
RELIABILITY OF THE ESTIMATES
1 Since the estimates in this publication are based on information obtained from a sample of persons, they are subject to sampling variability. That is, they may differ from those that would have been produced had all Indigenous persons aged 15 years or over 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 persons was included. There are about two chances in three that the sample estimate will differ by less than one SE from the number that would have been obtained if all persons had been surveyed, and about 19 chances in 20 that the difference will be less than two SEs.
2 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.
RSE% = (SE / estimate) x 100
3 Space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication. However, RSEs for all these estimates are available freeofcharge in the National Aboriginal and Torres Strait Islander Social Survey: Data Reference Package, 2002 (cat. no. 4714.0.55.002) on the ABS web site <www.abs.gov.au>.
4 In the tables in this publication, only estimates (numbers, percentages and means) with RSEs of less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (e.g. **2.1) to indicate that they are considered too unreliable for general use.
5 To assist users of this publication to ascertain the approximate levels of reliability of estimates throughout this publication, a table of SEs and RSEs for certain estimates of population counts appears at the end of the Technical Note. These values do not give a precise measure of the SEs or RSEs for a particular estimate, but will provide an indication of their magnitude.
CALCULATING STANDARD ERRORS FOR POPULATION ESTIMATES
6 An example of the calculation and use of SEs in relation to estimates of numbers of persons is as follows. Consider the estimate of the number of persons (aged 15 years or over) who hold a nonschool qualification, which is 73,500 (table 7). Since this estimate is between 50,000 and 75,000, the SE will be between 2,340 and 2,700 (as shown in the SE table), and can be approximated by interpolation using the following formula:
SE = lower SE + ((size of estimate  lower size) / (upper size  lower size)) x (upper SE  lower SE)
SE = 2,340 + ((73,500  50,000) / (75,000  50,000)) x (2,700  2,340)
SE = (approximately) 2680
Therefore, there are about two chances in three that the value that would have been produced if all persons had been included in the survey would have fallen within the range 70,820 to 76,180, and about 19 chances in 20 that the value would have fallen within the range 68,140 to 78,860.
CALCULATING STANDARD ERRORS FOR PROPORTIONS AND PERCENTAGES
7 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. For proportions where the denominator is an estimate of the number of persons in a group and the numerator is the number of persons in a subgroup of the denominator group, the formula to approximate the RSE is given by:
8 Consider the example given above of the number of persons who held a nonschool qualification. Of these, 59.1% (or approximately 43,400) identified with a clan, tribal or language group (table 7). As already noted, the SE of 73,500 is approximately 2,680, which equates to an RSE of 3.6%. The SE and RSE of 43,400 are approximately 2,210 and 5.1% respectively. Applying the formula above, the estimate of 59.1% will have an RSE of:
RSE = [RSE(43,400)]^{2}  [RSE(73,500)]^{2}
= SQRT([5.1]^{2}  [3.7]^{2})
= 3.5%
9 This gives a SE for the proportion (59.1%) of approximately 2.1 percentage points (0.035 x 59.1). Therefore, if all persons had been included in the survey, there are two chances in three that the proportion that would have been obtained is between 57.0% and 61.2% and about 19 chances in 20 that the proportion is within the range 54.9% to 63.3%.
RELATIVE STANDARD ERRORS FOR MEANS
10 Estimates of means shown throughout this publication are subject to sampling error. RSEs for these estimates are available freeofcharge in the National Aboriginal and Torres Strait Islander Social Survey: Data Reference Package, 2002 (cat. no. 4714.0.55.002) on the ABS web site <www.abs.gov.au>.
Comparison of estimates
11 Published estimates may also be used to calculate the difference between two survey estimates. 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 (xy) may be calculated by the following formula:
12 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
13 Significance testing has been undertaken for the comparison of estimates in the following tables:
 1  between remote and nonremote populations
 4  between remote and nonremote populations and Indigenous and nonIndigenous populations
 5  between remote and nonremote populations and Indigenous and nonIndigenous populations
 6  between 1994 NATSIS and 2002 NATSISS populations.
14 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 11.This standard error is then used to calculate the following test statistic:
15 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 cannot be stated with confidence that there is a real difference between the populations.
16 The selected tables in this publication that show the results of significance testing are annotated to indicate whether or not the estimates which have been compared are significantly different from each other with respect to the test statistic. In all other tables which do not show the results of significance testing, users should take account of RSEs when comparing estimates for different populations.
NONSAMPLING ERROR
17 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents and recording by interviewers, and errors made in coding and processing data. Inaccuracies of this kind are referred to as nonsampling error, and they occur in any enumeration, whether it be a full count or a sample. Every effort is made to reduce nonsampling error to a minimum by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.
AGE STANDARDISATION
18 For this publication the direct age standardisation method was used. The standard population used was the total estimated resident population of Australia as at 30 June 2001. Estimates of agestandardised rates were calculated using the following formula:
19 where Cdirect = the agestandardised rate for the population of interest, a = the age categories that have been used in the age standardisation, ca = the estimated rate for the population being standardised in age category a, and Psa = the proportion of the standard population in age category a. The age categories used in the standardisation for this publication are 1819 years, and then fiveyear age groups to 65 years or over.
CALCULATING STANDARD ERRORS
Standard errors of Indigenous Persons estimates 
 
