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3238.0.55.001 - Experimental Estimates of Aboriginal and Torres Strait Islander Australians, Jun 2006 Quality Declaration 
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TECHNICAL NOTE ESTIMATED ABORIGINAL AND TORRES STRAIT ISLANDER AUSTRALIAN RESIDENT POPULATION – METHOD OF CALCULATION


INTRODUCTION

1 This technical note outlines the method by which the Australian Bureau of Statistics (ABS) used data from the 2006 Census of Population and Housing and Census Post Enumeration Survey (PES) to produce final rebased estimates of the Aboriginal and Torres Strait Islander (Indigenous) population for 30 June 2006.


THE CENSUS POST ENUMERATION SURVEY

2 While every effort is made to ensure full coverage of people and dwellings in Australia in the census, small numbers of people will inevitably have been missed while others will have been counted more than once. In Australia more people are missed from the census than are counted more than once. The net effect of overcount and undercount is called net undercount.

3 To measure net undercount of the Australian population, the ABS conducts the PES shortly after the census. The PES is a sample survey that provides an independent check of census coverage. In 2006, the survey had a sample of around 40,000 households (approximately 88,000 persons). In PES processing, the survey information from the PES dwelling is matched against corresponding census forms for either the same census dwelling, or for a dwelling nominated by the PES respondent as a likely census night address, to determine whether each resident of the PES household was counted in the census. The PES also provides information about the consistency of data across the two collections.

4 The 2006 PES introduced several methodological changes including extending the scope of the survey to remote areas of Australia and discrete Indigenous communities. A new estimation method was also introduced. For more details on the PES, see Census of Population and Housing - Undercount, 2006 (cat. no. 2940.0), Information Paper: Measuring Net Undercount in the 2006 Population Census, 2007 (cat. no. 2940.0.55.001), Research Paper: An Estimating Equation Approach to Census Coverage Adjustment, May 2007 (cat. no. 1351.0.55.019) and Census of Population and Housing - Details of Undercount, Aug 2006 (cat. no. 2940.0).


Net undercount

5 The PES estimate of the Indigenous population at the time of the 2006 census was 514,000 people. This compares with the census count for Australia (excluding Other Territories) of 454,800 Indigenous people. This census count of Indigenous people excludes people whose Indigenous status was unknown in the census (see below). The Indigenous net undercount (the difference between the PES Indigenous population estimate and the actual Indigenous population census count) was 59,200 persons.

Net undercount, Indigenous status - 2006(a)

PES estimate(b)
Census count
Net undercount(c)
Undercount
adjustment
factor
(d)
no.
no.
no.
no.

Indigenous
513 977
454 799
59 178
1.130
Non-Indigenous
19 888 482
18 264 880
1 623 602
1.089
Not stated
. .
(e)1 133 294
. .
. .
Total
20 402 459
19 852 973
549 486
1.028

. . not applicable
(a) Excludes Other Territories.
(b) PES estimates of the population that should have been counted in the 2006 census.
(c) Difference between PES estimate and the census count.
(d) Ratio of the PES estimate to the census count.
(e) Census records where Indigenous status was unknown because the census form was not received or only partially completed.



UNKNOWN INDIGENOUS STATUS

6 There were 1,133,300 census records (5.7% of the total census count) with unknown Indigenous status in the 2006 census. Of these, 29% (or 1.7% of the total census count) were a result of item non-response; that is, the ABS received a partially completed census form for the person but with the Indigenous status question unanswered. The remaining and majority (71%) of records with unknown Indigenous status (4.1% of the total census count) were a result of imputation by the ABS for people who were identified as resident in dwellings (both private and non-private) at the time of the census but for whom no census form was received. While some of the records with unknown Indigenous status will be for people of Aboriginal and/or Torres Strait Islander origin and others for non-Indigenous people, no imputation was made for Indigenous status on the census file. For a detailed discussion of unknown Indigenous status in the 2006 census see Commentary: Interpreting the data in the ABS publication Population Distribution, Aboriginal and Torres Strait Islander Australians, 2006 (cat. no. 4705.0).


CALCULATING ESTIMATED RESIDENT POPULATION - PRELIMINARY

7 Estimated resident population (ERP) for Australia and the states and territories are compiled using the census, PES and other demographic information.

8 The census provides detailed information on the age and sex structure and location of the population, but it misses some people who should have been counted in the census. In addition, while census records with unknown Indigenous status remain not stated on the census file, for the purposes of population estimation they are allocated to either Indigenous or non-Indigenous according to the distribution of stated responses within each age group, sex, census form type and geographic area (Statistical Local Area).

9 Preliminary PES estimates of net undercount for Indigenous persons in the 2006 census were used at the national level and for five jurisdictional groups. These were:
  • New South Wales/Australian Capital Territory;
  • Victoria/South Australia/Tasmania;
  • Queensland;
  • Western Australia; and
  • Northern Territory.

10 Some level of geographic grouping was considered necessary because of the high sampling error for some states/territories.

11 The geographic level to which the 2006 PES results were disaggregated for ERP purposes was determined after consideration of the sampling error and possible bias resulting from the groupings. The Relative Standard Error (RSE) of the estimates of the Indigenous population in the five jurisdictional groups ranged from 3.5% for the Northern Territory (NT) to 7.3% for Western Australia (WA). The RSE for Australia (excluding Other Territories) was 2.6%.


