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 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, taken from Job Search Experience, is as follows. JSE table 3 shows that 249,300 unemployed females were looking for fulltime work. Since this estimate is between 200,000 and 300,000, table T2 shows that the SE for Australia will lie between 6,500 and 7,700 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 242,200 to 256,400 and about 19 chances in 20 that the value will fall within the range 235,100 to 263,500. This example is illustrated in the diagram below.
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. *3.4) 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. **0.2), 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%. Table T3 presents the levels at which estimates have RSEs of 25% and 50%.
MEANS AND MEDIANS
6 The RSEs of means and medians are obtained by first finding the RSE of the estimate of the total number of persons contributing to the mean or median (see table T2) and then multiplying the resulting number by the following factors for Australian estimates:
 For JSE
 mean duration of unemployment: 1.6
 median duration of unemployment: 2.5
 For UEW
 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. JSE table 4 shows that the estimated median duration of unemployment for unemployed females in Australia was 10 weeks and shows that the number of unemployed females was estimated as 407,600. The SE of 407,600 can be calculated from table T2 (by interpolation) as 8,700. To convert this to an RSE express the SE as a percentage of the estimate or 8,700/407,600 = 2.1%.
8 The RSE of the estimate of median duration of unemployment for unemployed females is calculated by multiplying this number (2.1%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.1 x 2.5 = 5.3%. The SE of this estimate of median duration of unemployment for unemployed females is therefore 5.3% of 10 weeks, i.e. approximately one week. Therefore, there are two chances in three that the median duration of unemployment for females that would have been obtained if all dwellings had been included in the survey would have been within the range 9 to 11 weeks and about 19 chances in 20 that it would have been within the range 8 weeks to 12 weeks.
9 Table T3 represents the minimum size of estimates, based on the SE model described in paragraph 2, required to have RSEs of less than 25% and 50% respectively. For example, an estimate of median duration of unemployment for Australia based on less than 35,600 persons will have an RSE of at least 25%, and an estimate of median duration of unemployment for Australia based on less than 12,800 will have an RSE of at least 50%. For all other estimates, (i.e. those estimates based purely on number of persons in a specific category), an estimate of less than 8,800 for the Australian total will have an RSE of at least 25% and an estimate of less than 2,300 will have an RSE of at least 50%.
PROPORTIONS AND PERCENTAGES
10 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:
11 Considering the example from paragraph 3, of the 249,300 unemployed females who were looking for fulltime work, 51,100 or 20.5% had been unemployed for one year or more. The SE of 51,100 may be calculated by interpolation as 4,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,000/51,100 = 7.8%. The SE for 249,300 was calculated previously as 7,100, which converted to an RSE is 7,100/249,300 = 2.8%. Applying the above formula, the RSE of the proportion is:
12 Therefore, the SE for the proportion of unemployed females looking for fulltime work who had been unemployed for one year or more is 1.5 percentage points (=20.5/100) x 7.3). Therefore, there are about two chances in three that the proportion of unemployed females looking for fulltime work who have been unemployed for one year or more is between 19.0% and 22.0% and 19 chances in 20 that the proportion is within the range 17.5% to 23.5%.
DIFFERENCES
13 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:
14 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 (PNILF) 

