
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 3 shows that the estimated number of migrants was 1,362,600. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows the SE for Australia will be between 12,150 and 16,050, 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 in the range 1,349,000 to 1,376,200, and about 19 chances in 20 that the value will fall within the range 1,335,400 to 1,389,800. 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.
PROPORTIONS AND PERCENTAGES
6 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.
7 Considering the example above, of the 1,362,600 who were migrants, 625,300 or 46% were males. The SE of 625,300 may be calculated by interpolation as 10,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 10,000/625,300 = 1.6%. The SE for 1,362,600 was calculated previously as 13,600, which converted to an RSE is 13,600/1,362,600 = 1.0%. Applying the above formula, the RSE of the proportion is
8 Therefore, the SE for the proportion of male migrants is 0.6 percentage points (=(46/100)x1.2). Therefore, there are about two chances in three that the proportion of male migrants is between 45.4% and 46.6% and 19 chances in 20 that the proportion is within the range 44.8% to 47.2%.
DIFFERENCES
9 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:
10 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  100  140  80  80.0  
200  170  180  270  220  230  150  140  170  140  70.0  
300  230  240  330  270  280  180  160  190  200  66.7  
500  340  340  420  330  350  220  200  230  290  58.0  
700  430  420  490  380  410  250  230  250  370  52.9  
1,000  550  530  580  440  480  290  270  280  470  47.0  
1,500  720  670  690  520  570  340  310  330  610  40.7  
2,000  860  790  790  590  650  380  350  360  730  36.5  
2,500  1,000  900  850  650  700  400  400  400  850  34.0  
3,000  1,100  1,000  950  700  750  450  400  400  950  31.7  
3,500  1,200  1,050  1,000  750  800  500  450  450  1,050  30.0  
4,000  1,300  1,150  1,100  800  850  500  450  450  1,100  27.5  
5,000  1,450  1,250  1,200  850  950  550  500  500  1,250  25.0  
7,000  1,700  1,500  1,400  1,000  1,100  650  550  600  1,550  22.1  
10,000  2,050  1,750  1,600  1,150  1,250  700  650  650  1,850  18.5  
15,000  2,450  2,100  1,900  1,350  1,500  850  750  800  2,250  15.0  
20,000  2,800  2,350  2,200  1,500  1,650  950  850  900  2,600  13.0  
30,000  3,300  2,750  2,600  1,800  1,950  1,100  1,000  1,050  3,150  10.5  
40,000  3,650  3,100  2,900  2,000  2,200  1,250  1,100  1,150  3,550  8.9  
50,000  3,950  3,300  3,200  2,200  2,350  1,350  1,150  1,300  3,900  7.8  
100,000  4,950  4,200  4,250  2,900  3,050  1,750  1,500  1,750  5,100  5.1  
150,000  5,600  4,850  5,050  3,400  3,500  2,000  1,750  2,100  5,900  3.9  
200,000  6,150  5,450  5,650  3,800  3,900  2,250  . .  2,400  6,550  3.3  
300,000  7,200  6,450  6,650  4,450  4,450  2,600  . .  2,850  7,650  2.6  
500,000  8,900  8,100  8,150  5,450  5,300  3,100  . .  . .  9,300  1.9  
1,000,000  12,450  11,350  10,700  7,150  6,600  . .  . .  . .  12,150  1.2  
2,000,000  18,300  16,450  13,950  9,350  8,150  . .  . .  . .  16,050  0.8  
5,000,000  32,850  28,350  19,650  . .  . .  . .  . .  . .  24,600  0.5  
10,000,000  54,050  . .  . .  . .  . .  . .  . .  . .  43,150  0.4  
15,000,000  . .  . .  . .  . .  . .  . .  . .  . .  66,850  0.4  
20,000,000  . .  . .  . .  . .  . .  . .  . .  . .  95,800  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%  6,800  5,200  4,600  2,600  3,200  1,300  1,100  1,200  5,100  
RSE of 50%  1,300  1,100  1,300  800  900  400  400  400  800  
 
(a) Refers to the number of people contributing to the estimate. 
