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 2008 was approximately onethird smaller than the sample size in September 2007. This is due to an 11% sample reduction that was implemented from November 2007 to June 2008 based on the 2006 sample design, and an additional 24% sample reduction implemented in July 2008. In combination, the two sample reductions are expected to increase the standard errors for estimates from the supplementary surveys by approximately 22% at the broad aggregate level, relative to the 2001 sample design (standard errors will vary at lower aggregate levels). Detailed information about the sample reduction is provided in Information Paper: Labour Force Survey Sample Design, Nov 2007 (Second 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 73,900. Since the estimate is between 50,000 and 100,000, table T1 shows that the SE for Australia will lie between 4,450 and 5,850 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 68,800 to 79,000 and about 19 chances in 20 that the value will fall within the range 63,700 to 84,100. 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 73,900 people who were discouraged job seekers, 39,300 or 53.2% were females. The SE of 39,300 may be calculated by interpolation as 4,100. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,100/39,300=10.4%. The SE for 73,900 was calculated previously as 5,100, which converted to an RSE is 5,100/73,900=6.9%. 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 4.1 percentage points (=(53.2/100)x7.8). Therefore, there are about two chances in three that the proportion of females who were discouraged job seekers was between 49.1% and 57.3% and 19 chances in 20 that the proportion is within the range 45.0% to 61.4%.
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.  % 

100  190  200  170  170  180  130  100  110  130  130.0 
200  300  310  270  250  280  190  140  180  230  115.0 
300  400  390  360  310  350  230  170  230  310  103.3 
500  540  530  490  410  470  290  220  310  440  88.0 
700  660  640  600  480  560  340  260  370  560  80.0 
1,000  810  770  740  570  670  390  310  430  700  70.0 
1,500  1 010  950  920  680  810  460  380  500  910  60.7 
2,000  1 180  1 100  1 060  770  920  510  440  540  1 070  53.5 
2,500  1 300  1 200  1 200  850  1 000  550  500  550  1 200  48.0 
3,000  1 450  1 350  1 300  900  1 100  600  550  600  1 350  45.0 
3,500  1 550  1 450  1 400  950  1 150  600  600  600  1 450  41.4 
4,000  1 650  1 500  1 500  1 000  1 250  650  650  650  1 550  38.8 
5,000  1 850  1 700  1 650  1 100  1 350  700  750  700  1 750  35.0 
7,000  2 100  1 950  1 900  1 250  1 500  800  950  850  2 050  29.3 
10,000  2 450  2 250  2 150  1 450  1 700  950  1 300  1 100  2 400  24.0 
15,000  2 900  2 600  2 500  1 700  2 000  1 200  1 850  1 450  2 850  19.0 
20,000  3 200  2 900  2 750  1 950  2 300  1 400  2 350  1 700  3 200  16.0 
30,000  3 700  3 350  3 200  2 400  2 900  1 750  3 200  2 100  3 700  12.3 
40,000  4 050  3 700  3 600  2 800  3 450  2 050  3 950  2 350  4 100  10.3 
50,000  4 450  4 050  4 000  3 150  3 900  2 250  4 600  2 500  4 450  8.9 
100,000  6 200  5 850  5 850  4 500  5 750  3 100  7 150  2 850  5 850  5.9 
150,000  7 850  7 500  7 400  5 400  7 050  3 700  9 000  2 850  6 950  4.6 
200,000  9 400  8 950  8 700  6 100  8 100  4 150  . .  . .  7 950  4.0 
300,000  11 850  11 350  10 700  7 200  9 750  4 850  . .  . .  9 700  3.2 
500,000  15 300  15 250  13 550  8 650  12 050  5 800  . .  . .  12 650  2.5 
1,000,000  20 450  22 450  17 750  10 750  15 600  . .  . .  . .  18 750  1.9 
2,000,000  25 500  32 500  22 000  12 850  19 450  . .  . .  . .  27 200  1.4 
5,000,000  30 600  51 750  26 950  . .  . .  . .  . .  . .  39 200  0.8 
10,000,000  32 450  72 250  . .  . .  . .  . .  . .  . .  47 050  0.5 

. . not applicable 
T2 levels at which estimates have relative standard errors of 25% and 50%(a) 

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

RSE of 25%  9 700  8 300  7 900  4 200  5 600  2 100  1 500  2 200  9 400 
RSE of 50%  2 800  2 400  2 300  1 300  1 700  700  400  800  2 300 

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