
INTRODUCTION
1 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 estimates 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 2 chances in 3 (67%) 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 (95%) 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.
2 Due to space limitations, it is impractical to print the SE of each estimate in the publication. Instead, tables of SEs are provided to enable readers to determine the SE for an estimate from the size of that estimate (see tables T1 and T2). Each SE table is derived from a mathematical model, referred to as the "SE model", which is created using the data collected in this survey. It should be noted that the SE model only gives an approximate value for the SE for any particular estimate, since there is some minor variation between SEs for different estimates of the same size.
3 This publication contains estimates for persons and households. Table T1 gives SEs for estimates of households, while SEs for estimates of persons are presented in T2. Tables containing estimates of households are found in Chapters 3 and 4, while Chapters 2 and 5 contains estimates of persons.
CALCULATION OF STANDARD ERROR
4 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Table 2.15 shows that the estimated number of persons in Australia who used signed petition as a means of registering an environmental concern was 390,700. Since this estimate is between 300,000 and 500,000, table T2 shows that the SE for Australia will lie between 18,550 and 23,550 and can be approximated by interpolation using the following general formula:
5 Therefore, there are about 2 chances in 3 that the value that would have been produced if all persons had been included in the survey will fall within the range 369,900 to 411,500 and about 19 chances in 20 that the value will fall within the range 349,100 to 432,300. This example is illustrated in the diagram below.
6 Similarly, SEs are calculated for household level estimates using table T1 instead of table T2. For example, table 3.23 shows that the estimated number of households in Victoria who have mains/town water as main source of water for gardening was 1,180,500. This estimate is between 1,000,000 and 2,000,000, so the SE for this estimate will be between 16,800 and 18,100, and can be approximated using the same interpolation formula as above, with the resulting SE being 17,000 (rounded to the nearest 100).
7 Therefore, there are about 2 chances in 3 that the value that would have been produced if all households in the population had been included in the survey will fall within the range 1,163,500 to 1,197,500 and about 19 chances in 20 that the value will fall within the range 1,146,500 to 1,214,500.
8 In general, the size of the SE increases as the size of the estimate increases. Conversely, the RSE decreases as the size of the estimate increases. Very small estimates are thus subject to such high RSEs so that their value for most practical purposes is unreliable. In the tables in this publication, only estimates with RSEs of 25% or less are considered reliable for most purposes. Estimates with RSEs greater than 25% are preceded by an asterisk (e.g. *1.8) to indicate they are subject to high SEs and should be used with caution.
PROPORTIONS AND PERCENTAGES
9 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. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y.
10 For example, in table 2.15, the estimate for the total number of persons aged 18 years and over, who registered an environmental concern in Australia was 1,090,800. The estimated number of persons who used signed petition as a means of registering that concern was 390,700, so the proportion of persons in Australia who registered an environmental concern by signed petition is 390,700/1,090,800 or 35.8%. The SE of the total number of persons in Australia registering an environmental concern may be calculated by interpolation as 33,026 or 33,000 rounded to the nearest 100. To convert this to a RSE we express the SE as a percentage of the estimate, or 33,000/1,090,800 = 3.1%. The SE for the number of persons in Australia who registerd environmental concerns by signed petition was calculated above as 20,800, which converted to a RSE is 20,800/ 390,700 = 5.3%. Applying the above formula, the RSE of the proportion is ; giving a SE for the proportion (35.8%) of 1.5 percentage points (=35.8**0.043).
11 Therefore, there are about 2 chances in 3 that the proportion of persons in Australia who registered an environmental concern by means of signed petition is between 34.3% and 37.3% and 19 chances in 20 that the proportion is within the range 32.8% to 38.8%.
12 Similarly, SEs can be calculated for household level estimates using the same formula.
DIFFERENCES
13 Published estimates may also be used to calculate the difference between two survey estimates (of numbers 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 (xy) may be calculated by the following formula:
14 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
NONSAMPLING ERROR
15 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfect reporting by respondents, errors made in collection such as in recording and coding data, and errors made in processing the data. Inaccuracies of this kind are referred to as nonsampling error, and they may occur in any enumeration, whether it be a full count or a sample. It is not possible to quantify nonsampling error, but every effort is made to reduce it to a minimum. This is done by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.
T1 STANDARD ERRORS FOR HOUSEHOLD LEVEL ESTIMATES 
 
 NSW  Vic.  Qld.  SA  WA  Tas.  NT  ACT  Aust.  
Size of estimate  no.  no.  no.  no.  no.  no.  no.  no.  no.  
 
