Current software makes it quite straightforward to estimate distributions whose parameters are a smooth function of continuous variable. A well-known example is growth charts determined by location, scale and shape parameters that evolve smoothly with age. When age-varying distributions of a variable of interest have been estimated for each of two populations, such as demographic or diagnostic groups, we may wish to use this information to test for group differences in an age-specific manner. Such tests might prove useful if, for example, a measure of brain structure tends to differ between children with and without a disorder, but only within a certain age range. We introduce a testing approach based on the age-varying Wasserstein distance between the estimated distributions, and apply it to data from a longitudinal magnetic resonance imaging study.