Once a month during the academic year, the statistics faculty select a paper for our students to read and discuss. Papers are selected based on their impact or historical value, or because they contain useful techniques or results.
Benjamini, Y. and Hochberg, Y. (1995), Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society: Series B (Methodological), 57: 289-300.
Notes preparer: Haim Bar
Controlling the probability of falsely rejecting the null hypothesis is critical for valid and meaningful statistical analysis. But how should this probability be defined and calculated when there are multiple, simultaneous hypotheses? For many years, this question was mostly investigated in the analysis of variance (ANOVA) setting, in which the number of comparisons is typically small or moderate. Until 1995, the common approach to this problem was to control the family-wise error rate (FWER) which ensures that the probability of falsely rejecting at least one of the hypotheses is smaller than a user-specified bound. However, the advent of high-throughput methods, such as in genetics, resulted in a much larger number of simultaneous hypotheses and rendered the FWER approach impractical, in the sense that it was too stringent and lacked power to reject any hypothesis.
In 1995, Benjamini and Hochberg published their breakthrough paper “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing” in which they defined the False Discovery Rate (FDR) as the expected proportion of falsely rejected hypotheses, out of the total number of rejected hypotheses. The paper proposed a very simple procedure to estimate the FDR, and showed that indeed, the procedure controls the FDR at the desired level. This approach enabled significant advances in many areas, and is particularly useful in this age of “Big Data”.
The paper appeared in the Journal of the Royal Statistical Society, Series B, Vol. 57, No. 1. (1995), pp. 289-300. For additional reading, we also suggest reading about the q-value in the paper “A direct approach to false discovery rates”, by John Storey, which appeared in 2002, in the Journal of the Royal Statistical Society, Series B, 64: 479-498.