Comparisons of distributions of Australian mental health scores

Bayesian non-parametric estimates of Australian distributions of mental health scores 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 Aboriginal/non-Aboriginal population subgroups. First-order and second-order 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-Aboriginal health status is better than that of the Aboriginal population.