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In many analyses in high energy physics, attempts are made to remove theeffects of detector smearing in data by techniques referred to as "unfolding"histograms, thus obtaining estimates of the true values of histogram bincontents. Such unfolded histograms are then compared to theoreticalpredictions, either to judge the goodness of fit of a theory, or to compare theabilities of two or more theories to describe the data. When doing this, eveninformally, one is testing hypotheses. However, a more fundamentally sound wayto test hypotheses is to smear the theoretical predictions by simulatingdetector response and then comparing to the data without unfolding; this isalso frequently done in high energy physics, particularly in searches for newphysics. One can thus ask: to what extent does hypothesis testing afterunfolding data materially reproduce the results obtained from testing bysmearing theoretical predictions? We argue that this "bottom-line-test" ofunfolding methods should be studied more commonly, in addition to commonpractices of examining variance and bias of estimates of the true contents ofhistogram bins. We illustrate bottom-line-tests in a simple toy problem withtwo hypotheses.

Should unfolded histograms be used to test hypotheses?