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

100  180  150  200  170  170  110  80  120  140  140.0 
200  300  230  330  250  260  160  110  210  240  120.0 
300  390  290  440  310  330  200  140  270  320  106.7 
500  530  400  600  400  440  250  170  370  460  92.0 
700  650  480  730  470  520  290  200  430  580  82.9 
1,000  800  580  900  560  620  340  240  500  730  73.0 
1,500  990  710  1 120  670  760  400  300  580  940  62.7 
2,000  1 150  820  1 300  760  860  440  340  630  1 120  56.0 
2,500  1 300  900  1 450  850  950  450  400  650  1 250  50.0 
3,000  1 400  1 000  1 600  900  1 050  500  400  700  1 400  46.7 
3,500  1 500  1 050  1 700  950  1 100  550  450  750  1 500  42.9 
4,000  1 600  1 150  1 800  1 000  1 150  550  500  750  1 650  41.3 
5,000  1 800  1 250  2 000  1 100  1 250  600  600  850  1 800  36.0 
7,000  2 100  1 450  2 300  1 250  1 450  700  750  1 000  2 150  30.7 
10,000  2 400  1 650  2 650  1 400  1 600  850  1 000  1 300  2 500  25.0 
15,000  2 800  1 950  3 050  1 650  1 900  1 050  1 450  1 700  3 000  20.0 
20,000  3 150  2 150  3 350  1 900  2 150  1 200  1 850  2 000  3 350  16.8 
30,000  3 600  2 500  3 900  2 350  2 700  1 500  2 500  2 450  3 850  12.8 
40,000  4 000  2 750  4 400  2 750  3 200  1 750  3 100  2 750  4 250  10.6 
50,000  4 350  3 000  4 850  3 100  3 650  1 950  3 600  2 950  4 600  9.2 
100,000  6 050  4 350  7 150  4 450  5 350  2 700  5 650  3 350  6 050  6.1 
150,000  7 700  5 600  9 050  5 350  6 600  3 200  7 100  3 350  7 250  4.8 
200,000  9 200  6 650  10 600  6 050  7 600  3 600  . .  . .  8 300  4.2 
300,000  11 600  8 450  13 050  7 100  9 100  4 200  . .  . .  10 100  3.4 
500,000  15 000  11 350  16 500  8 550  11 300  5 000  . .  . .  13 200  2.6 
1,000,000  20 050  16 750  21 650  10 600  14 600  . .  . .  . .  19 550  2.0 
2,000,000  24 950  24 200  26 850  12 650  18 250  . .  . .  . .  28 300  1.4 
5,000,000  30 000  38 550  32 900  . .  . .  . .  . .  . .  40 800  0.8 
10,000,000  31 800  53 850  . .  . .  . .  . .  . .  . .  49 000  0.5 
15,000,000  . .  . .  . .  . .  . .  . .  . .  . .  52 550  0.4 

. . not applicable 
T2 STANDARD ERRORS OF ESTIMATES (UEW/JSE) 

 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  180  400  700  70.0 
1,500  1 100  710  900  580  710  350  210  430  900  60.0 
2,000  1 230  800  1 010  640  790  390  230  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  400  700  2 000  28.6 
10,000  2 300  1 450  1 800  1 150  1 450  700  500  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  850  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  1 500  1 750  3 650  9.1 
50,000  4 100  2 600  3 050  2 200  2 550  1 650  1 800  2 000  3 950  7.9 
100,000  5 200  3 450  4 200  3 300  3 750  2 400  3 100  2 650  4 950  5.0 
150,000  6 100  4 150  5 150  4 250  4 950  2 850  4 250  3 000  5 800  3.9 
200,000  7 050  4 850  6 000  4 950  5 950  3 150  5 300  3 150  6 500  3.3 
300,000  8 850  6 250  7 650  6 100  7 500  3 650  7 200  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 
T3 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. 
Persons not in the labour force 

RSE of 25%  9 400  5 000  10 900  4 100  5 100  1 600  900  2 700  10 100 
RSE of 50%  2 700  1 300  3 300  1 200  1 500  500  300  1 000  2 600 
Underemployed Workers 25% RSE 

Mean duration of insufficient work  18 300  9 800  13 000  5 800  9 400  2 500  1 200  3 000  19 200 
Median duration of insufficient work  44 400  22 900  32 500  18 100  21 700  6 700  11 900  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 
Underemployed Workers 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  2 700  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 
Job Search Experience 25% RSE 

Mean duration of unemployment  15 300  7 500  10 100  5 000  7 400  2 200  800  3 100  18 400 
Median duration of unemployment  40 600  20 300  26 700  13 900  21 200  7 900  2 600  9 100  35 600 
All other estimates  8 600  4 200  6 100  3 000  4 200  1 400  500  1 800  8 800 
Job Search Experience 50% RSE 

Mean duration of unemployment  5 100  2 500  3 600  1 700  2 500  800  200  1 200  5 800 
Median duration of unemployment  13 700  6 800  9 800  4 800  7 200  2 800  900  3 000  12 800 
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. 
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