TECHNICAL NOTE DATA QUALITY
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 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.
3 Due to sample reduction/reinstatement, the sample size of the Labour Force Survey (LFS) and supplementary surveys has varied from July 2008. Detailed information about the sample reduction/reinstatement is provided in Information Paper: Labour Force Survey Sample Design, Nov 2007 (Third edition) (cat. no. 6269.0).
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 1 shows that the estimated number of people in Australia who were discouraged job seekers was 102,100. Since the estimate is between 100,000 and 150,000, table T1 shows that the SE for Australia will lie between 5,100 and 6,050 and can be approximated by interpolation using the following general formula:
5 Therefore, 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 within the range 97,000 to 107,200 and about 19 chances in 20 that the value will fall within the range 91,900 to 112,300. This example is illustrated in the following diagram.
6 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.*3.2) to indicate 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.**0.4), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of less than 25%.
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. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y.
8 Considering the example above, of the 102,100 people who were discouraged job seekers, 62,300 or 61.0% were females. The SE of 62,300 may be calculated by interpolation as 4,200. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,200/62,300=6.7%. The SE for 102,100 was calculated previously as 5,100 which converted to an RSE is 5,100/102,100=5.0%. Applying the above formula, the RSE of the proportion is:
9 Therefore, the SE for the proportion of discouraged job seekers who were females is 2.7 percentage points (=(61.0/100)x4.5). Therefore, there are about two chances in three that the proportion of females who were discouraged job seekers was between 58.3% and 63.7% and 19 chances in 20 that the proportion is within the range 55.6% to 66.4%.
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 approximate SE of the difference between two estimates (xy) may be calculated by the following formula:
11 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.
STANDARD ERRORS
T1 STANDARD ERRORS OF ESTIMATES 

         AUST. 
 NSW  Vic.  Qld  SA  WA  Tas.  NT  ACT  SE  RSE 
Size of estimate (persons)  no.  no.  no.  no.  no.  no.  no.  no.  no.  no. 

100  160  170  150  150  160  110  100  90  110  110.0 
200  270  270  240  220  240  160  140  160  200  100.0 
300  350  340  310  280  310  200  170  200  270  90.0 
500  470  460  430  360  410  250  210  270  390  78.0 
700  580  560  520  420  490  290  250  320  490  70.0 
1,000  710  680  640  490  580  340  290  370  620  62.0 
1,500  880  830  800  590  700  400  360  430  790  52.7 
2,000  1 030  960  930  670  800  440  420  470  930  46.5 
2,500  1 150  1 050  1 050  750  900  500  450  500  1 050  42.0 
3,000  1 250  1 150  1 150  800  950  500  500  500  1 150  38.3 
3,500  1 350  1 250  1 200  850  1 000  550  550  550  1 250  35.7 
4,000  1 450  1 350  1 300  900  1 050  550  600  550  1 350  33.8 
5,000  1 600  1 450  1 400  1 000  1 150  600  700  650  1 550  31.0 
7,000  1 850  1 700  1 650  1 100  1 350  700  900  750  1 800  25.7 
10,000  2 150  1 950  1 900  1 250  1 500  850  1 250  950  2 100  21.0 
15,000  2 500  2 300  2 200  1 500  1 750  1 050  1 750  1 250  2 500  16.7 
20,000  2 800  2 550  2 400  1 700  2 000  1 250  2 200  1 500  2 800  14.0 
30,000  3 200  2 900  2 750  2 100  2 500  1 550  3 050  1 850  3 250  10.8 
40,000  3 550  3 200  3 150  2 450  3 000  1 750  3 750  2 050  3 550  8.9 
50,000  3 850  3 550  3 500  2 750  3 400  2 000  4 400  2 200  3 850  7.7 
100,000  5 400  5 100  5 100  3 900  5 000  2 700  6 800  2 500  5 100  5.1 
150,000  6 850  6 550  6 450  4 700  6 150  3 250  8 600  2 500  6 050  4.0 
200,000  8 200  7 800  7 600  5 350  7 050  3 650  . .  . .  6 950  3.5 
300,000  10 350  9 900  9 300  6 300  8 500  4 250  . .  . .  8 450  2.8 
500,000  13 350  13 300  11 800  7 550  10 500  5 050  . .  . .  11 050  2.2 
1,000,000  17 850  19 600  15 450  9 400  13 600  . .  . .  . .  16 350  1.6 
2,000,000  22 250  28 350  19 200  11 200  16 950  . .  . .  . .  23 700  1.2 
5,000,000  26 700  45 150  23 500  . .  . .  . .  . .  . .  34 200  0.7 
10,000,000  28 300  63 050  . .  . .  . .  . .  . .  . .  41 050  0.4 
15,000,000  . .  . .  . .  . .  . .  . .  . .  . .  44 050  0.3 

. . not applicable 
T2 LEVELS AT WHICH ESTIMATES HAVE RELATIVE STANDARD ERRORS OF 25% AND 50%(a) 

 NSW  Vic.  Qld.  SA  WA  Tas.  NT  ACT  Australia 
Percentage  no.  no.  no.  no.  no.  no.  no.  no.  no. 

RSE of 25%  7 700  6 600  6 300  3 300  4 500  1 700  1 400  1 800  7 300 
RSE of 50%  2 100  1 800  1 700  1 000  1 300  500  400  600  1 700 

(a) Refers to the number of people contributing to the estimate. 
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