Objective response detection in the frequency domain.

Several different and related measures have been proposed for objective response detection in the frequency domain. We compared magnitude-squared coherence (MSC) to phase coherence (PC) using simulations with specified signal-to-noise ratios (SNRs) and varying numbers of subaverages; the performance measure was area under a receiver operating characteristic (ROC) curve. MSC was superior to PC; test time required for equivalent performance is about 3 times greater for PC than for MSC. MSC performance for a given final SNR increased with the number of subaverages, but reached a plateau at 16 subaverages. Simulations of noise non-stationarity (high-amplitude noise in some subaverages compared to the others) led to decreased performance advantage for MSC over PC. However, weighted averaging restored this advantage. MSC is shown to be a simple algebraic transform of Victor and Mast's (1991) "circular T2" statistic and of two earlier statistics; all have identical statistical power.