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 The LFS sample size in September 2009 was approximately 9% higher than the sample size in 2008. This is due to reinstated sample that was cut from Labour Force Survey (LFS) and supplementary surveys from July 2008. In combination, the sample reinstatement is expected to decrease the standard errors for estimates from the supplementary surveys by approximately 4% at the broad aggregate level, relative to estimates from 2008 (standard errors will vary at lower aggregate levels). 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 111,800. Since the estimate is between 100,000 and 150,000, table T1 shows that the SE for Australia will lie between 5,600 and 6,700 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 105,900 to 117,700 and about 19 chances in 20 that the value will fall within the range 100,000 to 123,600. 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 111,800 people who were discouraged job seekers, 59,500 or 53.2% were females. The SE of 59,500 may be calculated by interpolation as 4,500. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,500/59,500=7.6%. The SE for 111,800 was calculated previously as 5,900 which converted to an RSE is 5,900/111,800=5.3%. 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 2.9 percentage points (=(53.2/100)x5.4). Therefore, there are about two chances in three that the proportion of females who were discouraged job seekers was between 50.3% and 56.1% and 19 chances in 20 that the proportion is within the range 47.4% to 59.0%.
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 estimates (persons)  no.  no.  no.  no.  no.  no.  no.  no.  no.  no. 

100  180  190  160  170  170  120  110  100  130  130.0 
200  290  300  260  250  270  180  150  170  220  110.0 
300  380  380  340  300  340  220  180  230  300  100.0 
500  520  510  470  390  450  280  230  300  430  86.0 
700  640  620  580  460  540  330  270  360  540  77.1 
1,000  780  750  710  550  640  380  320  410  680  68.0 
1,500  980  920  880  650  780  440  390  480  870  58.0 
2,000  1 130  1 060  1 020  740  890  490  450  520  1 030  51.5 
2,500  1 250  1 200  1 150  800  1 000  550  500  550  1 150  46.0 
3,000  1 400  1 300  1 250  900  1 050  550  550  550  1 300  43.3 
3,500  1 500  1 400  1 350  950  1 100  600  600  600  1 400  40.0 
4,000  1 600  1 450  1 400  1 000  1 200  600  650  650  1 500  37.5 
5,000  1 750  1 600  1 550  1 100  1 300  650  750  700  1 700  34.0 
7,000  2 050  1 850  1 800  1 200  1 450  800  1 000  850  2 000  28.6 
10,000  2 350  2 150  2 100  1 400  1 650  950  1 350  1 050  2 350  23.5 
15,000  2 750  2 500  2 400  1 650  1 950  1 150  1 900  1 400  2 750  18.3 
20,000  3 100  2 800  2 650  1 850  2 200  1 350  2 400  1 650  3 100  15.5 
30,000  3 550  3 200  3 050  2 300  2 800  1 700  3 300  2 000  3 550  11.8 
40,000  3 900  3 550  3 450  2 700  3 300  1 950  4 050  2 250  3 950  9.9 
50,000  4 300  3 900  3 850  3 050  3 750  2 200  4 750  2 400  4 250  8.5 
100,000  5 950  5 650  5 650  4 300  5 500  3 000  7 350  2 750  5 600  5.6 
150,000  7 550  7 250  7 150  5 200  6 800  3 550  9 250  2 750  6 700  4.5 
200,000  9 050  8 600  8 350  5 900  7 800  4 000  . .  . .  7 650  3.8 
300,000  11 400  10 950  10 300  6 950  9 350  4 650  . .  . .  9 350  3.1 
500,000  14 750  14 700  13 000  8 350  11 600  5 600  . .  . .  12 200  2.4 
1,000,000  19 700  21 600  17 050  10 350  15 000  . .  . .  . .  18 050  1.8 
2,000,000  24 550  31 300  21 200  12 350  18 750  . .  . .  . .  26 200  1.3 
5,000,000  29 500  49 800  25 950  . .  . .  . .  . .  . .  37 750  0.8 
10,000,000  31 250  69 550  . .  . .  . .  . .  . .  . .  45 300  0.5 
15,000,000  . .  . .  . .  . .  . .  . .  . .  . .  48 600  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 
 no.  no.  no.  no.  no.  no.  no.  no.  no. 

RSE of 25%  9 100  7 800  7 400  3 900  5 300  1 900  1 600  2 100  8 800 
RSE of 50%  2 600  2 200  2 100  1 200  1 600  600  400  700  2 200 

(a) Refers to the number of people contributing to the estimate. 
Follow us on...
Like us on Facebook Follow us on Twitter Add the ABS on Google+ ABS RSS feed Subscribe to ABS updates