Steady-state evoked potentials are often characterized by the amplitude and phase of the Fourier component at one or more frequencies of interest. We introduce a new statistic for the evaluation of these Fourier components. This statistic, denoted T2circ, is based on the same physiologic assumptions concerning the sources of variability of a Fourier component that are made in the use of the Rayleigh phase-coherence statistic as well as the standard T2 statistic (Hotelling 1931) for multivariate data. However, the T2circ statistic also exploits the relationship between the real and imaginary components of Fourier estimates, which is not exploited by T2, and utilizes amplitude information, which is ignored by the Rayleigh criterion. For these reasons, the T2circ statistic is more efficient than previously-used criteria for detection and quantitation of steady-state responses, both in principle and in practice.