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Hypothesis tests for the presence of new sources of Poisson counts amidst background processes are frequently performed in high energy physics, gamma ray astronomy, and other branches of science. This talk briefly summarizes work in which we evaluate two classes of algorithms for dealing with uncertainty in the mean background in such tests. This talk briefly summarizes studies, performed with Robert Cousins and described in Ref. , of two methods for incorporating a systematic uncertaintydoi:10.5170/cern-2008-001.40 fatcat:6avpcy5qmvcopgn76dki3e3hsi