Development of appropriate models for the interpretation of impedance spectra in terms of physical properties re quires, in addition to insight into the chemistry and physics of the system, an understanding of the measurement error structure. The time-varying character of electrochemical systems has prevented experimental determination of the stochastic contribution to the error structure. A method is presented by which the stochastic contribution to the error structure can be determined, even for systems for which successive measurements are not replicate. Although impedance measurements are known to be heteroskedastic in frequency (i.e., have standard deviations that are functions of frequency) and time varying over the duration of the experiment, the analysis conducted in the impedance plane suggests that the standard deviations for the real and imaginary parts of the impedance have the same magnitude, even at frequencies at which the imaginary part of the impedance asymptotically approaches zero. On this basis, a general model for the error structure was developed which shows good agreement for a broad variety of experimental measurements.