Australian Bureau of Statistics
Celebrating the International Year of Statistics 2013

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CALCULATING FINAL ERP

8.11 To address the issues of the high standard errors on the preliminary undercount rates (using the five group method) and high sampling error for the state/territory ERP estimates, particularly the high Indigenous undercount in Western Australia (a single-state group) the Empirical Bayes method was applied for final ERP.


Empirical Bayes estimation

8.12 The Empirical Bayes method was applied to the undercount adjustment rate for 15 regions (each state and the Northern Territory split into capital city and balance of state/territory, and the Australian Capital Territory). The undercount adjustment rate is the ratio between the PES estimate of the Indigenous population and the value obtained from the Census after assigning an Indigenous status to records where it was unknown (as described in paragraph 8.3). The Empirical Bayes method assigned each state and territory a mix of its own PES estimate of the undercount adjustment rate, and an overall estimate based on the 15 regions mentioned above..

8.13 The mix used was dependent on the standard error of the PES estimate, with regions having high standard errors being more influenced by the overall estimate, while regions with lower standard errors receive a greater proportion of their individual region estimate.

8.14 The overall amount of smoothing used was determined by a smoothing constant. The ABS used the 'method of moments' constant from a technique developed by Morris (1983), after checking that the indicated value gave estimates with a suitably low standard error conditional on the chosen constant. For more information on Empirical Bayes and its use in estimating the Indigenous population, see Appendix 2 - Empirical Bayes estimation of Indigenous undercount.

8.15 Estimates of the Indigenous population of the states and territories for 8 August 2006, as a result of adopting the Empirical Bayes method, are shown in the table below.

8.1 Results from Empirical Bayes estimation(a), States and territories
	Census count (b)	Indigenous population at Census date			Undercount rate
	no.	no.	Standard error	Relative standard error (%)	%	Standard error (%)
New South Wales	138 505	151 510	5 707	3.8	8.6	3.4
Victoria	30 144	33 266	976	2.9	9.4	2.7
Queensland	127 581	144 375	4 289	3.0	11.6	2.6
South Australia	25 556	27 954	895	3.2	8.6	2.9
Western Australia	58 710	70 371	2 669	4	16.6	3.2
Tasmania	16 767	18 386	510	2.8	8.8	2.5
Northern Territory	53 662	63 864	1 764	2.8	16.0	2.3
Australian Capital Territory	3 874	4 250	118	2.8	8.9	2.5
Australia(c)	454 799	513 977	13 309	2.6	11.5	2.3
(a) Conditional on the method of movements value of A = 0.0044142.
(b) With no imputation.
(c) Excludes Other Territories.

8.16 Estimates of the Indigenous (and non-Indigenous) population were then adjusted to include RTOs and backdated to 30 June 2006 using data on births, deaths, overseas and interstate migration. However, for the Other Territories (which are not included in the PES), a combined net undercount estimate for New South Wales and the Australian Capital Territory was applied to the Census count of Indigenous people identified as being usually resident in those territories. This estimate is used as the majority of Indigenous people in the Other Territories reside in Jervis Bay Territory.


Sub-state/territory Indigenous estimates

8.17 The PES is the best available data source for determining what the Indigenous population should have been on Census Night, if the whole population was counted. However, as standard errors on the PES are too high for producing reliable estimates of the Indigenous population at sub-state/territory levels, Census is the only data source for calculating estimates of the Indigenous population for geographic areas smaller than a state or territory.

8.18 In producing estimates of the Indigenous and non-Indigenous populations of SLAs, PES estimates produced by the Empirical Bayes method for each state/territory were used as upper level constraints on the SLA-level Indigenous populations as at Census Night. State/territory net undercount was distributed pro rata to individual SLAs, having regard to capital city/balance of state/territory undercount for the total population according to their demographic characteristics such as age and sex.

8.19 At the sub-state/territory level, differences between Census counts and estimates of the Indigenous population are not indicative of, nor should be interpreted as, the true level of undercount; rather, these differences are a by-product of the assumptions that contribute to the estimation process.

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