scholarly journals The control of the false discovery rate in fixed sequence multiple testing

2017 ◽  
Vol 11 (2) ◽  
pp. 4649-4673
Author(s):  
Gavin Lynch ◽  
Wenge Guo ◽  
Sanat K. Sarkar ◽  
Helmut Finner
Keyword(s):  
False Discovery Rate ◽  
Multiple Testing ◽  
Fixed Sequence ◽  
False Discovery

On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics

2000 ◽  
Vol 25 (1) ◽  
pp. 60-83 ◽  
Author(s):  
Yoav Benjamini ◽  
Yosef Hochberg
Keyword(s):  
False Discovery Rate ◽  
Multiple Testing ◽  
Meta Analysis ◽  
Test Statistics ◽  
Adaptive Procedure ◽  
New Approach ◽  
False Discovery ◽  
Behavioral Studies ◽  
Simultaneous Testing ◽  
Independent Test

A new approach to problems of multiple significance testing was presented in Benjamini and Hochberg (1995), which calls for controlling the expected ratio of the number of erroneous rejections to the number of rejections–the False Discovery Rate (FDR). The procedure given there was shown to control the FDR for independent test statistics. When some of the hypotheses are in fact false, that procedure is too conservative. We present here an adaptive procedure, where the number of true null hypotheses is estimated first as in Hochberg and Benjamini (1990), and this estimate is used in the procedure of Benjamini and Hochberg (1995). The result is still a simple stepwise procedure, to which we also give a graphical companion. The new procedure is used in several examples drawn from educational and behavioral studies, addressing problems in multi-center studies, subset analysis and meta-analysis. The examples vary in the number of hypotheses tested, and the implication of the new procedure on the conclusions. In a large simulation study of independent test statistics the adaptive procedure is shown to control the FDR and have substantially better power than the previously suggested FDR controlling method, which by itself is more powerful than the traditional family wise error-rate controlling methods. In cases where most of the tested hypotheses are far from being true there is hardly any penalty due to the simultaneous testing of many hypotheses.

On the Operational Characteristics of the Benjamini and Hochberg False Discovery Rate Procedure

2007 ◽  
Vol 6 (1) ◽  
Author(s):  
Gerwyn H Green ◽  
Peter J. Diggle
Keyword(s):  
False Discovery Rate ◽  
Multiple Testing ◽  
False Positives ◽  
Experimental Conditions ◽  
Single Experiment ◽  
Testing Procedures ◽  
False Discovery ◽  
Expression Studies ◽  
Operational Characteristics ◽  
Gene Expression Studies

Multiple testing procedures are commonly used in gene expression studies for the detection of differential expression, where typically thousands of genes are measured over at least two experimental conditions. Given the need for powerful testing procedures, and the attendant danger of false positives in multiple testing, the False Discovery Rate (FDR) controlling procedure of Benjamini and Hochberg (1995) has become a popular tool. When simultaneously testing hypotheses, suppose that R rejections are made, of which Fp are false positives. The Benjamini and Hochberg procedure ensures that the expectation of Fp/R is bounded above by some pre-specified proportion. In practice, the procedure is applied to a single experiment. In this paper we investigate the across-experiment variability of the proportion Fp/R as a function of three experimental parameters. The operational characteristics of the procedure when applied to dependent hypotheses are also considered.

scholarly journals Wavelet analysis for non-stationary, nonlinear time series

2016 ◽  
Vol 23 (4) ◽  
pp. 257-267 ◽  
Author(s):  
Justin A. Schulte
Keyword(s):  
Time Series ◽  
Phase Transitions ◽  
Wavelet Analysis ◽  
False Discovery Rate ◽  
Multiple Testing ◽  
Nonstationary Time Series ◽  
Nonlinear Interactions ◽  
Quasi Biennial Oscillation ◽  
False Discovery ◽  
Biennial Oscillation

Abstract. Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum facilitated the detection of local nonlinearities and the quantification of cycle geometry. The local autobicoherence spectrum of the QBO time series showed that the QBO time series contained a mode with a period of 28 months that was phase coupled to a harmonic with a period of 14 months. An additional nonlinearly interacting triad was found among modes with periods of 10, 16 and 26 months. Local biphase spectra determined that the nonlinear interactions were not quadratic and that the effect of the nonlinearities was to produce non-smoothly varying oscillations. The oscillations were found to be skewed so that negative QBO regimes were preferred, and also asymmetric in the sense that phase transitions between the easterly and westerly phases occurred more rapidly than those from westerly to easterly regimes.

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