About 95% of right-handers and 70% of left-handers have a left-hemispheric specialization for language. Dichotic listening is often used as an indirect measure of this language asymmetry. However, while it reliably produces a right-ear advantage (REA), corresponding to the left-hemispheric specialization of language, it paradoxically often fails to obtain statistical evidence of mean differences between left- and right-handers. We hypothesized that non-normality of the underlying distributions might be in part responsible for the similarities in means. Here, we compare the mean ear advantage scores, and also contrast the distributions at multiple quantiles, in two large independent samples (Ns = 1,358 and 1,042) of right-handers and left-handers. Right-handers had an increased mean REA, and a larger proportion had an REA than in the left-handers. We also found that more left-handers are represented in the left-eared end of the distribution. These data suggest that subtle shifts in the distributions of DL scores for right- and left-handers may be at least partially responsible for the unreliability of significantly reduced mean REA in left-handers.