A framework is presented for characterizing the statistical properties of frequency-domain measurements. The correlation between the variance in the complex impedance and the variances in the complex current and voltage are examined by means of a Taylor series expansion for the impedance. Both sufficient-only and necessary and sufficient conditions for equality of the variances of real and imaginary impedance are identified and verified using stochastic simulations of techniques commonly employed in frequency-domain measurements. (C) 2003 The Electrochemical Society.