Accreditation and Quality Assurance

, Volume 19, Issue 1, pp 1–10 | Cite as

Multiple hypothesis testing for metrology applications

Review

Abstract

Scrutiny of hypotheses by means of statistical tests is a common practice in experimental research. However, valid inference drawn from data analysis needs scientific grounds, whereas conclusions based on significance tests or hypothesis testing may be problematic, especially when dealing with a multiplicity of tested hypotheses, as in experiments performed on bio-molecules. The problem of false discovery rate is focused in the present paper, aiming at eliciting application of sound criteria for rejection/acceptance of hypotheses, with a view of addressing related methods for uncertainty characterization.

Keywords

Measurement science Statistical significance Multiple hypothesis tests False discoveries 

Defined functions

FDP

False discovery proportion, Eqs. (4, 5)

FDR

False discovery rate, Eqs. (7a, 7b, 19, 22)

FNR

False non-discovery rate, Eq. (20)

FPP

False positive proportion, Eqs. (2, 3)

FWER

Family-wise error rate Eqs. (6, 14)

mFDR

Marginal FDR, Eq. (9)

PCER

Per-comparison error rate, Eq. (10)

pFDR

Positive FDR, Eq. (8)

PFER

Per-family error rate, Eq. (11)

pFNR

Positive FNR, Eq. (21)

Abbreviations

B–H

Benjamini–Hochberg

N–P

Neyman–Pearson

PDF

Probability density function

p-value

Probability value

RV

Random variable

List of symbols

\( p(b|a) \)

Probability of b conditional on a

E[·]

Expectation

#{·}

Cardinality (number of elements belonging to the set)

^

(“Hat”) indicates estimation, e.g., \( \hat{J} \) is an estimation of a quantity J

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Istituto Nazionale di Ricerca Metrologica (INRIM)TurinItaly

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