terms of the same set of constants: reject the single intersection hypothesis if there exist an i s.t. p i ≤ i mα. Simes (1986) showed that when the test statistics are continuous and independent, and all hypotheses are true, the level of the test is α. The equality is referred to as Simes’ equality, and the test has been known in recent years as Simes’ global test. However the result had already been proved by Seeger (1968) [Shaffer (1995) brought this forgotten reference to the current literature....
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...Formally, as in Benjamini and Hochberg (1995), let V denote the number of true null hypotheses rejected and R the total number of hypotheses rejected, and let Q be the unobservable random quotient,...
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...The FDR controlling multiple testing procedure [Benjamini and Hochberg (1995)], given by (1), is a step-up procedure that involves a linear set of constants on the p-value scale (step-up in terms of test statistics, not p-values)....
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20,459 citations
"The control of the false discovery ..." refers methods in this paper
...Still, even if only a small proportion of the tested hypotheses are detected as not true [approximately log� m� /m], the procedure is more powerful than the comparable FWE controlling procedure of Holm (1979) ....
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...Still, even if only a small proportion of the tested hypotheses are detected as not true [approximately log m /m], the procedure is more powerful than the comparable FWE controlling procedure of Holm (1979)....
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15,571 citations
"The control of the false discovery ..." refers background in this paper
...The study of uterine weights of mice reported by Steel and Torrie (1980) and discussed in Westfall and Young (1993) comprised a comparison of six groups receiving different solutions to one control group....
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"The control of the false discovery ..." refers background in this paper
...In genetics research, the need for multiplicity control has been recognized as one of the fundamental questions, especially since entire genome scans are now common [see Lander and Botstein (1989) , Barinaga (1994), Lander and Kruglyak (1995), Weller, Song, Heyen, Lewin and Ron (1998)]....
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...In genetics research, the need for multiplicity control has been recognized as one of the fundamental questions, especially since entire genome scans are now common [see Lander and Botstein (1989), Barinaga (1994), Lander and Kruglyak (1995), Weller, Song, Heyen, Lewin and Ron (1998)]....
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...The appropriate balance between lack of type I error control and low power [“the choice between Scylla and Charybdis” in Lander and Kruglyak (1995)] has been heavily debated....
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