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6206.0 - Labour Force Experience, Australia, Feb 2005  
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 28/07/2005   
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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 people is as follows. Table 1 shows that the estimated number of people aged 15-69 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:


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 3,329,100 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.

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: 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 15-69 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 15-69 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 15-69 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 15-69 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.


Equation: Calculation of relative standard errors of proportions and percentages


11 Considering the example above, of the 3,349,000 people aged 15-69 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:


Equation: Example calculation of relative standard errors of proportions


12 Therefore, the SE for the proportion of people aged 15-69 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 15-69 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 (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
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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