
WEIGHTING, BENCHMARKING, ESTIMATION AND STANDARDISATION
Weighting
1 Weighting is the process of adjusting results from a sample survey to infer results for the total population. To do this, a 'weight' is allocated to each sample unit. The weight is a value which indicates how many population units are represented by the sample unit.
2 The first step in calculating weights for the total sample of Indigenous persons in the 2001 National Health Survey (NHS) was to assign an initial weight. Initial weights were based on whether the respondent was selected in the main NHS or the supplementary Indigenous sample. A person's initial weight was calculated as the inverse of the probability of being selected in their respective sample. For example, if the probability of a person being selected in the supplementary sample was 1 in 600, then the person would have an initial weight of 600 (i.e. they represent 600 others).
Benchmarking
3 The initial weights were calibrated to align with independent estimates of the population of interest, referred to as 'benchmarks', in designated sex by age and area of usual residence categories. Weights calibrated against population benchmarks compensate for over or underenumeration of particular categories of persons and ensure that the survey estimates conform to the independently estimated distribution of the population by age, sex and area of usual residence, rather than to the distribution within the sample itself.
4 The Indigenous component of the 2001 NHS was benchmarked to the estimated Indigenous population at 30 June 2001 based on results from the 2001 Census of Population and Housing.
Estimation
5 Survey estimates of counts of persons are obtained by summing the weights of persons with the characteristic of interest. Estimates of nonperson counts (e.g. days away from work, millilitres of alcohol consumed) are obtained by multiplying the characteristic of interest with the weight of the reporting person and aggregating.
Standardisation
6 Age standardisation techniques have been used to remove the effect of the differing age structures in the Indigenous and nonIndigenous populations for 2001, and over time. The age structure of the Indigenous population is considerably younger than that of the nonIndigenous population, and age is strongly related to many health measures. Therefore, estimates of prevalence which do not take account of age may be misleading. The age standardised estimate of prevalence is that which would have prevailed should the Indigenous and nonIndigenous populations have the standard age composition. The standard population used is the total Australian population at 30 June 2001 based on the 2001 Census of Population and Housing, adjusted for the scope of the survey.
7 The direct age standardisation method was used and the formula is as follows:
where C_{direct} = the age standardised estimate of prevalence for the population of interest, a = the age categories that have been used in the age standardisation, c_{a} = the estimate of prevalence for the population being standardised in age category a, and P_{sa} = the proportion of the standard population in age category a. The age categories used in the standardisation were 5 year age groups to age 44, 4554, and 55+ years of age.
RELIABILITY OF ESTIMATES
Nonsampling error
8 In addition to sampling error, survey estimates are subject to nonsampling errors. Sources of nonsampling error include:
 nonresponse, when people are unable or unwilling to provide the information being sought;
 errors in reporting by respondents, e.g. answers were based on memory, or because of misunderstanding or unwillingness of respondents to reveal all details;
 mistakes by interviewers when recording answers; and
 errors in the coding and processing of data.
9 Every effort is made to keep nonsampling errors in ABS surveys to a minimum by careful design and testing of questionnaires, training of interviewers, asking respondents to refer to records where appropriate, and extensive editing and quality control procedures at all stages of data processing.
Sampling error
10 Since the survey estimates are based on a sample, they are subject to sampling error. Sampling error is the difference between the published estimates, derived from a sample of persons, and the value that would have been produced if the entire population had been surveyed.
11 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 a sample of the population was taken. There are about two chances in three that a sample estimate will differ by less than one SE from the figure that would have been obtained if the entire population had been included, and about 19 chances in 20 that the difference will be less than two SEs.
12 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. A table of SEs and RSEs for estimates of numbers of persons has been included in these Technical notes. These figures will not give a precise measure of the SE for a particular estimate but will provide an indication of its magnitude.
13 As can be seen from the SE table, the smaller the estimate the higher the RSE. Very small estimates are thus subject to such high RSEs as to detract seriously from their value for most uses. Estimates with a RSE of 25% to 50% are preceded by a single asterisk (e.g. *2.7) to indicate the estimate is subject to high RSEs and should be used with caution. Estimates with a RSE over 50% are preceded by a double asterisk ( e.g. **4.2) to indicate they are subject to very high sampling error and should be considered too unreliable for most purposes.
STANDARD ERRORS OF RATES AND PERCENTAGES
Comparisons of estimates
14 Published estimates may also be used to calculate the difference between two survey estimates (of number or percentages). Such an estimate is subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x  y) may be calculated by the following formula:
SE (x  y) = sqrt [SE(x)]2 + [SE(y)]2
15 While the above formula will be exact only for differences between separate and uncorrelated (unrelated) characteristics of subpopulations, it is expected that it will provide a reasonable approximation for all differences likely to be of interest in this publication.
SIGNIFICANCE TESTING
16 Significance testing has been undertaken for the comparison of estimates included in table 1 (between the Indigenous and nonIndigenous populations) and table 2 (between Indigenous estimates for 1995 and 2001). The statistical significance test for any of the comparisons between estimates was performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 14.
17 This standard error is then used to calculate the following test statistic:
xy
SE(xy)
18 If the value of this test statistic is greater than 1.96, then there are 19 chances in 20 that there is a real difference in the two populations with respect to that characteristic. Otherwise, it can not be stated with confidence that there is a real difference between the populations.
POPULATION TABLES
19 The estimates in this publication are presented as proportions. However, the populations presented in the following tables can be used to calculate the estimates as numbers.
T1: Population estimates by age and sex, Australia, 2001
T2: Population estimates, Australia, 2001
STANDARD ERROR TABLES
20 The following table should be used for Indigenous persons for all variables. Where Indigenous estimates from the 2001 collection have been age standardised, the standard errors are, on average, between 10% and 30% higher than the corresponding standard error of unstandardised estimates. Therefore, an adjustment factor of approximately 1.2 should be applied to the estimated RSE of 2001 Indigenous age standardised estimates. Where Indigenous estimates from the 1995 collection have been age standardised, the RSE factors presented in T4 should be applied to the estimated RSE of the Indigenous age standardised estimates.
T3: Standard and Relative Standard Errors for 1995 and 2001 Indigenous estimates

