Educational achievement distributions for Australian indigenous and nonindigenous populations in the years 2001, 2006, 2014 and 2017 are considered. Bayesian inference is used to analyse how these ordinal categorical distributions have changed over time and to compare indigenous and nonindigenous distributions. Both the level of educational achievement and inequality in educational achievement are considered. To compare changes in levels over time, as well as inequality between the two populations, first order stochastic dominance and an index of educational poverty are used. To examine changes in inequality over time, two inequality indices and generalised Lorenz dominance are considered. Results are presented in terms of posterior densities for the indices and posterior probabilities for dominance for the dominance comparisons. We find some evidence of improvement over time, especially in the lower parts of the indigenous distribution and that inequality has significantly increased from 2001 to 2017.
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