Building on previous work linking changes in the electroencephalogram (EEG) spectral slope to arousal level, Lendner et al. (2021) reported that wake, non rapid eye movement (NREM) sleep and rapid eye movement (REM) sleep exhibit progressively steeper 30-45 Hz slopes, interpreted in terms of increasing cortical inhibition. Here we sought to replicate Lendner et al.'s scalp EEG findings (based on 20 individuals) in a larger sample of 11,630 individuals from multiple cohorts in the National Sleep Research Resource (NSRR). In a final analytic sample of N = 10,255 distinct recordings, there was unambiguous statistical support for the hypothesis that, within individuals, the mean spectral slope grows steeper going from wake to NREM to REM sleep. We found that the choice of mastoid referencing scheme modulated the extent to which electromyogenic or electrocardiographic artifacts were likely to bias 30-45 Hz slope estimates, as well as other sources of technical, device-specific bias. Nonetheless, within individuals, slope estimates were relatively stable over time. Both cross-sectionally and longitudinal, slopes tended to become shallower with increasing age, particularly for REM sleep; males tended to show flatter slopes than females across all states. Although conceptually distinct, spectral slope did not predict sleep state substantially better than other summaries of the high frequency EEG power spectrum (>20 Hz, in this context) including beta band power, however. Finally, to more fully describe sources of variation in the spectral slope and its relationship to other sleep parameters, we quantified state-dependent differences in the variances (both within and between individuals) of spectral slope, power and interhemispheric coherence, as well as their covariances. In contrast to the common conception of the REM EEG as relatively wake-like (i.e. 'paradoxical' sleep), REM and wake were the most divergent states for multiple metrics, with NREM exhibiting intermediate profiles. Under a simplified modelling framework, changes in spectral slope could not, by themselves, fully account for the observed differences between states, if assuming a strict power law model. Although the spectral slope is an appealing, theoretically inspired parameterization of the sleep EEG, here we underscore some practical considerations that should be borne in mind when applying it in diverse datasets. Future work will be needed to fully characterize state-dependent changes in the aperiodic portions of the EEG power spectra, which appear to be consistent with, albeit not fully explained by, changes in the spectral slope.