  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. 2 sigma, or at the 95% confidence level. When using FDR,
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 when
conducting multiple hypothesis tests.