1995  1995  1995  2001  2001  2001 
Size of Estimate  Standard Error  Relative Standard Error  Size of Estimate  Standard Error  Relative Standard Error 
 no.  %   no.  % 
500  290  58.3  500  270  54.3 
600  330  55.0  600  310  51.2 
700  370  52.4  700  340  48.6 
800  400  50.1  800  370  46.4 
900  430  48.2  900  400  44.5 
1 000  460  46.5  1 000  430  42.8 
1 100  490  45.0  1 100  450  41.3 
1 200  520  43.6  1 200  480  40.0 
1 300  550  42.4  1 300  500  38.8 
1 400  580  41.3  1 400  530  37.7 
1 500  600  40.3  1 500  550  36.7 
1 600  630  39.3  1 600  570  35.8 
1 700  650  38.5  1 700  590  34.9 
1 800  680  37.7  1 800  610  34.1 
1 900  700  36.9  1 900  630  33.4 
2 000  720  36.2  2 000  650  32.7 
2 100  750  35.6  2 100  670  32.0 
2 200  770  34.9  2 200  690  31.4 
2 300  790  34.3  2 300  710  30.8 
2 400  810  33.8  2 400  730  30.3 
2 500  830  33.3  2 500  740  29.8 
3 000  930  31.0  3 000  830  27.5 
3 500  1 020  29.1  3 500  900  25.7 
4 000  1 100  27.6  4 000  970  24.2 
4 500  1 180  26.3  4 500  1 030  22.9 
5 000  1 260  25.2  5 000  1 090  21.8 
6 000  1 400  23.3  6 000  1 200  20.0 
7 000  1530  21.8  7 000  1 300  18.6 
8 000  1 650  20.6  8 000  1 390  17.4 
9 000  1760  19.6  9 000  1 470  16.4 
10 000  1 870  18.7  10 000  1 550  15.5 
20 000  2 700  13.5  20 000  2 130  10.7 
30 000  3 320  11.1  30 000  2 540  8.5 
40 000  3 830  9.6  40 000  2 850  7.1 
50 000  4 270  8.5  50 000  3 110  6.2 
100 000  5 870  5.9  100 000  3 980  4.0 
200 000  7 910  4.0  200 000  4 940  2.5 
300 000  9 320  3.1  300 000  5 520  1.8 
400 000  10 430  2.6  400 000  5 940  1.5 

T4: Standard Error factors for age standardised 1995 Indigenous estimates

Population  Factor 
All persons  1.261 
All persons aged 5 years and over  1.233 
All persons aged 15 years and over  1.189 
All persons aged 18 years and over  1.181 

