It has been shown that previously published [1] probability density functions (PDFs) for several common signal-to-noise ratio (SNR) definitions are simply minor algebraic variants of the noncentral t distribution- based PDF results recently published by Nadarajah and Kotz [2]. The previously published, but unevaluated, integral expression for the PDF of quotients of SNRs has been shown to be in excellent quantitative agreement with Monte Carlo results. Furthermore, it has been shown that the same integral expression also yields the PDF for quotients of relative standard deviations (RSDs) and the PDF for quotients of simple detection limits. The latter was validated by comparison with detailed Monte Carlo simulations, with the result that accurate expectation values and detection limit 95% confidence intervals were obtained. As a consequence, a major step has been taken toward the goal of being able to compare simple detection limits on a fair basis and being able to perform a statistical test, precisely analogous to a standard F test, to determine whether a given pair of experimental detection limits are plausibly from the same chemical measurement system with the same measurement system parameters and measurement protocol