CALCULATING ESTIMATED RESIDENT POPULATION - FINAL

12 The method for calculating PES estimates used for preliminary ERP was subsequently reviewed by ABS. The standard errors on the preliminary undercount rates (using the 5 group method) were high, leading to high sampling error for the state/territory ERP estimates. In particular the high Indigenous undercount in WA (a single-state group) was subject to very high sampling error which limited the confidence that could be placed in the estimates.

13 In light of these concerns, a study was undertaken to determine a way of producing more reliable Indigenous undercount adjustment rates for individual states/territories than were available by using a single smoothed undercount adjustment (as was done in 2001) or by using PES estimates separately for individual states/territories or for state/territory groups. The result of the study was that an Empirical Bayes method was chosen.


Empirical Bayes estimation

14 The Empirical Bayes method was applied to the undercount adjustment rate for 15 regions (each state and the NT split into capital city and balance of state, and the Australian Capital Territory (ACT)). 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). The Empirical Bayes method assigned each region a mix of its own PES estimate of the undercount adjustment rate, and an overall estimate based on all the regions.

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

16 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 the method of moments estimator see Everson (2007, p.54).

17 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.

Results from Empirical Bayes estimation, State/territory(a)

Census count
(no imputation)
Indigenous population
at Census date
Undercount rate
no.
no.
Standard error
Relative standard error (%)
%
Standard error (% pts)

NSW
138 505
151 510
5 707
3.77
8.58
3.44
Vic.
30 144
33 266
976
2.93
9.39
2.66
Qld
127 581
144 375
4 289
2.97
11.63
2.63
SA
25 556
27 954
895
3.20
8.58
2.93
WA
58 710
70 371
2 669
3.79
16.57
3.16
Tas.
16 767
18 386
510
2.77
8.81
2.53
NT
53 662
63 864
1 764
2.76
15.97
2.32
ACT
3 874
4 250
118
2.77
8.85
2.53
Australia
454 799
513 977
13 309
2.59
11.51
2.29

(a) Conditional on the method of movements value of the smoothing constant.


18 Estimates of the Indigenous (and non-Indigenous) population were then adjusted to include Australian residents temporarily overseas at the time of the census (8 August 2006) and backdated to the estimated resident population reference date of 30 June 2006 using data on births, deaths, and interstate and overseas migration. Estimates were also assumed for net undercount in Other Territories, which were added to the census count of Indigenous people identified as being usually resident in those territories. At the national level, this resulted in a net increase of 3,100 from the 2006 PES estimate of 514,000 Indigenous people (excluding Other Territories) at 8 August 2006 to the final estimate of the resident Indigenous population at 30 June 2006 of 517,000 (including Other Territories).

19 The table below shows final Indigenous ERP compared with preliminary Indigenous ERP, as well as projections of the Indigenous population based on results of the 2001 census, for 30 June 2006. For Australia, the final estimates are around 150 persons lower than the preliminary estimate. The WA estimate has the highest numeric change, decreasing by 7,000 or 8.9%. Other states/territories with large changes are NSW (up by 4,500 or 3.0%), Victoria (up by 2,700 or 8.7%) and Tasmania (up by 1,500 or 9.0%).

Experimental Indigenous ERP, State/territory, Preliminary and final rebased - 30 June 2006

Indigenous ERP
Indigenous projections(a)
Preliminary
Final
Difference
Low series
High series
no.
no.
no.
%
no.
no.

NSW
148 178
152 685
4 507
3.04
146 159
163 141
Vic.
30 839
33 517
2 678
8.68
30 988
35 031
Qld
146 429
144 885
-1 544
-1.05
139 527
151 825
SA
26 044
28 055
2 011
7.72
28 105
29 550
WA
77 928
70 966
-6 962
-8.93
72 243
77 113
Tas.
16 900
18 415
1 515
8.96
18 586
18 982
NT
66 582
64 005
-2 577
-3.87
61 232
61 886
ACT
4 043
4 282
239
5.91
4 396
5 115
Australia(b)
517 174
517 043
-131
-0.03
501 479
542 886

(a) Projected Indigenous population at 30 June 2006, based on 2001 Census.
(b) Includes Other Territories.


20 The final Indigenous ERP for 30 June 2006 (517,000 persons) was higher than the 8 August 2006 census count (454,800 persons). This difference (up 13.7% or 62,200 persons) represents the combined and net effects of census net undercount (including people whose Indigenous status was unknown in the census), residents temporarily overseas on census night, demographic adjustments, and backdating to 30 June. The highest proportional increases from census count to final ERP were in WA (up 20.9%) and the NT (up 19.3%).


Sub-state/territory Indigenous estimates

21 The PES is the best available data source for determining what the Indigenous population should have been on census night, if the complete population was counted. However, as standard errors on the PES are too high for reliable estimates of the Indigenous population to be produced 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.

22 In producing estimates of the Indigenous and non-Indigenous populations of Statistical Local Areas (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 undercount for the total population according to their demographic characteristics such as age and sex.

23 It is important to note that 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.


Plans for further output

24 A time series of Indigenous population estimates and projections is scheduled for release in August 2009 in Experimental Estimates and Projections, Aboriginal and Torres Strait Islander Australians, 1991 to 2021 (cat. no. 3238.0).


FURTHER INFORMATION

25 Related ABS publications and references that may be of interest to users of this product include:

REFERENCES

26 Other references that may be of interest are:
  • Everson, P. (2007). A Statistician reads the sports pages, Stein's Paradox Revisited. Chance. Vol. 20 (Issue 3):49-56.
  • Morris, C. (1983). Parametric Empirical Bayes Inference: Theory and Applications. Journal of the American Statistical Association. 78(381): 47-55.


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