A comparison of t test, F test, and coherence methods of detecting steady-state auditory-evoked potentials, distortion-product otoacoustic emissions, or other sinusoids

Sinusoids in background noise can conveniently be detected using unsegmented power spectra, comparing power at the signal frequency to average power at several neighbor frequencies. In this case, the F test is preferable to t tests based on rms or dB values, because of the skewed distributions of rms and dB when signal-to-noise ratio (SNR)=0. F-test performance improves as the number of frequencies increases, to about 15, but can be degraded if the background noise is not white, with a slope exceeding about 10dB for the range of frequencies sampled. Segment analysis, using magnitude-squared coherence (MSC) or related statistics, has equivalent statistical power; MSC and F each yield unbiased SNR estimates that have identical distributions when SNR=0. Selection of F or MSC for detection of sinusoids will usually be a matter of convenience.