One of the fundamental problems in the analysis of experimental data is determining the statistical significance of a putative signal. Such a problem can be cast in terms of classical “hypothesis testing”, where a null hypothesis describes the background and an alternative hypothesis characterizes the signal as a perturbation of the background. This testing problem is often addressed by a chi- square goodness-of-fit or a likelihood ratio test (LRT) statistic. In general, the former does not yield good power in detecting the signal and the latter has lacked an analytically tractable reference distribution required to calibrate a test statistic. Pilla and Loader have introduced a new test statistic based on “perturbation theory” to detect the presence of a signal. We review its reference distribution, which has an elegant geometrical interpretation and broad applicability, and note the connection with the LRT. We illustrate the technique in the context of a model problem from particle physics: the search for a new particle resonance. Mont-Carlo results demonstrate that the proposed score test is significantly more powerful, resulting in a higher rate of signal detection when a signal is present in the data.