# Controlling the false discovery rate: a practical and powerful approach to multiple testing

@article{Benjamini1995ControllingTF, title={Controlling the false discovery rate: a practical and powerful approach to multiple testing}, author={Yoav Benjamini and Yosef Hochberg}, journal={Journal of the royal statistical society series b-methodological}, year={1995}, volume={57}, pages={289-300} }

SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to problems of multiple significance testing is presented. It calls for controlling the expected proportion of falsely rejected hypotheses -the false discovery rate. This error rate is equivalent to the FWER when all hypotheses are true but is smaller otherwise. Therefore, in problems where the control of…

## 72,969 Citations

Implementing false discovery rate control: increasing your power

- Computer Science
- 2005

Keeping the proportion of type I errors low among all significant results is a sensible, powerful, and easy-to-interpret way of addressing the multiple testing issue.

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

- Mathematics
- 2000

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…

Controlling the False Discovery Rate: A New Application to Account for Multiple and Dependent Tests in Local Statistics of Spatial Association

- Mathematics
- 2006

Assessing the significance of multiple and dependent comparisons is an important, and often ignored, issue that becomes more critical as the size of data sets increases. If not accounted for,…

A direct approach to false discovery rates

- Mathematics
- 2002

Multiple-hypothesis testing involves guarding against much more complicated errors than single-hypothesis testing. Whereas we typically control the type I error rate for a single-hypothesis test, a…

Comparison of Methods for Estimating the Number of True Null Hypotheses in Multiplicity Testing

- Mathematics, MedicineJournal of biopharmaceutical statistics
- 2003

Five methods used to estimate the number of true null hypotheses over a large number of hypotheses are compared and the lowest slope method, developed by Benjamini and Hochberg (2000), and the mean of differences method appear to perform the best.

Stepwise normal theory multiple test procedures controlling the false discovery rate

- Mathematics
- 2000

Abstract The false discovery rate (FDR), or the expected proportion of falsely rejected null hypotheses to rejected null hypotheses, has recently been proposed as an error rate that multiple testing…

THE CONTROL OF THE FALSE DISCOVERY RATE IN MULTIPLE TESTING UNDER DEPENDENCY

- Mathematics
- 2001

Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR…

A modified Benjamini–Hochberg multiple comparisons procedure for controlling the false discovery rate

- Mathematics
- 2002

When performing simultaneous statistical tests, the Type I error concept most commonly controlled by analysts is the familywise error rate, i.e., the probability of committing at least one Type I…

Some Results on the Control of the False Discovery Rate under Dependence.

- Mathematics
- 2007

Controlling the false discovery rate (FDR) is a powerful approach to multiple testing, with procedures developed with applications in many areas. Dependence among the test statistics is a common…

Control of generalized error rates in multiple testing

- Mathematics
- 2005

Consider the problem of testing s hypotheses simultaneously. The usual approach restricts attention to procedures that control the probability of even one false rejection, the familywise error rate…

## References

SHOWING 1-10 OF 16 REFERENCES

An improved Bonferroni procedure for multiple tests of significance

- Mathematics
- 1986

SUMMARY A modification of the Bonferroni procedure for testing multiple hypotheses is presented. The method, based on the ordered p-values of the individual tests, is less conservative than the…

Statistical “Discoveries” and Effect-Size Estimation

- Mathematics
- 1989

Abstract Current methods of statistical inference are correct but incomplete. Small probability (α) of wrong null-hypothesis rejections can be misunderstood. Definitive rejections of null hypotheses,…

A sequentially rejective test procedure based on a modified Bonferroni inequality

- Mathematics
- 1990

SUMMARY A sharper Bonferroni procedure for multiple tests of significance is derived. This procedure is an improvement of Hochberg's (1988) procedure which contrasts the individual P-values with…

On the Optimality of Some Multiple Comparison Procedures

- Mathematics
- 1972

Abstract : Optimality criteria formulated in terms of the power functions of the individual tests are given for problems where several hypotheses are tested simultaneously. Subject to the constraint…

A sharper Bonferroni procedure for multiple tests of significance

- Mathematics
- 1988

SUMMARY A simple procedure for multiple tests of significance based on individual p-values is derived. This simple procedure is sharper than Holm's (1979) sequentially rejective procedure. Both…

A stagewise rejective multiple test procedure based on a modified Bonferroni test

- Mathematics
- 1988

SUMMARY Simes (1986) has proposed a modified Bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses. In contrast to the classical Bonferroni…

A Simple Sequentially Rejective Multiple Test Procedure

- Mathematics
- 1979

This paper presents a simple and widely ap- plicable multiple test procedure of the sequentially rejective type, i.e. hypotheses are rejected one at a tine until no further rejections can be done. It…

Multiple Comparison Procedures: The Practical Solution

- Mathematics
- 1990

Abstract A practicing statistician looks at the multiple comparison controversy and related issues through the eyes of the users. The concept of consistency is introduced and discussed in relation to…

More powerful procedures for multiple significance testing.

- MedicineStatistics in medicine
- 1990

Some new, general and simple procedures are discussed and demonstrated by two examples from the medical literature: the neuropsychologic effects of unidentified childhood exposure to lead, and the sleep patterns of sober chronic alcoholics.

Impact of multiple comparisons in randomized clinical trials.

- MedicineThe American journal of medicine
- 1987

There still exists a great need for future work to clarify further the problem of multiple comparisons and determine how the impact of this problem can best be minimized in subsequent research.