21 The following table should be used for nonIndigenous persons for all variables except alcohol consumption (where T7 should be used). Although all 1995 estimates have been age standardised, the RSE factors for the nonIndigenous population are very close to 1 since this population is very similar in age structure to the standard population. The RSE factors for the nonIndigenous population can be found in T6.
T5: Standard and Relative Standard Errors for 1995 and 2001 nonIndigenous estimates

1995  1995  1995  2001  2001  2001 
Size of Estimate  Standard Error  Relative Standard Error  Size of Estimate  Standard Error  Relative Standard Error 
 no.  %   no.  % 
500  230  46.1  500  468  93.7 
1 000  350  35.1  1 000  750  75.0 
1 500  450  29.8  1 500  978  65.2 
2 000  530  26.5  2 000  1 174  58.7 
2 500  600  24.1  2 500  1 350  54.0 
3 000  670  22.3  3 000  1 512  50.4 
3 500  730  20.9  3 500  1 659  47.4 
4 000  790  19.8  4 000  1 800  45.0 
4 500  850  18.8  4 500  1 930  42.9 
5 000  900  17.9  5 000  2 055  41.1 
6 000  990  16.6  6 000  2 286  38.1 
8 000  1 170  14.6  8 000  2 696  33.7 
10 000  1 320  13.2  10 000  3 060  30.6 
20 000  1 920  9.6  20 000  4 440  22.2 
30 000  2 380  7.9  30 000  5 490  18.3 
40 000  2 770  6.9  40 000  6 320  15.8 
50 000  3 100  6.2  50 000  7 050  14.1 
100 000  4 400  4.4  100 000  9 700  9.7 
200 000  6 190  3.1  200 000  13 200  6.6 
300 000  7 510  2.5  300 000  15 600  5.2 
400 000  8 600  2.1  400 000  17 600  4.4 
500 000  9 540  1.9  500 000  19 000  3.8 
1 000 000  13 070  1.3  1 000 000  24 000  2.4 
2 000 000  17 720  0.9  2 000 000  30 000  1.5 
5 000 000  26 070  0.5  5 000 000  40 000  0.8 
10 000 000  34 480  0.3  10 000 000  50 000  0.5 
20 000 000  45 130  0.2  20 000 000  60 000  0.3 

T6 Standard Error factors for age standardised 1995 non–Indigenous estimates

Population  Factor 
All persons  1.002 
All persons aged 5 years and over  1.002 
All persons aged 15 years and over  1.003 
All persons aged 18 years and over  1.003 

22 For the 1995 nonIndigenous population, a different set of SEs exists for the tables relating to alcohol consumption. This is because the questions on alcohol consumption were only administered to half the nonIndigenous sample and weightings were calculated differently as a result.
T7: Standard and Relative Standard Errors for 1995 nonIndigenous estimates of alcohol consumption

1995  1995  1995 
Size of Estimate  Standard Error  Relative Standard Error 
 no.  % 
100  470  472.1 
200  640  320.6 
300  770  255.1 
400  870  216.7 
500  950  190.9 
600  1 030  172.0 
700  1 100  157.5 
800  1 170  145.8 
900  1 230  136.3 
1 000  1 280  128.3 
1 100  1 340  121.4 
1 200  1 390  115.4 
1 300  1 430  110.2 
1 400  1 480  105.6 
1 500  1 520  101.4 
1 600  1 560  97.7 
1 700  1 600  94.3 
1 800  1 640  91.2 
1 900  1 680  88.4 
2 000  1 720  85.8 
2 100  1 750  83.4 
2 200  1 790  81.2 
2 300  1 820  79.1 
2 400  1 850  77.1 
2 500  1 880  75.3 
3 000  2 030  67.7 
3 500  2 160  61.8 
4 000  2 290  57.1 
4 500  2 400  53.3 
5 000  2 500  50.1 
6 000  2 700  44.9 
8 000  3 030  37.9 
10 000  3 320  33.2 
20 000  4 370  21.8 
30 000  5 120  17.1 
40 000  5 730  14.3 
50 000  6 250  12.5 
100 000  8 150  8.2 
200 000  10 590  5.3 
300 000  12 310  4.1 
400 000  13 680  3.4 
500 000  14 850  3.0 
1 000 000  19 080  1.9 
2 000 000  24 400  1.2 
5 000 000  33 550  0.7 
10 000 000  42 470  0.4 
20 000 000  53 520  0.3 


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