Comparisons of Australian Mental Health Distributions

Bayesian nonparametric estimates of Australian mental health distributions are obtained to assess how the mental health status of the population has changed over time, and to compare the mental health status of female/male and indigenous/non-indigenous population subgroups. First-order and secondorder stochastic dominance are used to compare distributions, with results presented in terms of the posterior probability of dominance and the posterior probability of no dominance. If a criterion for dominance is satisfied, then, in terms of that criterion, the mental health status of the dominant population is superior to that of the dominated population. If neither distribution is dominant, then the mental health status of neither population is superior in the same sense. Our results suggest mental health has deteriorated in recent years, that males' mental health status is better than that of females, and that non-indigenous health status is better than that of the indigenous population.