Using data from the US National Longitudinal Survey of Youth, and fitting family fixed-effects models of child health and cognitive development, we test if left-handed children do significantly worse than their right-handed counterparts. The health measures cover both physical and mental health, and the cognitive development test scores span (1) Memory, (2) Vocabulary, (3) Mathematics, (4) Reading and (5) Comprehension. We find that while left-handed children have a significantly higher probability of suffering an injury needing medical attention, there is no difference in their experience of illness or poor mental health. We also find that left-handed children have significantly lower cognitive development test scores than right-handed children for all areas of development with the exception of reading. Moreover, the left-handedness disadvantage is larger for boys than girls, and remains roughly constant as children grow older for most outcomes. We also find that the probability of a child being left-handed is not related to the socioeconomic characteristics of the family, such as income or maternal education. All these results tend to support a difference in brain functioning or neurological explanation for handedness differentials rather than one based on left-handed children living in a right-handed world.