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6359.0 - Forms of Employment, Australia, Nov 2007 Quality Declaration 
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 28/04/2008   
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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 people is as follows. Table 2 shows that the estimated number of people in Australia who were owner managers of incorporated enterprises was 674,100. Since this estimate is between 500,000 and 1,000,000, table T1 shows the SE for Australia will be between 7,500 and 10,550 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 665,500 to 682,700, and about 19 chances in 20 that the value will fall within the range 656,900 to 691,300. This example is illustrated in the diagram below.

Diagram: Confidence intervals of estimates


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 and percentages


7 Considering the example above, of the 674,100 people who were owner managers of incorporated enterprises, 199,600 or 29.6% were women. The SE of 199,600 may be calculated by interpolation as 5,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 5,000/199,600 = 2.5%. The SE for 674,100 was calculated previously as 8,600 which converted to an RSE is 8,600/674,100 = 1.3%. Applying the above formula, the RSE of the proportion is:


Equation: Example calculation of relative standard errors of proportions


8 Therefore, the SE for the proportion of women who were owner managers of incorporated enterprises, is 0.6 percentage points (=(29.6/100)x2.1). Therefore, there are about two chances in three that the proportion of women who were owner managers of incorporated enterprises is between 29.6% and 30.2% and 19 chances in 20 that the proportion is within the range 29.0% to 30.8%.


9 All other estimates produced from population estimates smaller than the values in T2 have RSEs larger than 25% and should be used with caution. T2 also indicates the size of the population estimates that would produce all other estimates with RSEs greater than 50% are considered too unreliable for general use.



DIFFERENCES

10 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 between estimates


11 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

NSW
Vic.
Qld
SA
WA
Tas.
NT
ACT
Aust.
Size of estimate (persons)
No.
No.
No.
No.
No.
No.
No.
No.
No.
%

100
270
260
190
160
180
100
110
90
100
100.0
200
360
340
280
210
240
150
170
140
170
85.0
300
430
400
340
250
280
180
210
180
240
80.0
500
530
490
440
310
340
220
270
230
340
68.0
700
610
550
510
350
390
250
320
260
430
61.4
1,000
700
640
590
400
450
290
370
290
550
55.0
1,500
830
740
700
470
520
340
430
310
700
46.7
2,000
930
830
790
530
580
370
480
330
830
41.5
2,500
1 000
900
850
550
650
400
500
350
950
38.0
3,000
1 100
950
900
600
700
400
550
350
1 050
35.0
3,500
1 150
1 050
1 000
650
700
450
550
400
1 100
31.4
4,000
1 200
1 100
1 050
700
750
450
600
400
1 200
30.0
5,000
1 300
1 150
1 100
750
800
500
650
450
1 350
27.0
7,000
1 500
1 350
1 250
850
950
550
800
500
1 550
22.1
10,000
1 700
1 500
1 400
950
1 050
650
1 000
600
1 800
18.0
15,000
2 000
1 750
1 550
1 100
1 200
800
1 400
700
2 100
14.0
20,000
2 200
1 950
1 700
1 200
1 350
900
1 750
850
2 300
11.5
30,000
2 550
2 250
1 950
1 400
1 550
1 150
2 450
1 050
2 600
8.7
40,000
2 850
2 500
2 200
1 600
1 700
1 400
3 100
1 250
2 850
7.1
50,000
3 100
2 750
2 400
1 800
1 900
1 600
3 750
1 450
3 050
6.1
100,000
3 950
3 550
3 250
2 700
2 750
2 250
6 450
1 900
3 850
3.9
150,000
4 600
4 350
4 000
3 450
3 650
2 700
. .
2 150
4 500
3.0
200,000
5 300
5 050
4 700
4 050
4 400
3 000
. .
2 300
5 050
2.5
300,000
6 700
6 500
5 950
5 000
5 500
3 450
. .
. .
5 950
2.0
500,000
9 350
9 000
8 050
6 250
7 000
. .
. .
. .
7 500
1.5
1,000,000
13 900
13 700
11 500
. .
8 950
. .
. .
. .
10 550
1.1
2,000,000
18 750
20 250
15 450
. .
. .
. .
. .
. .
15 300
0.8
5,000,000
23 900
32 400
. .
. .
. .
. .
. .
. .
25 550
0.5
10,000,000
. .
. .
. .
. .
. .
. .
. .
. .
34 100
0.3
15,000,000
. .
. .
. .
. .
. .
. .
. .
. .
38 500
0.3

. . 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%
5 500
4 500
4 200
2 200
2 600
1 300
1 900
1 200
5 600
RSE of 50%
1 800
1 500
1 300
700
800
400
600
400
1 300

(a) Refers to the number of people contributing to the estimate.


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