
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.
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 5 shows the estimated number of female parttime workers who want more hours was 382,600. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 7,250 and 8,800 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 374,700 to 390,500 and about 19 chances in 20 that the value will fall within the range 366,800 to 398,400. 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: 1.7
 median duration of insufficient work: 2.1
 mean preferred number of extra hours: 0.8.
7 The following is an example of the calculation of SEs where the use of a factor is required. Table 5 shows that the estimated number of male parttime workers who want more hours was 230,300 with a median duration of insufficient work of 26 weeks. The SE of 230,300 can be calculated from table T1 (by interpolation) as 6,600. To convert this to a RSE we express the SE as a percentage of the estimate or 6,600/230,300 =2.9%.
8 The RSE of the estimate of median duration of insufficient work is calculated by multiplying this number (2.9%) by the appropriate factor shown in paragraph 6 (in this case 2.1): 2.9 x 2.1 = 6.1%. The SE of this estimate of median duration of insufficient work is therefore 6.1% of 26, i.e. about 2 (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 2428 weeks, and about 19 chances in 20 that it would have been within the range 2230 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 382,600 females who usually work part time and want more hours, 143,400 or 37.5% had insufficient work for 52 weeks or more. The SE of 143,400 may be calculated by interpolation as 5,500. To convert this to an RSE we express the SE as a percentage of the estimate, or 5,500/143,400 = 3.8%. The SE for 382,600 was calculated previously as 7,900, which converted to an RSE is 7,900/382,600 = 2.1%. 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 1.2 percentage points (=(37.5/100)x3.2). 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 36.3% and 38.7% and 19 chances in 20 that the proportion is within the range 35.1% to 39.9%.
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.
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.  %  
 
100  90  100  180  160  160  110  110  130  80  80.0  
200  160  170  260  220  220  140  150  160  140  70.0  
300  220  230  310  260  260  170  180  180  190  63.3  
500  330  320  390  320  340  210  220  220  270  54.0  
700  420  400  460  370  390  240  250  240  350  50.0  
1,000  530  500  540  420  460  280  290  270  440  44.0  
1,500  690  630  650  500  550  330  340  310  580  38.7  
2,000  820  750  740  570  620  370  380  350  700  35.0  
2,500  950  850  800  600  700  400  400  400  800  32.0  
3,000  1,050  950  900  650  750  450  450  400  900  30.0  
3,500  1,150  1,000  950  700  800  450  450  450  1,000  28.6  
4,000  1,250  1,100  1,000  750  850  500  500  450  1,050  26.3  
5,000  1,400  1,200  1,100  850  900  550  550  500  1,200  24.0  
7,000  1,650  1,400  1,300  950  1,050  600  600  550  1,450  20.7  
10,000  1,950  1,700  1,500  1,100  1,200  700  700  650  1,750  17.5  
15,000  2,350  2,000  1,800  1,300  1,450  800  800  750  2,150  14.3  
20,000  2,700  2,250  2,050  1,450  1,600  900  900  850  2,450  12.3  
30,000  3,150  2,650  2,450  1,700  1,850  1,050  1,050  1,000  2,950  9.8  
40,000  3,500  2,900  2,750  1,900  2,100  1,200  1,150  1,100  3,350  8.4  
50,000  3,800  3,150  3,000  2,100  2,250  1,300  1,250  1,250  3,700  7.4  
100,000  4,750  4,000  4,000  2,750  2,900  1,700  1,600  1,650  4,850  4.9  
150,000  5,350  4,600  4,750  3,250  3,350  1,950  1,850  2,000  5,600  3.7  
200,000  5,900  5,150  5,300  3,650  3,750  2,150  2,050  2,300  6,250  3.1  
300,000  6,900  6,100  6,250  4,300  4,300  2,500  . .  2,750  7,250  2.4  
500,000  8,550  7,700  7,650  5,250  5,050  3,050  . .  . .  8,800  1.8  
1,000,000  11,950  10,800  10,050  6,850  6,350  . .  . .  . .  11,550  1.2  
2,000,000  17,600  15,650  13,100  9,000  7,800  . .  . .  . .  15,250  0.8  
5,000,000  31,550  26,900  18,450  . .  . .  . .  . .  . .  23,400  0.5  
10,000,000  . .  . .  . .  . .  . .  . .  . .  . .  40,950  0.4  
 
. . 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%  
 
Mean duration of current period of insufficient work  11,800  10,800  8,300  4,600  5,600  2,000  1,300  2,100  12,000  
Median duration of current period of insufficient work  18,900  14,300  12,200  6,700  8,000  3,200  2,800  2,900  16,300  
Mean preferred number of extra hours  5,300  4,400  4,200  2,300  2,700  900  800  1,100  4,100  
All other estimates  6,200  4,700  4,100  2,500  2,900  1,200  1,000  1,100  4,600  
RSE OF 50%  
 
Mean duration of current period of insufficient work  2,800  2,800  2,400  1,400  1,700  600  400  700  2,500  
Median duration of current period of insufficient work  5,000  3,900  3,500  2,100  2,400  1,000  900  1,000  3,700  
Mean preferred number of extra hours  900  900  1,200  700  800  300  300  400  600  
All other estimates  1,200  1,000  1,200  800  900  400  300  400  700  
 
(a) Refers to the number of persons contributing to the estimate. 

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