6222.0 - Job Search Experience, Australia, Jul 2005  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 16/12/2005   
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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 ERROR

3 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Table 4 shows the estimated number of unemployed males in Australia who were looking for full-time work was 202,200. Since this estimate is between 200,000 and 300,000, table T1 shows that the SE for Australia will lie between 6,550 and 7,650 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 195,600 to 208,800 and about 19 chances in 20 that the value will fall within the range 189,000 to 215,400. 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 aterisk (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 less than 25%.



MEANS AND MEDIANS

6 The RSEs of estimates of mean duration of unemployment and median duration of unemployment are obtained by first finding the RSE of the estimate of the total number of persons contributing to the mean or median (see table T1) and then multiplying the resulting number by the following factors:

  • mean duration of unemployment: 1.5
  • median duration of unemployment: 1.7

7 The following is an example of the calculation of SEs where the use of a factor is required. Table 4 shows that the estimated median duration of unemployment for unemployed males in Australia was 13 weeks and shows that the number of unemployed males was estimated as 250,800. The SE of 250,800 can be calculated from table T1 (by interpolation) as 7,100. To convert this to an RSE we express the SE as a percentage of the estimate or 7,100/250,800 =2.8%.


8 The RSE of the estimate of median duration of unemployment for unemployed males is calculated by multiplying this number (2.8%) by the appropriate factor shown in the previous paragraph (in this case 1.7): 2.8 x 1.7 = 4.8%. The SE of this estimate of median duration of unemployment for unemployed males is therefore 4.8% of 13, i.e. almost one week. Therefore, there are two chances in three that the median duration of unemployment for males that would have been obtained if all dwellings had been included in the survey would have been within the range 12 weeks to 14 weeks, and about 19 chances in 20 that it would have been within the range 11 weeks to 15 weeks.



PROPORTIONS AND PERCENTAGES

9 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


10 Considering the example from the previous page, of the 202,200 unemployed males who were looking for full-time work, 45,100 or 22.3% had been unemployed for one year or more. The SE of 45,100 may be calculated by interpolation as 3,700. To convert this to an RSE we express the SE as a percentage of the estimate, or 3,700/45,100 = 8.2%. The SE for 202,200 was calculated previously as 6,600, which converted to an RSE is 6,600/202,200 = 3.3%. Applying the above formula, the RSE of the proportion is


Equation: Example calculation of relative standard errors of proportions


11 Therefore, the SE for the proportion of unemployed males looking for full-time work who had been unemployed for one year or more is 1.7 percentage points (=(22.3/100)x7.5). Therefore, there are about two chances in three that the proportion of unemployed males looking for full-time work who have been unemployed for one year or more is between 20.6% and 24.0% and 19 chances in 20 that the proportion is within the range 18.9% to 25.7%.



DIFFERENCES

12 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


13 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
120
140
80
80.0
200
170
180
270
220
230
150
160
170
140
70.0
300
230
240
330
270
280
180
180
190
200
66.7
500
340
340
420
330
350
220
230
230
290
58.0
700
430
420
490
380
410
250
260
250
370
52.9
1,000
550
530
580
440
480
290
300
280
470
47.0
1,500
720
670
690
520
570
340
350
330
610
40.7
2,000
860
790
790
590
650
380
400
360
730
36.5
2,500
1 000
900
850
650
700
400
450
400
850
34.0
3,000
1 100
1 000
950
700
750
450
450
400
950
31.7
3,500
1 200
1 050
1 000
750
800
500
500
450
1 050
30.0
4,000
1 300
1 150
1 100
800
850
500
500
450
1 100
27.5
5,000
1 450
1 250
1 200
850
950
550
550
500
1 250
25.0
7,000
1 700
1 500
1 400
1 000
1 100
650
650
600
1 550
22.1
10,000
2 050
1 750
1 600
1 150
1 250
700
750
650
1 850
18.5
15,000
2 450
2 100
1 900
1 350
1 500
850
850
800
2 250
15.0
20,000
2 800
2 350
2 200
1 500
1 650
950
950
900
2 600
13.0
30,000
3 300
2 750
2 600
1 800
1 950
1 100
1 100
1 050
3 150
10.5
40,000
3 650
3 100
2 900
2 000
2 200
1 250
1 200
1 150
3 550
8.9
50,000
3 950
3 300
3 200
2 200
2 350
1 350
1 300
1 300
3 900
7.8
100,000
4 950
4 200
4 250
2 900
3 050
1 750
1 700
1 750
5 100
5.1
150,000
5 600
4 850
5 050
3 400
3 500
2 000
1 950
2 100
5 900
3.9
200,000
6 150
5 450
5 650
3 800
3 900
2 250
2 150
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
. .
. .
. .
. .
. .
. .
. .
. .
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 unemployment
11 800
10 800
8 200
4 600
5 600
2 000
1 500
2 100
12 000
Median duration of unemployment
18 900
14 300
12 200
6 700
8 000
3 200
3 300
2 900
16 300
All other estimates
6 800
5 200
4 600
2 600
3 200
1 300
1 400
1 200
5 100

50% RSE

Mean duration of unemployment
2 800
2 800
2 400
1 400
1 700
600
500
700
2 500
Median duration of unemployment
5 000
3 900
3 500
2 100
2 400
1 000
1 100
1 000
3 700
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.