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ESTIMATION PROCEDURES
1 Estimates of numbers of persons with particular characteristics were derived from the survey using a ratio estimation procedure which ensured that the survey estimates conform to an independently estimated distribution of the total population by age, sex and area. The benchmark for persons was the estimated resident population for 30 June 2003. The benchmark population included special dwellings and Australian defence force personnel, but excluded people from remote and sparsely settled areas of Australia.
2 The responses from persons in the cared-accommodation component and persons in the household component of the survey were weighted together, using factors to account for the different sampling fractions, in order to represent the entire Australian population.
3 The post-stratification weighting for person estimation used the variables:
- state or territory
- part of state - capital city or balance of state (Australian Capital Territory and Northern Territory are not split)
- age group (0-4, 5-9,...75-79, 80-84, 85+)
- sex (male or female).
RELIABILITY OF ESTIMATES
4 Since the estimates in this publication are based on information obtained from occupants of a sample of dwellings, they are subject to sampling variability, that is, they may differ from those that would have been produced if all dwellings had been included in the survey. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of dwellings was included. There are about two chances in three that a sample estimate will differ by less than one SE from the number that would have been obtained if all dwellings had been included, and about 19 chances in 20 that the difference will be less than two SEs. Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate.
5 The size of the SE increases with the level of the estimate, so that the larger the estimate the larger is the SE. However, it should be noted that the larger the sample estimate the smaller will be the SE in percentage terms (that is, the RSE). Thus, larger estimates will be relatively more reliable than smaller estimates. In the tables in this publication, only estimates with RSEs of 25% or less, and percentages based on such estimates, are considered sufficiently reliable for most purposes. However, estimates and percentages with RSEs between 25% and 50% have been included and are preceded by an asterisk (e.g. *3.4) to indicate that they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are also included and are preceded by a double asterisk (e.g. **0.1). Such estimates are considered too unreliable for general use.
CALCULATION OF STANDARD ERRORS
Standard error of an estimate
6 Included in this publication are tables which present an approximate SE for each estimate in the publication. Tables T1 to T4 below repeat the layout of the publication tables but rather than survey estimates, they contain estimates of the SEs or RSEs. For example, from Table 3 we see that 598,100 persons had a severe core activity limitation. Table T3 indicates that the standard error for this estimate is 21,990 (3.7%).
7 Therefore, there are about two chances in three that the actual number of persons with a core activity limitation was within the range 576,110 to 620,090 and about 19 chances in 20 that it was within the range 554,120 to 642,080.
Standard error of a proportion
8 Proportions and percentages formed from the ratio of two estimates are also subject to sampling error. The size of the error depends on the accuracy of both the numerator and the denominator. The formula for the RSE of a proportion or percentage is :
9 In using the formula, the numerator and the denominator will be estimates over subsets of the population. The formula is only valid when the set for the numerator is a subset of the set for the denominator.
10 The SE of an estimated percentage or rate, computed by using sample data for both numerator and denominator, depends on both the size of the numerator and the size of the denominator. However, the RSE of the estimated percentage or rate will generally be lower than the RSE of the estimate of the numerator.
11 An example from Table 3 is the proportion of persons with a disability who had a severe level of core activity limitation, 15%. The numerator, the number of persons with a severe level of core activity limitation, is 598,100. The denominator, the number of persons with a disability, is 3,951,000.
SE for 598,100 = 21,990 or 3.7% RSE
SE for 3,951,000 = 48,532 or 1.2% RSE
The difference of the RSE squares = 12.25
The square root of the difference is 3.5%, the RSE of the proportion.
Standard error of a difference
12 Published estimates may also be used to calculate the difference between two survey estimates (numbers or percentages). The difference between two survey estimates is itself an estimate and is therefore subject to sampling error. The SE of the difference between two survey estimates depends on the SEs of the original estimates and on the relationship (correlation) between the two original estimates. An approximate SE of the difference between two estimates (x-y) may be calculated using the following formula:
13 While this formula will only be exact for differences between separate and uncorrelated (unrelated) characteristics or sub-populations, it is expected to provide a good enough approximation for all of the differences likely to be of interest.
