Australian Bureau of Statistics

Rate the ABS website
ABS Home > Statistics > By Release Date
ABS @ Facebook ABS @ Twitter ABS RSS ABS Email notification service
6222.0 - Job Search Experience, Australia, Jul 2010 Quality Declaration 
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 18/01/2011   
   Page tools: Print Print Page Print all pages in this productPrint All RSS Feed RSS Bookmark and Share Search this Product

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 women in Australia who were looking for full-time work was 168,200. Since this estimate is between 150,000 and 200,000, table T1 shows that the SE for Australia will lie between 5,000 and 5,600 and can be approximated by interpolation using the following general formula:

Equation: Calculation of standard error

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 163,000 to 173,400 and about 19 chances in 20 that the value will fall within the range 157,800 to 178,600. 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. **0.2), 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%. Table T2 presents the levels at which estimates have RSEs of 25% and 50%.


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 for Australian estimates:
  • mean duration of unemployment: 1.6
  • median duration of unemployment: 2.5

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 women in Australia was 12 weeks and shows that the number of unemployed women was estimated as 271,500. The SE of 271,500 can be calculated from table T1 (by interpolation) as 6,400. To convert this to an RSE we express the SE as a percentage of the estimate or 6,400/271,500 =2.4%.

8 The RSE of the estimate of median duration of unemployment for unemployed women is calculated by multiplying this number (2.4%) by the appropriate factor shown in the previous paragraph (in this case 2.5): 2.4 x 2.5 = 6%. The SE of this estimate of median duration of unemployment for unemployed women is therefore 6% of 12 weeks, i.e. almost one week. Therefore, there are two chances in three that the median duration of unemployment for women that would have been obtained if all dwellings had been included in the survey would have been within the range 11 to 13 weeks and about 19 chances in 20 that it would have been within the range 10 weeks to 14 weeks.

9 Table T2 represents the minimum size of estimates, based on the SE model described in paragraph 2, required to have RSEs of less than 25% and 50% respectively. For example, an estimate of median duration of unemployment for Australia based on less than 29,000 people will have an RSE of at least 25%, and an estimate of median duration of unemployment for Australia based on less than 10,000 will have an RSE of at least 50%. For all other estimates, (i.e. those estimates based purely on number of people in a specific category), an estimate of less than 6,800 for the Australian total will have an RSE of at least 25% and an estimate of less than 1,600 will have an RSE of at least 50%.


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 168,200 unemployed women who were looking for full-time work, 34,800 or 20.7% had been unemployed for one year or more. The SE of 34,800 may be calculated by interpolation as 3,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 3,000/34,800 = 8.6%. The SE for 168,200 was calculated previously as 5,200, which converted to an RSE is 5,200/168,200 = 3.1%. 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 unemployed women looking for full-time work who had been unemployed for one year or more is 1.7 percentage points (=(20.7/100)x8.0). Therefore, there are about two chances in three that the proportion of unemployed women looking for full-time work who have been unemployed for one year or more is between 19.0% and 22.4% and 19 chances in 20 that the proportion is within the range 17.3% to 24.1%.


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

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

100
290
290
220
180
220
110
80
100
110
110.0
200
400
380
320
240
290
160
120
170
190
95.0
300
470
440
390
280
340
190
150
210
260
86.7
500
580
540
500
340
420
240
200
270
380
76.0
700
660
620
580
390
480
270
230
300
480
68.6
1,000
760
710
680
450
550
310
270
330
610
61.0
1,500
900
830
810
530
640
360
310
360
780
52.0
2,000
1 010
930
910
590
710
390
350
390
920
46.0
2,500
1 100
1 000
1 000
650
800
400
350
400
1 050
42.0
3,000
1 200
1 100
1 050
700
850
450
400
450
1 150
38.3
3,500
1 250
1 150
1 100
700
900
450
400
450
1 250
35.7
4,000
1 300
1 200
1 200
750
900
500
450
450
1 350
33.8
5,000
1 450
1 300
1 250
800
1 000
500
500
500
1 500
30.0
7,000
1 650
1 500
1 450
900
1 150
600
550
600
1 700
24.3
10,000
1 850
1 700
1 600
1 050
1 300
700
750
700
2 000
20.0
15,000
2 150
1 950
1 800
1 200
1 500
850
1 000
850
2 350
15.7
20,000
2 400
2 200
1 950
1 350
1 650
1 000
1 300
1 000
2 550
12.8
30,000
2 800
2 550
2 250
1 550
1 900
1 250
1 800
1 250
2 900
9.7
40,000
3 100
2 800
2 500
1 800
2 100
1 500
2 250
1 500
3 150
7.9
50,000
3 350
3 050
2 750
2 000
2 300
1 700
2 700
1 650
3 400
6.8
100,000
4 250
4 000
3 750
3 000
3 400
2 400
4 700
2 250
4 300
4.3
150,000
5 000
4 850
4 600
3 850
4 450
2 850
6 450
2 500
5 000
3.3
200,000
5 750
5 650
5 400
4 550
5 350
3 200
8 050
2 650
5 600
2.8
300,000
7 250
7 250
6 850
5 550
6 750
3 700
10 950
2 800
6 650
2.2
500,000
10 150
10 050
9 250
7 000
8 600
4 250
. .
2 800
8 350
1.7
1,000,000
15 100
15 250
13 200
8 900
10 950
4 850
. .
. .
11 750
1.2
2,000,000
20 350
22 550
17 700
10 600
12 700
. .
. .
. .
17 050
0.9
5,000,000
25 900
36 100
23 900
11 900
13 250
. .
. .
. .
28 450
0.6
10,000,000
27 750
49 750
27 950
. .
. .
. .
. .
. .
37 950
0.4
15,000,000
. .
. .
. .
. .
. .
. .
. .
. .
42 850
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.

25% RSE

Mean duration of unemployment
11 200
9 500
8 600
4 400
6 200
2 300
1 600
2 400
14 700
Median duration of unemployment
29 800
25 700
22 600
12 100
18 100
8 100
5 100
6 700
29 000
All other estimates
6 300
5 400
5 100
2 600
3 500
1 400
1 100
1 400
6 800

50% RSE

Mean duration of unemployment
3 700
3 100
3 000
1 500
2 100
800
500
1 000
4 400
Median duration of unemployment
9 900
8 600
8 400
4 100
6 200
2 800
1 700
2 400
10 000
All other estimates
2 000
1 800
1 700
800
1 200
500
300
600
1 600

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



Bookmark and Share. Opens in a new window

Commonwealth of Australia 2014

Unless otherwise noted, content on this website is licensed under a Creative Commons Attribution 2.5 Australia Licence together with any terms, conditions and exclusions as set out in the website Copyright notice. For permission to do anything beyond the scope of this licence and copyright terms contact us.