In an experimental design involving replicate time series, on a number of experimental units, we consider the statistical problem of modelling the signal-to-noise ratio (SNR) of a number of sinusoidal features of interest, observed in the presence of nuisance sinusoids and non-white Gaussian errors. Based on local spectral F statistics, we introduce non-central F mixed effect models to assess and characterize the variability in the SNRs over units and experimental conditions. We apply these non-central F mixed models to the analysis of distortion product otoacoustic emissions (DPOAEs), retrograde sinusoidal pressure variations produced in the nonlinear cochlea by two-tone stimulation. Due to the narrowband nature of both the evoking stimuli and the emission, DPOAEs potentially represent a non-behavioural analogue of the pure-tone audiogram. However, substantial inter- and intra-subject variability currently limits their diagnostic validity. We model the cubic distortion product, the strongest such DPOAE, in a sample of 15 normal-hearing subjects. Our results demonstrate the ability to detect established gender- and evoking stimuli-dependent features, while being able to characterize the inter- and intra-subject variability. A demonstration that these methods can be readily applied to healthy patient populations indicates their utility in studying clinical populations.