Very large gaps exist between Indigenous and non-Indigenous Australians in the areas of income, educational achievement, health and life expectancy. Cognitive abilities may be related to differences in social attainment. The authors used data on four and five year olds from the Longitudinal Survey of Australian Children, focussing on the Peabody Picture Vocabulary Test and the 'Who Am I?' test. The results suggested that that a typical Indigenous five year old has a similar test score to a non-Indigenous four year old. One-third to two-thirds of the test score gaps seemed to be due to socio-economic differences such as income and parents education. A review of the literaure implies that these gaps may widen during school years. This has ramifications for developing policies that aim to improve educational opportunities for Indigenous children.