6359.0 - Forms of Employment, Australia, Nov 2004  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 19/05/2005   
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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 persons is as follows. Table 2 shows that the estimated number of persons in Australia who were Owner managers of incorporated enterprises was 687,200. Since this estimate is between 500,000 and 1,000,000, table T1 shows the SE for Australia will be between 8,800 and 11,550 and can be approximated by interpolation using the following general formula:


Equation: Calculation of standard errors


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 677,400 to 697,000, and about 19 chances in 20 that the value will fall within the range 667,600 to 706,800. This example is illustrated in the diagram below.

Diagram: Confidence interval


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.


Equation: Calculation of relative standard errors of proportions


7 Considering the example above, of the 687,200 persons who were Owner managers of incorporated enterprises, 188,900 or 27.5% were females. The SE of 188,900 may be calculated by interpolation as 6,100. To convert this to an RSE we express the SE as a percentage of the estimate, or 6,100/188,900 = 3.2%. The SE for 687,200 was calculated previously as 9,800, which converted to an RSE is 9,800/687,200 = 1.4%. Applying the above formula, the RSE of the proportion is


Equation: Example of calculation of relative standard errors of proportions


8 Therefore, the SE for the proportion of females who were Owner managers of incorporated enterprises, is 0.8 percentage points (=(27.5/100)x2.9). Therefore, there are about two chances in three that the proportion of females who were Owner managers of incorporated enterprises is between 26.7% and 28.3% and 19 chances in 20 that the proportion is within the range 25.9% to 29.1%.



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 (x-y) may be calculated by the following formula:


Equation: Calculation of differences


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.

T1 STANDARD ERRORS OF ESTIMATES
AUST.
NSW
Vic.
Qld
SA
WA
Tas.
NT
ACT
SE
RSE
Size of estimates (persons)
'000
'000
'000
'000
'000
'000
'000
'000
'000
%
100
90
100
180
160
160
110
100
130
80
80.0
200
160
170
260
220
220
140
130
160
140
70.0
300
220
230
310
260
260
170
160
180
190
63.3
500
330
320
390
320
340
210
190
220
270
54.0
700
420
400
460
370
390
240
220
240
350
50.0
1,000
530
500
540
420
460
280
250
270
440
44.0
1,500
690
630
650
500
550
330
300
310
580
38.7
2,000
820
750
740
570
620
370
330
350
700
35.0
2,500
950
850
800
600
700
400
350
400
800
32.0
3,000
1,050
950
900
650
750
450
400
400
900
30.0
3,500
1,150
1,000
950
700
800
450
400
450
1,000
28.6
4,000
1,250
1,100
1,000
750
850
500
450
450
1,050
26.3
5,000
1,400
1,200
1,100
850
900
550
500
500
1,200
24.0
7,000
1,650
1,400
1,300
950
1,050
600
550
550
1,450
20.7
10,000
1,950
1,700
1,500
1,100
1,200
700
600
650
1,750
17.5
15,000
2,350
2,000
1,800
1,300
1,450
800
700
750
2,150
14.3
20,000
2,700
2,250
2,050
1,450
1,600
900
800
850
2,450
12.3
30,000
3,150
2,650
2,450
1,700
1,850
1,050
950
1,000
2,950
9.8
40,000
3,500
2,900
2,750
1,900
2,100
1,200
1,050
1,100
3,350
8.4
50,000
3,800
3,150
3,000
2,100
2,250
1,300
1,100
1,250
3,700
7.4
100,000
4,750
4,000
4,000
2,750
2,900
1,700
1,450
1,650
4,850
4.9
150,000
5,350
4,600
4,750
3,250
3,350
1,950
1,650
2,000
5,600
3.7
200,000
5,900
5,150
5,300
3,650
3,750
2,150
1,800
2,300
6,250
3.1
300,000
6,900
6,100
6,250
4,300
4,300
2,500
2,100
2,750
7,250
2.4
500,000
8,550
7,700
7,650
5,250
5,050
3,050
. .
3,500
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%
6,200
4,700
4,100
2,500
2,900
1,200
1,000
1,100
4,600
RSE of 50%
1,200
1,000
1,200
800
900
400
300
400
700
(a) Refers to the number of persons contributing to the estimate.