 Remote
 Nonremote
 Australia
 
Size of estimate  Standard error  Relative standard error  Standard error  Relative standard error  Standard error  Relative standard error  
 
200  110  57  110  54  100  52  
500  180  37  210  43  200  41  
1,000  260  26  340  34  320  32  
1,500  320  22  440  29  420  28  
2,000  380  19  520  26  500  25  
2,500  420  17  590  24  570  23  
3,000  470  16  660  22  630  21  
3,500  510  14  720  20  690  20  
4,000  540  14  770  19  740  19  
4,500  580  13  820  18  790  18  
5,000  610  12  870  17  840  17  
7,000  730  10  1,020  15  1,000  14  
10,000  870  9  1,210  12  1,190  12  
15,000  1,080  7  1,450  10  1,430  10  
20,000  1,250  6  1,630  8  1,630  8  
30,000  1,550  5  1,910  6  1,930  6  
40,000  1,800  5  2,120  5  2,150  5  
50,000  2,020  4  2,280  5  2,340  5  
75,000  2,500  3  2,590  3  2,690  4  
100,000  . .  . .  2,800  3  2,950  3  
150,000  . .  . .  3,110  2  3,330  2  
200,000  . .  . .  3,320  2  3,600  2  
250,000  . .  . .  . .  . .  3,800  1  
 
. . not applicable 
Number of Indigenous Persons, Estimates with relative standard errors of 25% and 50% 
 
 Size of estimate
 
 Remote  NonRemote  Australia  
 no.  no.  no.  
 
RSE of 25%  1,110  2,220  2,000  
RSE of 50%  260  280  240  
 
Standard and Relative Standard Errors for NonIndigenous Estimates 
 
 Standard error  Relative standard error  
Size of estimate  no.  %  
 
4,000  2,100  52  
4,500  2,250  50  
5,000  2,390  48  
6,000  2,660  44  
8,000  3,140  39  
10,000  3,550  36  
20,000  5,160  26  
30,000  6,330  21  
40,000  7,320  18  
50,000  8,150  16  
100,000  11,200  11  
200,000  15,000  8  
300,000  17,700  6  
400,000  19,600  5  
500,000  21,500  4  
1,000,000  27,000  3  
2,000,000  34,000  2  
5,000,000  45,000  1  
10,000,000  50,000  1  
 
Standard and Relative Standard Errors for 1994 Indigenous Estimates 
 
 STANDARD ERROR  RELATIVE STANDARD ERROR  
Size of estimate  no.  %  
 
200  110  56  
500  230  46  
1,000  370  37  
1,500  480  32  
2,000  570  29  
2,500  660  26  
3,000  730  24  
3,500  790  23  
4,000  850  21  
4,500  910  20  
5,000  960  19  
7,000  1,130  16  
10,000  1,330  13  
15,000  1,580  11  
20,000  1,770  9  
30,000  2,050  7  
40,000  2,250  6  
50,000  2,400  5  
75,000  2,680  4  
100,000  2,870  3  
150,000  3,110  2  
200,000  3,270  2  
250,000  3,380  1  
 
This page last updated 29 October 2009