STANDARD ERROR TABLES
T1 RELATIVE STANDARD ERRORS FOR TABLE 1 |
|  |
| 1998
| 2003
| |
| Males | Females | Persons | Males | Females | Persons | |
| Age group (years) | % | % | % | % | % | % | |
| |
| 0-4 | 12.0 | 16.7 | 9.2 | 11.3 | 16.9 | 9.6 | |
| 5-14 | 4.2 | 6.3 | 3.2 | 5.7 | 8.3 | 4.8 | |
| 15-24 | 4.8 | 5.7 | 3.3 | 8.3 | 8.6 | 6.0 | |
| 25-34 | 4.1 | 4.6 | 2.8 | 5.2 | 6.7 | 4.5 | |
| 35-44 | 3.3 | 3.5 | 2.2 | 4.5 | 5.9 | 3.8 | |
| 45-54 | 2.8 | 2.8 | 3.3 | 4.3 | 3.5 | 3.0 | |
| 55-59 | 4.2 | 4.2 | 2.5 | 5.4 | 4.2 | 3.7 | |
| 60-64 | 3.7 | 4.2 | 2.0 | 4.7 | 4.3 | 3.3 | |
| 65-69 | 3.8 | 4.2 | 1.8 | 4.6 | 5.3 | 3.5 | |
| 70-74 | 3.5 | 3.5 | 0.2 | 3.9 | 3.9 | 2.3 | |
| 75-79 | 3.5 | 3.3 | 2.2 | 4.8 | 3.3 | 3.3 | |
| 80-84 | 4.7 | 3.3 | 2.5 | 2.8 | 3.0 | 1.9 | |
| 85 and over | 3.6 | 2.1 | 1.8 | 3.1 | 2.6 | 2.0 | |
| Total | 0.8 | 0.9 | 0.5 | 1.4 | 1.4 | 1.2 | |
| Total, age standardised | 1.2 | 1.5 | 0.8 | 1.4 | 1.4 | 1.2 | |
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T2 RELATIVE STANDARD ERRORS FOR TABLE 2 |
| |
| 1998
| 2003
| |
| Males | Females | Persons | Males | Females | Persons | |
| Age group (years) | % | % | % | % | % | % | |
| |
| 0-4 | 15.4 | 27.1 | 12.8 | 14.4 | 23.5 | 12.6 | |
| 5-14 | 6.7 | 10.4 | 5.2 | 9.7 | 12.9 | 8.3 | |
| 15-24 | 12.5 | 14.6 | 8.8 | 16.0 | 16.2 | 12.7 | |
| 25-34 | 11.1 | 11.1 | 7.1 | 15.3 | 12.8 | 9.9 | |
| 35-44 | 9.7 | 8.1 | 5.8 | 12.5 | 10.7 | 10.0 | |
| 45-54 | 7.2 | 6.5 | 4.5 | 10.6 | 9.6 | 7.4 | |
| 55-59 | 10.3 | 11.2 | 6.8 | 14.3 | 11.4 | 8.7 | |
| 60-64 | 12.0 | 11.1 | 7.3 | 13.8 | 11.7 | 8.1 | |
| 65-69 | 13.1 | 11.6 | 7.7 | 15.2 | 12.2 | 8.0 | |
| 70-74 | 11.1 | 8.6 | 5.8 | 9.1 | 9.7 | 6.5 | |
| 75-79 | 10.1 | 6.8 | 5.3 | 10.2 | 8.4 | 6.5 | |
| 80-84 | 12.0 | 6.5 | 5.4 | 10.9 | 6.3 | 5.3 | |
| 85 and over | 7.7 | 3.4 | 3.0 | 4.0 | 6.3 | 4.6 | |
| Total | 3.7 | 2.8 | 1.2 | 3.4 | 3.0 | 2.5 | |
| Total, age standardised | 4.3 | 3.7 | 1.5 | 3.4 | 3.0 | 2.5 | |
| |
T3 STANDARD ERRORS FOR TABLE 3 |
| |
| Profound core activity limitation | Severe core activity limitation | Moderate core activity limitation | Mild core activity limitation | Schooling or employment restriction | All with specific restrictions or limitations | All with disability | No reported disability | Total | |
MALES | |
| |
| 0-4 | 2,604 | 1,763 | 713 | - | . . | 2,916 | 3,366 | 3,366 | - | |
| 5-14 | 5,423 | 5,973 | 2,436 | 4,019 | 8,902 | 9,101 | 9,584 | 8,863 | 2,603 | |
| 15-24 | 3,366 | 3,709 | 2,512 | 4,212 | 8,602 | 8,751 | 10,577 | 11,539 | 6,133 | |
| 25-34 | 3,255 | 3,674 | 3,048 | 5,298 | 7,933 | 8,168 | 9,081 | 9,081 | - | |
| 35-44 | 3,759 | 3,625 | 4,768 | 5,538 | 8,519 | 8,669 | 9,715 | 9,715 | - | |
