Australian Bureau of Statistics
Celebrating the International Year of Statistics 2013

APPENDIX 1 CONFIDENCE INTERVALS


ESTIMATING SAMPLE ERROR

This appendix describes the basis for estimating the sample error of estimates of Indigenous life expectancy at birth and for assessing the sensitivity of this life expectancy to assumptions made when calculating it. Broadly, a process of replication was used where the inputs to the Indigenous life expectancy calculations were replicated based on sample error information obtained from the Post Enumeration Survey (PES) and on plausible deviations from the assumptions. Variation between the replicate estimates of Indigenous life expectancy corresponding to replicate estimates from PES gave estimates of the sample error of life expectancy and the additional variation from deviations from the assumptions measured the sensitivity of the method to the assumptions.

The immediate inputs to Indigenous life expectancy are:

• Indigenous estimated resident population (ERP) at 30 June 2006 by 5-year age groups; and
• Indigenous deaths for 2005-2007 adjusted for differences in reporting Indigenous status.

The method of calculating Indigenous ERP is described in Experimental Estimates of Aboriginal and Torres Strait Islander Australians, Jun 2006 (cat. no. 3238.0.55.001). The method of adjusting Indigenous deaths for differential identification is given in Chapter 3: Data linkage to derive Indigenous deaths identification rates.

The inputs to the calculation of Indigenous ERP are:

• Census counts at fine levels;
• estimates of total population (both Indigenous and non-Indigenous) at intermediate levels; and
• estimates of Indigenous population at broad levels.

The main input for adjusted Indigenous deaths are Indigenous deaths registered during 2005-2007, modified using the Indigenous deaths identification rate [previously referred to as the coverage rate in Discussion Paper: Assessment of Methods for Developing Life Tables for Aboriginal and Torres Strait Islander Australians, 2006 (cat. no. 3302.0.55.002)]. This adjusts the Indigenous status of death registrations to correspond to the Indigenous status in ERP, which is as reported in PES. The identification rate is calculated from a probabilistic linking of death registrations between August 2006 and June 2007 to the 2006 Census and from PES data. The inputs are:

• number of deaths in linked records reported as Indigenous in death registrations, by state/territory;
• number of deaths in linked records by Census Indigenous status, by state/territory;
• propensity of being Indigenous in PES given Census Indigenous status = 'Indigenous', by state/territory; and
• propensities of being Indigenous in PES given Census Indigenous status = 'non-Indigenous' and 'not stated'.

Estimates of the total and Indigenous populations incorporate components of PES undercount adjustment and the propensities are calculated from PES, and so the sample error in PES generates sample error in Indigenous life expectancy. Standard errors (SEs) were calculated by replication of PES inputs, based on estimated PES sampling error.

Note that PES data are weighted to estimate the propensities but unweighted data were used in the discussion paper.


ESTIMATING SENSITIVITY ERROR

In calculating and applying the identification rate the following assumptions were made:

• identification rates for unlinked deaths were assumed to be the same as those for linked deaths;
• identification rates for 2005-2007 were assumed to be the same as those observed for August 2006 to June 2007;
• identification rates were assumed to apply uniformly across age and sex;
• propensities for Indigenous identification in the Census and PES were assumed to be applicable to death registrations, in spite of the different age distributions; and
• Census/PES non-Indigenous and not stated propensities for Australia were assumed to apply uniformly across states/territories.

There was no direct information on possible deviation from the first two assumptions, but deviations within plus or minus five percentage points of identification rate for each state were used for the first assumption, and within plus or minus two percentage points for each age, sex and state for the second assumption. Data from the linked file and PES were analysed to give ranges of deviations in identification rates for the last three assumptions.


RESULTS

The 95% confidence intervals for Indigenous life expectancy at birth estimates from the sensitivity analysis and sample error are given in Table A1.1 below.

A1.1 Confidence intervals for Indigenous life expectancy at birth - 2005-2007
			95% confidence intervals
		Life expectancy at birth	Sensitivity error(a)	Sample error
State/territory		years	years	years
Males
	NSW	69.9	67.9-71.9	68.6-71.2
	Qld	68.3	66.8-69.8	67.3-69.3
	WA	65.0	63.4-66.6	63.8-66.2
	NT	61.5	60.1-62.9	60.5-62.5
	Aust.(b)	67.2	65.8-68.6	66.3-68.1
Females
	NSW	75.0	73.3-76.7	73.9-76.1
	Qld	73.6	72.3-74.9	72.8-74.4
	WA	70.4	68.9-71.9	69.4-71.4
	NT	69.2	67.9-70.5	68.4-70.0
	Aust.(b)	72.9	71.7-74.1	72.1-73.7
(a) Sensitivity to assumptions. Includes sample error.
(b) Includes all states and territories.

The 95% confidence intervals for Indigenous deaths identification rates from the sensitivity analysis and sample error are given in Table A1.2 below.

These errors are produced during the process of calculating the errors for life expectancy, but because the sensitivity errors are applied at a finer level than the sample errors, the process for aggregating them to state level was slightly different.

A1.2 Confidence intervals for Indigenous deaths identification rates - 2005-2007
		95% confidence intervals
	Identification rate	Sensitivity error(a)	Sample error
State/territory	no.	no.	no.
NSW	0.87	0.73-1.01	0.80-0.95
Qld	0.94	0.84-1.05	0.89-1.00
WA	1.11	1.01-1.22	1.06-1.16
NT	1.09	1.01-1.16	1.07-1.10
Aust.(b)	0.92	0.83-1.01	0.87-0.97
(a) Sensitivity to assumptions. Includes sample error.
(b) Includes all states and territories.