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Table 1 Definitions of FDR quantities contrasted with that of specificity and sensitivity.

From: A unified approach to false discovery rate estimation

Quantity

Definition

 

Fdr

= Prob("not interesting"|Y ≥ y)

= F P T P + F P MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeyypa0tcfa4aaSaaaeaacqWGgbGrcqWGqbauaeaacqWGubavcqWGqbaucqGHRaWkcqWGgbGrcqWGqbauaaaaaa@3531@

Fndr

= Prob("interesting"|Y ≤ y)

= F N F N + T N MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeyypa0tcfa4aaSaaaeaacqWGgbGrcqWGobGtaeaacqWGgbGrcqWGobGtcqGHRaWkcqWGubavcqWGobGtaaaaaa@3525@

Sensitivity, Power

= Prob(Y ≥ y|"interesting")

= T P T P + F N MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeyypa0tcfa4aaSaaaeaacqWGubavcqWGqbauaeaacqWGubavcqWGqbaucqGHRaWkcqWGgbGrcqWGobGtaaaaaa@3549@

Specificity

= Prob(Y ≤ y|"not interesting")

= T N T N + F P MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeyypa0tcfa4aaSaaaeaacqWGubavcqWGobGtaeaacqWGubavcqWGobGtcqGHRaWkcqWGgbGrcqWGqbauaaaaaa@3545@

fdr

= Prob("not interesting"|Y = y)

 

fndr

= Prob("interesting" |Y = y)

= 1 - fdr

  1. Note that in the above definitions TP, FP, FN, FP are assumed to be the true fractions – see Fig. 1. If instead observed counts are used, additionally the expectation E(.) must be taken, conditioned on seeing a non-zero denominator (cf. [7, 11]).