| 45-54 | 2,703 | 4,383 | 6,898 | 7,329 | 10,155 | 11,222 | 12,491 | 12,491 | - | |
| 55-59 | 1,673 | 3,809 | 5,551 | 5,268 | 7,418 | 8,849 | 9,079 | 9,158 | 652 | |
| 60-64 | 2,057 | 3,389 | 4,475 | 5,525 | 8,464 | 9,056 | 8,264 | 8,400 | 652 | |
| 65-69 | 2,981 | 3,109 | 5,061 | 5,750 | . . | 6,668 | 6,765 | 6,943 | 890 | |
| 70-74 | 2,719 | 2,545 | 3,747 | 5,162 | . . | 5,420 | 5,654 | 5,823 | 890 | |
| 75-79 | 3,683 | 2,770 | 4,033 | 5,752 | . . | 6,533 | 6,679 | 6,776 | 658 | |
| 80-84 | 2,679 | 3,020 | 2,885 | 5,044 | . . | 4,432 | 3,931 | 4,175 | 3,198 | |
| 85 and over | 2,362 | 1,763 | 2,133 | 4,421 | . . | 3,266 | 3,253 | 3,190 | 3,200 | |
| Total | 13,127 | 12,690 | 15,271 | 15,716 | 23,942 | 24,848 | 28,339 | 28,606 | 8,308 | |
FEMALES | |
| |
| 0-4 | 2,511 | 2,637 | 799 | 598 | . . | 3,756 | 4,026 | 4,026 | - | |
| 5-14 | 2,848 | 3,884 | 1,368 | 3,346 | 7,305 | 7,746 | 8,083 | 8,433 | 2,884 | |
| 15-24 | 3,035 | 3,366 | 2,563 | 4,489 | 7,373 | 8,461 | 10,735 | 11,971 | 4,366 | |
| 25-34 | 2,295 | 3,859 | 2,696 | 4,470 | 7,228 | 7,857 | 9,560 | 9,560 | - | |
| 35-44 | 1,950 | 4,255 | 4,684 | 5,283 | 10,920 | 11,188 | 12,104 | 12,104 | - | |
| 45-54 | 3,909 | 4,573 | 5,858 | 7,209 | 9,749 | 10,925 | 10,097 | 10,097 | - | |
| 55-59 | 2,533 | 3,916 | 5,984 | 7,413 | 7,153 | 8,489 | 7,487 | 7,487 | - | |
| 60-64 | 3,372 | 3,307 | 4,137 | 5,040 | 7,626 | 6,671 | 6,680 | 6,680 | - | |
| 65-69 | 2,891 | 3,352 | 4,665 | 4,815 | . . | 7,491 | 7,285 | 7,285 | - | |
| 70-74 | 3,277 | 4,734 | 4,557 | 5,442 | . . | 5,532 | 6,354 | 6,354 | - | |
| 75-79 | 4,710 | 3,706 | 4,129 | 5,138 | . . | 6,003 | 5,603 | 5,593 | 611 | |
| 80-84 | 4,088 | 5,243 | 2,976 | 3,892 | . . | 4,530 | 4,527 | 4,574 | 620 | |
| 85 and over | 7,352 | 2,577 | 6,318 | 4,329 | . . | 4,216 | 4,088 | 4,023 | 515 | |
| Total | 14,734 | 15,678 | 18,079 | 17,367 | 19,909 | 25,070 | 28,323 | 31,824 | 7,241 | |
PERSONS | |
| |
| 0-4 | 3,861 | 3,286 | 1,038 | 598 | . . | 4,512 | 5,119 | 5,119 | - | |
| 5-14 | 5,650 | 7,085 | 2,788 | 4,253 | 13,040 | 13,366 | 12,693 | 12,489 | 5,320 | |
| 15-24 | 5,015 | 5,267 | 3,549 | 5,647 | 10,553 | 11,757 | 15,013 | 17,014 | 8,835 | |
| 25-34 | 3,655 | 5,459 | 4,386 | 6,098 | 9,796 | 10,750 | 14,140 | 14,140 | - | |
| 35-44 | 4,888 | 5,810 | 6,338 | 8,435 | 15,962 | 15,349 | 16,028 | 16,028 | - | |
| 45-54 | 5,724 | 5,880 | 10,081 | 9,900 | 16,268 | 17,354 | 17,536 | 17,536 | - | |
| 55-59 | 2,680 | 5,763 | 8,211 | 7,504 | 10,617 | 13,084 | 12,691 | 12,724 | 652 | |
| 60-64 | 3,576 | 4,197 | 5,894 | 8,569 | 9,988 | 10,569 | 10,938 | 11,116 | 652 | |
| 65-69 | 3,640 | 4,218 | 6,689 | 7,274 | . . | 9,586 | 10,042 | 10,131 | 890 | |
