TECHNICAL NOTE DATA QUALITY
INTRODUCTION
1 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 two chances in three (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, a table of SEs is provided to enable readers to determine the SE for an estimate from the size of that estimate (see table T1). The SE table is derived from a mathematical model, referred to as the 'SE model', which is created using data from a number of past Labour Force Surveys. 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.
CALCULATION OF STANDARD ERRORS
3 An example of the calculation and the use of SEs in relation to estimates of people is as follows. Table 2 shows that the estimated number of persons in Australia who were other business operators was 1,013,500. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows the SE for Australia will be between 13,600 and 19.750 and can be approximated by interpolation using the following general formula:
4 There are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall in the range 999,800 to 1,013,500, and about 19 chances in 20 that the value will fall within the range 986,100 to 1,040,900. This example is illustrated in the diagram below:
5 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 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% but less than or equal to 50% 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 of greater than 50%, preceded by a double asterisk (e.g. **0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of 25% or less.
PROPORTIONS AND PERCENTAGES
6 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:
7 Considering the example above, of the 1,013,500 persons who were other business operators, 404,000 or 39.9% were female. The SE of 404,000, may be calculated by interpolation as 8,700. To convert this to an RSE we express the SE as a percentage of the estimate, or 8,700/404,000 = 2.2%. The SE for 1,013,500 was calculated previously as 13,700, which converted to an RSE is 13,700/1,013,500 = 1.4%. Applying the above formulae, the RSE of the proportion is:
8 The SE for the proportion of females who were other business operators, is 0.6 percentage points, calculated as (39.9/100)x1.7. There are about two chances in three that the proportion of female business operators is between 39.2% and 40.6% and 19 chances in 20 that the proportion is within the range 38.5% to 41.3%.
9 All other estimates produced from population estimates smaller than the values in T2 have RSEs larger than 25% and should be used with caution. T2 also indicates the size of the population estimates that would produce all other estimates with RSEs greater than 50% are considered too unreliable for general use.
DIFFERENCES
10 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 appropriate SE of the difference between two estimates (xy) may be calculated by the following formulae:
11 While this formulae 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.
STANDARD ERRORS
T1 Standard Errors of Estimates 

         AUST. 
 NSW  Vic.  Qld.  SA  WA  Tas.  NT  ACT   
Size of estimate  no.  no.  no.  no.  no.  no.  no.  no.  no.  % 

100  360  250  250  190  240  110  50  120  130  130.0 
200  480  320  360  260  320  150  80  200  220  110.0 
300  570  380  440  310  380  190  100  250  310  103.3 
500  700  470  560  380  460  230  120  320  440  88.0 
700  810  530  650  430  530  270  140  360  560  80.0 
1000  930  610  760  490  610  310  170  400  700  70.0 
1500  1 100  710  900  580  710  350  200  430  900  60.0 
2000  1 230  800  1 010  640  790  390  220  460  1 070  53.5 
2500  1 350  850  1 100  700  850  400  250  500  1 200  48.0 
3000  1 450  950  1 200  750  900  450  250  500  1 350  45.0 
3500  1 550  1 000  1 250  800  1 000  450  250  550  1 450  41.4 
4000  1 600  1 050  1 300  850  1 050  500  250  550  1 550  38.8 
5000  1 750  1 150  1 400  900  1 100  500  300  600  1 700  34.0 
7000  2 000  1 300  1 600  1 000  1 250  600  350  700  2 000  28.6 
10000  2 300  1 450  1 800  1 150  1 450  700  450  800  2 300  23.0 
15000  2 650  1 700  2 000  1 300  1 650  850  650  1 000  2 700  18.0 
20000  2 950  1 900  2 200  1 450  1 850  950  800  1 150  3 000  15.0 
30000  3 400  2 200  2 500  1 700  2 100  1 250  1 150  1 500  3 350  11.2 
40000  3 800  2 400  2 800  1 950  2 350  1 450  1 450  1 750  3 650  9.1 
50000  4 100  2 600  3 050  2 200  2 550  1 650  1 700  2 000  3 950  7.9 
100000  5 200  3 450  4 200  3 300  3 750  2 400  2 950  2 650  4 950  5.0 
150000  6 100  4 150  5 150  4 250  4 950  2 850  4 050  3 000  5 800  3.9 
200000  7 050  4 850  6 000  4 950  5 950  3 150  5 100  3 150  6 500  3.3 
300000  8 850  6 250  7 650  6 100  7 500  3 650  6 950  3 300  7 700  2.6 
500000  12 400  8 650  10 300  7 650  9 550  4 200  . .  3 300  9 650  1.9 
1000000  18 400  13 150  14 700  9 750  12 150  4 800  . .  . .  13 600  1.4 
2000000  24 800  19 450  19 800  11 600  14 100  . .  . .  . .  19 750  1.0 
5000000  31 600  31 100  26 700  13 050  14 700  . .  . .  . .  32 950  0.7 
10000000  33 850  42 900  31 200  . .  . .  . .  . .  . .  44 000  0.4 
15000000  . .  . .  . .  . .  . .  . .  . .  . .  49 600  0.3 

. . not applicable 
T2 POPULATION LEVELS AT WHICH ESTIMATES HAVE RSES OF 25% AND 50% 

 NSW  Vic.  Qld.  SA  WA  Tas.  NT  ACT  Aust. 
 no.  no.  no.  no.  no.  no.  no.  no.  no. 

Relative Standard Error (RSE) of 25%  8 600  4 200  6 100  3 000  4 200  1 400  500  1 800  8 800 
Relative Standard Error (RSE) of 50%  2 800  1 400  2 000  1 000  1 400  400  100  700  2 300 
