Performance was measured on seven common psychoacoustical tasks for about 75 highly trained subjects. Because some psychoacoustical outcomes varied by race, the subjects were partitioned into White and Non-White categories for analysis. Sex, race, and menstrual-cycle differences in performance are described in a companion paper [McFadden, Pasanen, Maloney, Leshikar, and Pho (2018). J. Acoust. Soc. Am. 143, 2338-2354]. Also measured for all subjects were three types of otoacoustic emissions (OAEs): spontaneous otoacoustic emissions (SOAEs), click-evoked otoacoustic emissions (CEOAEs), and distortion-product otoacoustic emissions (DPOAEs). The experimental question was whether and how OAEs were correlated with psychoacoustical performance. In accord with past findings, the SOAEs and CEOAEs exhibited substantial sex and race differences, but the DPOAEs did not. Somewhat surprisingly, the correlations between OAEs and psychoacoustical performance were generally weak. No form of OAE was highly correlated with any psychoacoustical task for both sexes within a race category. Thus, there was no compelling evidence that the mechanisms underlying OAEs also contribute systematically to performance in any of the simultaneous or temporal masking tasks studied here. Especially surprising were the weak correlations between OAEs and detection of a tone in the quiet. Apparently individual differences in psychoacoustical performance reside more in post-cochlear (neural) mechanisms than in individual differences in the cochlear ("mechanical") mechanisms underlying the OAEs measured here.