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6206.0 - Labour Force Experience, Australia, Feb 2007  
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 17/08/2007   
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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 3 shows that the estimated number of people aged 15 years and over in the labour force for part of the year was 3,490,700. Since this estimate is between 2,000,000 and 5,000,000, table T1 shows that the SE for Australia will lie between 17,150 and 29,250 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 within the range 3,467,500 to 3,513,900, and about 19 chances in 20 that the value will fall within the range 3,444,300 to 3,537,100. 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.



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 (weeks): 0.76
  • median duration of time spent looking for work (weeks): 1.63

7 The following is an example of the calculation of SEs where the use of a factor is required. Table 11 shows that the estimated number of males aged 15 years and over looking for work at some time during the year was 774,700 with a median duration of time spent looking for work of 10 weeks. The SE of 774,700 can be calculated from table T1 (by interpolation) as 10,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 10,000/774,700 = 1.3%.


8 The RSE of the estimate of median duration of time spent looking for work for males aged 15 years and over is calculated by multiplying this number (1.3%) by the appropriate factor shown in the previous paragraph (in this case 1.63): 1.3 x 1.63 = 2.1%. The approximate SE of this estimate of median duration of time spent looking for work for males aged 15 years and over is therefore 2.1% of 10 weeks, i.e. about 0.2 weeks. Therefore, there are two chances in three that the median duration of time spent looking for work for males aged 15 years and over that would have been obtained if all dwellings had been included in the survey would have been within the range 9.8 weeks to 10.2 weeks, and about 19 chances in 20 that it would have been within the range 9.6 weeks to 10.4 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.


Equation: Calculation of relative standard errors of proportions and percentages


11 Considering the example from the previous page, of the 3,490,700 people aged 15 years and over in the labour force for part of the year, 515,000, or 14.8%, looked for work at some time during the year. The SE of 515,000 may be calculated by interpolation as 8,200. To convert this to an RSE we express the SE as a percentage of the estimate, or 8,200/515,000 = 1.6%. The SE for 3,490,700 was calculated previously as 23,200, which converted to an RSE is 23,200/3,490,700 = 0.7%. Applying the above formula, the RSE of the proportion is:


Equation: Example calculation of relative standard errors of proportions


12 Therefore, the SE for the proportion of people aged 15 years and over who looked for work at some time during the year is 0.2 percentage points (=(14.8/100)x1.4). Therefore, there are about two chances in three that the proportion of people aged 15 years and over who looked for work at some time during the year is between 14.6% and 15%, and 19 chances in 20 that the proportion is within the range 14.4% to 15.2%.



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


Equation: Calculation of differences between estimates


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
290
250
250
150
160
100
90
140
100
100.0
200
380
330
330
210
220
140
140
180
180
90.0
300
440
390
390
250
260
180
170
200
240
80.0
500
540
470
470
300
330
220
230
230
350
70.0
700
620
540
540
350
380
260
270
260
430
61.4
1000
710
620
610
400
440
300
320
280
540
54.0
1500
830
730
710
470
520
340
380
320
690
46.0
2000
920
810
790
530
590
370
420
340
820
41.0
2500
1 000
900
850
550
650
400
450
350
900
36.0
3000
1 100
950
900
600
700
400
500
400
1 000
33.3
3500
1 150
1 000
950
650
750
450
500
400
1 100
31.4
4000
1 200
1 050
1 000
700
750
450
500
400
1 200
30.0
5000
1 300
1 150
1 100
750
850
500
550
450
1 300
26.0
7000
1 500
1 300
1 250
850
950
550
700
500
1 550
22.1
10000
1 700
1 500
1 400
950
1 100
650
850
600
1 800
18.0
15000
2 000
1 750
1 600
1 100
1 250
800
1 150
750
2 100
14.0
20000
2 200
1 950
1 800
1 200
1 400
950
1 450
850
2 300
11.5
30000
2 600
2 300
2 050
1 450
1 600
1 250
1 950
1 100
2 650
8.8
40000
2 850
2 550
2 250
1 700
1 750
1 500
2 500
1 350
2 900
7.3
50000
3 100
2 800
2 450
1 900
1 950
1 750
2 950
1 500
3 100
6.2
100000
4 050
3 600
3 400
2 900
3 050
2 600
5 300
2 050
4 000
4.0
150000
4 800
4 350
4 250
3 700
4 100
3 200
7 500
2 350
4 700
3.1
200000
5 550
5 200
5 100
4 400
4 950
3 650
9 700
2 450
5 300
2.7
300000
7 100
6 800
6 800
5 450
6 250
4 300
14 050
2 550
6 350
2.1
500000
9 950
9 300
9 550
6 900
7 950
5 150
. .
. .
8 100
1.6
1000000
14 950
13 700
13 500
9 000
10 050
6 250
. .
. .
11 600
1.2
2000000
21 350
19 350
16 550
11 000
11 400
. .
. .
. .
17 150
0.9
5000000
31 500
28 550
17 350
13 000
11 500
. .
. .
. .
29 250
0.6
10000000
39 750
36 450
15 250
. .
. .
. .
. .
. .
39 200
0.4
15000000
. .
. .
. .
. .
. .
. .
. .
. .
44 050
0.3
20000000
. .
. .
. .
. .
. .
. .
. .
. .
46 700
0.2

. . 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
3 500
2 800
2 700
1 400
1 700
800
900
800
3 200
Median duration of time spent looking for work
11 900
9 800
8 700
4 700
5 800
2 700
3 100
2 400
12 800
All other estimates
5 400
4 400
4 100
2 200
2 600
1 300
1 500
1 200
5 500

50% RSE

Mean duration of time spent looking for work
1 100
900
900
400
500
200
200
300
600
Median duration of time spent looking for work
3 900
3 200
3 000
1 600
1 900
900
1 100
900
3 700
All other estimates
1 800
1 400
1 400
700
800
400
400
400
1 200

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


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