TECHNICAL NOTE DATA QUALITY
INTRODUCTION
1 Estimates in this publication are based on information obtained from occupants of a sample of dwellings, and 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 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 ERROR
3 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Table 4 shows the estimated number of female underemployed parttime workers was 493,800. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 7,700 and 9,650 and can be approximated by interpolation using the following general formula:
4 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 484,200 to 503,400 and about 19 chances in 20 that the value will fall within the range 474,600 to 513,000. This example is illustrated in the following diagram.
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.*3.2) 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.**0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of less than 25%.
MEANS AND MEDIANS
6 The RSEs of estimates of mean duration of insufficient work, median duration of insufficient work and mean preferred number of extra hours are obtained by first finding the RSE of the estimate of the total number of persons contributing to the mean or median ( see table T1) and then multiplying the resulting number by the following factors:
 mean duration of insufficient work: 1.6
 median duration of insufficient work: 2.5
 mean preferred number of extra hours: 0.7
7 The following is an example of the calculation of SEs where the use of a factor is required. Table 4 shows that the estimated number of male underemployed parttime workers was 323,400 with a median duration of insufficient work of 30 weeks. The SE of 323,400 can be calculated from table T1 (by interpolation) as 7,700. To convert this to an RSE we express the SE as a percentage of the estimate or 7,700/323,400 = 2.4%.
8 The RSE of this estimate of median duration of insufficient work is calculated by multiplying this number (2.4%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.5 x 2.4 = 6.0%. The SE of this estimate of median duration of insufficient work is therefore 6.0% of 30, i.e. about 2 weeks (rounded to the nearest whole week). Therefore, there are two chances in three that the median duration of insufficient work for males that would have been obtained if all dwellings had been included in the survey would have been within the range 2832 weeks, and about 19 chances in 20 that it would have been within the range 2634 weeks.
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 Considering the example from paragraph 3, of the 493,800 female underemployed parttime workers, 199,800 or 40.5% had insufficient work for 52 weeks and over. The SE of 199,800 may be calculated by interpolation as 6,500. To convert this to an RSE we express the SE as a percentage of the estimate, or 6,500/199,800 = 3.3%. The SE for 493,800 was calculated previously as 9,600, which converted to an RSE is 9,600/493,800 = 1.9%. Applying the above formula, the RSE of the proportion is:
11 Therefore, the SE for the proportion of females who have a current period of insufficient work of 52 weeks or more is 1.1 percentage points (=(40.5/100)x2.7). Therefore, there are about two chances in three that the proportion of females who have a current period of insufficient work of 52 weeks or more was between 39.4% and 41.6% and 19 chances in 20 that the proportion is within the range 38.3% and 42.7%.
DIFFERENCES
12 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:
13 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  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  130  320  440  88.0 
700  810  530  650  430  530  270  150  360  560  80.0 
1,000  930  610  760  490  610  310  170  400  700  70.0 
1,500  1 100  710  900  580  710  350  200  430  900  60.0 
2,000  1 230  800  1 010  640  790  390  220  460  1 070  53.5 
2,500  1 350  850  1 100  700  850  400  250  500  1 200  48.0 
3,000  1 450  950  1 200  750  900  450  250  500  1 350  45.0 
3,500  1 550  1 000  1 250  800  1 000  450  250  550  1 450  41.4 
4,000  1 600  1 050  1 300  850  1 050  500  300  550  1 550  38.8 
5,000  1 750  1 150  1 400  900  1 100  500  300  600  1 700  34.0 
7,000  2 000  1 300  1 600  1 000  1 250  600  350  700  2 000  28.6 
10,000  2 300  1 450  1 800  1 150  1 450  700  450  800  2 300  23.0 
15,000  2 650  1 700  2 000  1 300  1 650  850  650  1 000  2 700  18.0 
20,000  2 950  1 900  2 200  1 450  1 850  950  800  1 150  3 000  15.0 
30,000  3 400  2 200  2 500  1 700  2 100  1 250  1 150  1 500  3 350  11.2 
40,000  3 800  2 400  2 800  1 950  2 350  1 450  1 450  1 750  3 650  9.1 
50,000  4 100  2 600  3 050  2 200  2 550  1 650  1 700  2 000  3 950  7.9 
100,000  5 200  3 450  4 200  3 300  3 750  2 400  3 000  2 650  4 950  5.0 
150,000  6 100  4 150  5 150  4 250  4 950  2 850  4 100  3 000  5 800  3.9 
200,000  7 050  4 850  6 000  4 950  5 950  3 150  5 150  3 150  6 500  3.3 
300,000  8 850  6 250  7 650  6 100  7 500  3 650  7 000  3 300  7 700  2.6 
500,000  12 400  8 650  10 300  7 650  9 550  4 200  . .  3 300  9 650  1.9 
1,000,000  18 400  13 150  14 700  9 750  12 150  4 800  . .  . .  13 600  1.4 
2,000,000  24 800  19 450  19 800  11 600  14 100  . .  . .  . .  19 750  1.0 
5,000,000  31 600  31 100  26 700  13 050  14 700  . .  . .  . .  32 950  0.7 
10,000,000  33 850  42 900  31 200  . .  . .  . .  . .  . .  44 000  0.4 
15,000,000  . .  . .  . .  . .  . .  . .  . .  . .  49 600  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  Aust. 
 no.  no.  no.  no.  no.  no.  no.  no.  no. 
25% RSE 

Mean duration of insufficient work  18 300  9 800  13 000  5 800  9 400  2 500  1 100  3 000  19 200 
Median duration of insufficient work  44 400  22 900  32 500  18 100  21 700  6 700  10 300  13 400  35 300 
Mean preferred number of extra hours  5 300  3 100  3 800  2 000  2 900  1 000  400  1 100  5 000 
All other estimates  8 600  4 200  6 100  3 000  4 200  1 400  500  1 800  8 800 
50% RSE 

Mean duration of insufficient work  6 100  3 200  4 700  2 000  3 200  900  300  1 200  6 100 
Median duration of insufficient work  15 000  7 600  11 800  6 300  7 400  2 400  2 600  4 000  12 600 
Mean preferred number of extra hours  1 700  1 000  1 200  600  1 000  300  100  400  1 100 
All other estimates  2 800  1 400  2 000  1 000  1 400  400  100  700  2 300 

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