
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 ERRORS
3 An example of the calculation and the use of SEs in relation to estimates of people is as follows. Table 1 shows that the estimated number of people aged 1569 years in the labour force for part of the year was 3,349,000. Since this estimate is between 2,000,000 and 5,000,000, table T1 shows that the SE for Australia will lie between 16,050 and 24,600 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 3,329,100 to 3,368,900 and about 19 chances in 20 that the value will fall within the range 3,309,200 to 3,388,800. 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. **0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of 25% or less.
MEANS AND MEDIANS
6 The RSEs of estimates of mean and median duration of time spent looking for work are obtained by first finding the RSE of the estimate of the total number of people contributing to the estimate (see table T1) and then multiplying the resulting number by the following factors:
 mean duration of time spent looking for work: 0.76
 median duration of time spent looking for work: 1.63
7 The following is an example of the calculation of SEs where the use of a factor is required. Table 10 shows that the estimated number of males aged 1569 years looking for work at some time during the year was 782,000 with a median duration of time spent looking for work of 12 weeks. The SE of 782,000 can be calculated from table T1 (by interpolation) as 10,900. To convert this to an RSE we express the SE as a percentage of the estimate, or 10,900/782,000 = 1.4%.
8 The RSE of the estimate of median duration of time spent looking for work for males aged 1569 years is calculated by multiplying this number (1.4%) by the appropriate factor shown in the previous paragraph (in this case 1.63): 1.4 x 1.63 = 2.3%. The approximate SE of this estimate of median duration of time spent looking for work for males aged 1569 years is therefore 2.3% of 12 weeks, i.e. about 0.3 weeks. Therefore, there are two chances in three that the median duration of time spent looking for work for males aged 1569 years that would have been obtained if all dwellings had been included in the survey would have been within the range 11.7 weeks to 12.3 weeks, and about 19 chances in 20 that it would have been within the range 11.4 weeks to 12.6 weeks.
9 Estimates of means and medians produced from population estimates smaller than the values provided in table T2 have RSEs larger than 25% and should be used with caution. Table T2 also indicates the size of population estimates that would produce means and medians with RSEs greater than 50%, which are considered too unreliable for general use.
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 above, of the 3,349,000 people aged 1569 years in the labour force for part of the year, 461,500, or 13.8%, looked for work at some time during the year. The SE of 461,500 may be calculated by interpolation as 9,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 9,000/461,500 = 2.0%. The SE for 3,349,000 was calculated previously as 19,900, which converted to an RSE is 19,900/3,349,000 = 0.6%. Applying the above formula, the RSE of the proportion is:
12 Therefore, the SE for the proportion of people aged 1569 years who looked for work at some time during the year is 0.3 percentage points (=(13.8/100)x1.9). Therefore, there are about two chances in three that the proportion of people aged 1569 years who looked for work at some time during the year is between 13.5% and 14.1%, and 19 chances in 20 that the proportion is within the range 13.2% to 14.4%.
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 
 
         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  100  110  190  170  160  110  110  140  80  80.0  
200  170  180  270  220  230  150  150  170  140  70.0  
300  230  240  330  270  280  180  180  190  200  66.7  
500  340  340  420  330  350  220  220  230  290  58.0  
700  430  420  490  380  410  250  250  250  370  52.9  
1000  550  530  580  440  480  290  290  280  470  47.0  
1500  720  670  690  520  570  340  340  330  610  40.7  
2000  860  790  790  590  650  380  380  360  730  36.5  
2500  1,000  900  850  650  700  400  400  400  850  34.0  
3000  1,100  1,000  950  700  750  450  450  400  950  31.7  
3500  1,200  1,050  1,000  750  800  500  450  450  1,050  30.0  
4000  1,300  1,150  1,100  800  850  500  500  450  1,100  27.5  
5000  1,450  1,250  1,200  850  950  550  550  500  1,250  25.0  
7000  1,700  1,500  1,400  1,000  1,100  650  600  600  1,550  22.1  
10000  2,050  1,750  1,600  1,150  1,250  700  700  650  1,850  18.5  
15000  2,450  2,100  1,900  1,350  1,500  850  800  800  2,250  15.0  
20000  2,800  2,350  2,200  1,500  1,650  950  900  900  2,600  13.0  
30000  3,300  2,750  2,600  1,800  1,950  1,100  1,050  1,050  3,150  10.5  
40000  3,650  3,100  2,900  2,000  2,200  1,250  1,150  1,150  3,550  8.9  
50000  3,950  3,300  3,200  2,200  2,350  1,350  1,250  1,300  3,900  7.8  
100000  4,950  4,200  4,250  2,900  3,050  1,750  1,600  1,750  5,100  5.1  
150000  5,600  4,850  5,050  3,400  3,500  2,000  1,850  2,100  5,900  3.9  
200000  6,150  5,450  5,650  3,800  3,900  2,250  . .  2,400  6,550  3.3  
300000  7,200  6,450  6,650  4,450  4,450  2,600  . .  2,850  7,650  2.6  
500000  8,900  8,100  8,150  5,450  5,300  3,100  . .  . .  9,300  1.9  
1000000  12,450  11,350  10,700  7,150  6,600  . .  . .  . .  12,150  1.2  
2000000  18,300  16,450  13,950  9,350  8,150  . .  . .  . .  16,050  0.8  
5000000  32,850  28,350  19,650  . .  . .  . .  . .  . .  24,600  0.5  
10000000  . .  . .  . .  . .  . .  . .  . .  . .  43,150  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.  
25% RSE  
 
Mean duration of time spent looking for work  3,900  3,100  2,900  1,500  2,300  700  900  600  2,700  
Median duration of time spent looking for work  17,100  12,900  10,900  6,100  7,300  2,900  2,800  2,600  14,500  
All other estimates  6,800  5,200  4,600  2,600  3,200  1,300  1,300  1,200  5,100  
50% RSE  
 
Mean duration of time spent looking for work  600  600  800  500  700  200  300  200  300  
Median duration of time spent looking for work  4,400  3,400  3,200  1,900  2,200  900  900  900  3,200  
All other estimates  1,300  1,100  1,300  800  900  400  400  400  800  
 
(a) Refers to the number of persons contributing to the estimate. 

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