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**Controlling the False Discover Rate in Astrophysical Data Analysis**

**Christopher J. Miller, Christopher Genovese, Robert C. Nichol,
Larry Wasserman, Andrew Connolly, Daniel Reichart, Andrew Hopkins,
Jeff Schneider and Andrew Moore**

### Abstract:

The False Discovery Rate (FDR) is a new statistical procedure to
control the number of mistakes made when performing multiple
hypothesis tests, i.e. when comparing many data against a given model
hypothesis. The key advantage of FDR is that it allows one to *a
priori* control the average fraction of false rejections made (when
comparing to the null hypothesis) over the total number of rejections
performed. We compare FDR to the standard procedure of rejecting all
tests that do not match the null hypothesis above some arbitrarily
chosen confidence limit, *e.g.* , or at the 95%
confidence level. We find a similar rate of correct detections, but
with significantly fewer false detections. Moreover, the FDR
procedure is quick and easy to compute and can be trivially adapted
to work with correlated data. The purpose of this paper is to
introduce the FDR procedure to the astrophysics community. We
illustrate the power of FDR through several astronomical examples,
including the detection of features against a smooth one-dimensional
function, *e.g.* seeing the ``baryon wiggles'' in a power
spectrum of matter fluctuations, and source pixel detection in
imaging data. In this era of large datasets and high precision
measurements, FDR provides the means to adaptively control a
scientifically meaningful quantity - the number of false discoveries
made conducting multiple hypothesis tests.

*Heidi Sestrich*

*8/1/2001*
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