  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.