100  90  50  100  90  130  60  90  70  100  
200  180  100  170  170  210  110  160  140  170  
300  250  150  240  230  270  160  220  190  220  
500  380  250  360  330  380  240  310  280  320  
700  500  340  460  420  480  310  390  350  400  
1,000  650  470  590  540  590  410  490  450  500  
1,500  880  670  790  700  760  540  630  570  650  
2,000  1,080  850  950  840  900  650  740  680  770  
2,500  1,250  1,000  1,100  950  1,000  750  850  750  900  
3,000  1,450  1,150  1,250  1,050  1,150  850  900  850  1,000  
3,500  1,600  1,300  1,350  1,150  1,250  900  1,000  900  1,100  
4,000  1,750  1,450  1,500  1,250  1,350  1,000  1,050  1,000  1,200  
5,000  2,000  1,700  1,700  1,450  1,500  1,100  1,200  1,100  1,350  
7,000  2,500  2,150  2,100  1,700  1,800  1,300  1,400  1,250  1,650  
10,000  3,100  2,750  2,550  2,050  2,150  1,550  1,650  1,450  2,000  
15,000  3,900  3,500  3,200  2,500  2,650  1,850  1,900  1,700  2,500  
20,000  4,550  4,150  3,700  2,850  3,000  2,050  2,150  1,850  2,950  
30,000  5,650  5,200  4,500  3,400  3,600  2,350  2,450  2,050  3,650  
40,000  6,550  6,000  5,200  3,800  4,100  2,550  2,650  2,200  4,250  
50,000  7,300  6,700  5,750  4,150  4,550  2,750  2,850  2,300  4,750  
100,000  9,950  9,000  7,750  5,300  6,000  3,150  3,400  2,600  6,700  
150,000  11,800  10,500  9,050  6,000  7,000  3,350  3,700  2,700  8,150  
200,000  13,150  11,550  10,100  6,500  7,750  3,450  3,850  2,700  9,300  
300,000  15,250  13,000  11,600  7,200  8,900  3,550    2,750  11,200  
500,000  18,100  14,750  13,650  8,050  10,500  3,550      14,000  
1,000,000  22,050  16,800  16,550  9,100  12,850        18,650  
2,000,000  26,050  18,100  19,400  9,950  15,350        24,500  
5,000,000  30,750  18,500  22,850            34,200  
10,000,000                  43,150  
 
 nil or rounded to zero (including null cells) 
T2 STANDARD ERRORS FOR PERSON LEVEL ESTIMATES 
 
 NSW  Vic.  Qld.  SA  WA  Tas.  NT  ACT  Aust.  
Size of estimate  no.  no.  no.  no.  no.  no.  no.  no.  no.  
 
100  260  240  210  160  130  110  110  160  120  
200  400  370  340  260  230  190  220  250  200  
300  520  480  440  350  310  260  320  310  270  
500  720  670  600  490  450  370  480  420  400  
700  880  820  740  600  570  470  620  500  510  
1,000  1,090  1,010  910  750  730  590  790  610  650  
1,500  1,390  1,290  1,160  960  960  760  1,020  760  860  
2,000  1,640  1,520  1,370  1,140  1,150  910  1,210  890  1,050  
2,500  1,850  1,700  1,550  1,300  1,350  1,050  1,350  1,000  1,200  
3,000  2,050  1,900  1,700  1,450  1,500  1,150  1,500  1,100  1,350  
3,500  2,250  2,100  1,850  1,550  1,650  1,250  1,600  1,200  1,500  
4,000  2,450  2,250  2,000  1,650  1,750  1,350  1,700  1,250  1,650  
5,000  2,750  2,550  2,250  1,900  2,000  1,500  1,850  1,400  1,900  
7,000  3,350  3,050  2,700  2,250  2,450  1,800  2,100  1,650  2,350  
10,000  4,050  3,650  3,300  2,700  2,950  2,100  2,400  2,000  2,950  
15,000  5,000  4,550  4,050  3,250  3,650  2,550  2,650  2,400  3,750  
20,000  5,800  5,250  4,700  3,700  4,250  2,900  2,800  2,750  4,450  
30,000  7,150  6,400  5,700  4,450  5,150  3,400  3,000  3,300  5,600  
40,000  8,250  7,400  6,550  5,000  5,900  3,800  3,050  3,800  6,550  
50,000  9,200  8,200  7,300  5,500  6,500  4,100  3,100  4,150  7,400  
100,000  12,850  11,350  10,000  7,150  8,700  5,100  3,050  5,600  10,750  
150,000  15,500  13,600  12,000  8,250  10,150  5,750  2,900  6,650  13,200  
200,000  17,700  15,450  13,550  9,100  11,300  6,200  2,800  7,450  15,250  
300,000  21,200  18,350  16,050  10,350  12,950  6,800    8,750  18,550  
500,000  26,450  22,650  19,750  12,000  15,250  7,500      23,550  
1,000,000  35,300  29,850  25,850  14,350  18,500        32,050  
2,000,000  46,450  38,650  33,250  16,750  21,800        42,800  
5,000,000  65,500  53,300  45,400            60,950  
10,000,000                  77,950  
 
 nil or rounded to zero (including null cells) 
This page last updated 20 June 2006