| 70-74 | 4,736 | 5,071 | 6,049 | 6,788 | . . | 5,703 | 7,069 | 7,129 | 890 | |
| 75-79 | 5,724 | 5,070 | 6,295 | 7,607 | . . | 10,038 | 10,075 | 10,146 | 900 | |
| 80-84 | 5,705 | 5,930 | 4,062 | 6,852 | . . | 5,692 | 5,562 | 5,874 | 3,318 | |
| 85 and over | 7,531 | 3,360 | 7,289 | 6,136 | . . | 4,826 | 5,123 | 5,367 | 3,150 | |
| Total | 22,072 | 21,990 | 28,760 | 20,206 | 37,304 | 41,970 | 48,532 | 53,286 | 13,794 | |
| |
| . . not applicable |
| - nil or rounded to zero (including null cells) |
T4 STANDARD ERRORS FOR TABLE 4 |
| |
| | Profound core activity limitation | Severe core activity limitation | Moderate core activity limitation | Mild core activity limitation | Schooling or employment restriction | All with specific restrictions or limitations | All with disability | No reported disability | Total | |
| |
| Level of highest non-school qualification | | | | | | | | | | |
| Postgraduate Degree | 762 | 1,730 | 1,368 | 2,619 | 2,178 | 2,833 | 3,878 | 14,008 | 13,737 | |
| Graduate Diploma / Graduate Certificate | 608 | 2,558 | 2,118 | 2,694 | 4,212 | 5,027 | 5,659 | 14,885 | 15,776 | |
| Bachelor Degree | 3,281 | 4,227 | 5,504 | 6,228 | 7,599 | 10,564 | 12,993 | 35,782 | 37,891 | |
| Advanced Diploma / Diploma | 1,827 | 3,274 | 4,326 | 4,723 | 6,450 | 7,303 | 11,162 | 26,253 | 29,892 | |
| Certificate III / IV | 2,957 | 7,592 | 9,357 | 10,076 | 16,368 | 19,419 | 22,016 | 32,591 | 40,182 | |
| Certificate I / II | 1,276 | 1,890 | 2,502 | 2,116 | 3,511 | 4,353 | 5,154 | 11,764 | 13,971 | |
| Certificate not further defined | 1,451 | 2,014 | 2,127 | 2,602 | 3,995 | 4,577 | 5,726 | 10,821 | 12,506 | |
| No non-school qualification | 8,847 | 11,592 | 14,865 | 13,323 | 23,477 | 26,380 | 30,986 | 41,360 | 49,868 | |
| Level not determined | 209 | 1,441 | 1,649 | 1,583 | 3,246 | 3,619 | 4,058 | 7,520 | 8,492 | |
| Labour force status | | | | | | | | | | |
| Employed full-time | 2,575 | 4,708 | 8,209 | 8,662 | 14,110 | 16,410 | 20,541 | 49,020 | 50,137 | |
| Employed part-time | 2,026 | 4,933 | 5,864 | 9,144 | 14,643 | 16,690 | 16,925 | 42,729 | 47,066 | |
| Total employed | 3,090 | 7,147 | 10,149 | 14,115 | 20,832 | 25,624 | 29,666 | 39,032 | 46,794 | |
| Unemployed | 1,521 | 3,294 | 3,580 | 4,368 | 7,647 | 8,308 | 9,360 | 21,499 | 23,371 | |
| Total in the labour force | 3,559 | 8,589 | 10,792 | 16,597 | 22,557 | 27,975 | 32,925 | 42,505 | 45,942 | |
| Not in the labour force | 9,611 | 13,437 | 13,273 | 10,775 | 27,057 | 27,892 | 27,554 | 32,817 | 44,668 | |
| Total | 10,851 | 15,501 | 20,276 | 17,278 | 34,208 | 36,155 | 40,412 | 42,234 | 9,395 | |
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