Australian Bureau of Statistics

Rate the ABS website
ABS Home > Statistics > By Catalogue Number
6209.0 - Labour Mobility, Australia, February 2013 Quality Declaration 
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 21/08/2013   
   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 Estimates in this publication are based on information obtained from occupants of a sample of dwellings, and 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 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 11 shows that 366,600 people involuntarily ceased their last job during the year and their duration in that job was less than 12 months. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 7,150 and 9,000 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 358,800 to 374,400 and about 19 chances in 20 that the value will fall within the range 351,000 to 382,200. This example is illustrated in the following diagram.

Diagram: Example of estimate plus or minus two standard errors

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.*3.2) 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%.


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 previous example from Table 11, of the 366,600 people who ceased their last job involuntarily during the year ending February 2013, and their duration of last job was less than 12 months, 210,900 or 57.5% gave their reason as 'Job was temporary or seasonal'. The SE of 210,900 may be calculated by interpolation as 6,200. To convert this to an RSE we express the SE as a percentage of the estimate, or 6,200/210,900 = 2.9%. The SE for 366,600 was calculated previously as 7,800, which converted to an RSE 7,800/366,600=2.1%. Applying the above formula, the RSE of the proportion is:

Equation: Example of calculation of relative standard errors

8 Therefore, the SE for the proportion of people who reported their reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 12 months is 1.2 percentage points (=(57.5/100)x2.0). Therefore, there are about two chances in three that the proportion of people who reported their reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 12 months or more was between 56.3% and 58.7% and 19 chances in 20 that the proportion is within the range 55.1% to 59.9%.


DIFFERENCES

9 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 standard error of difference between estimates

10 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, 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
SE
RSE
Size of Estimate (persons)
no.
no.
no.
no.
no.
no.
no.
no.
no.
%

100
320
310
240
190
230
120
90
110
120
120.0
200
430
410
340
260
310
170
130
180
210
105.0
300
510
480
420
300
370
210
160
230
290
96.7
500
620
580
540
370
450
260
210
290
410
82.0
700
720
670
630
420
510
290
250
330
520
74.3
1,000
830
770
740
490
590
340
290
360
660
66.0
1,500
970
900
870
570
690
390
340
390
840
56.0
2,000
1 090
1 000
980
630
770
430
380
420
990
49.5
2,500
1 200
1 100
1 050
700
850
450
400
450
1 100
44.0
3,000
1 250
1 150
1 150
750
900
500
450
450
1 250
41.7
3,500
1 350
1 250
1 200
800
950
500
450
500
1 350
38.6
4,000
1 400
1 300
1 250
800
1 000
550
450
500
1 450
36.3
5,000
1 550
1 400
1 400
900
1 100
550
500
550
1 600
32.0
7,000
1 750
1 600
1 550
1 000
1 250
650
600
650
1 850
26.4
10,000
2 000
1 850
1 750
1 150
1 400
750
800
750
2 150
21.5
15,000
2 350
2 150
1 950
1 300
1 600
900
1 100
900
2 500
16.7
20,000
2 600
2 350
2 100
1 450
1 800
1 050
1 400
1 050
2 750
13.8
30,000
3 000
2 750
2 450
1 700
2 050
1 350
1 950
1 350
3 150
10.5
40,000
3 350
3 050
2 700
1 950
2 250
1 600
2 450
1 600
3 400
8.5
50,000
3 600
3 300
2 950
2 150
2 500
1 800
2 950
1 800
3 650
7.3
100,000
4 600
4 300
4 050
3 250
3 650
2 600
5 100
2 400
4 650
4.7
150,000
5 400
5 200
4 950
4 150
4 800
3 100
7 000
2 700
5 400
3.6
200,000
6 250
6 100
5 800
4 900
5 800
3 450
8 750
2 850
6 050
3.0
300,000
7 850
7 800
7 400
6 000
7 300
4 000
11 950
3 000
7 150
2.4
500,000
11 000
10 850
9 950
7 550
9 300
4 600
. .
3 000
9 000
1.8
1,000,000
16 300
16 500
14 250
9 600
11 850
5 250
. .
. .
12 700
1.3
2,000,000
21 950
24 350
19 150
11 450
13 700
. .
. .
. .
18 400
0.9
5,000,000
28 000
39 000
25 850
12 900
14 300
. .
. .
. .
30 700
0.6
10,000,000
30 000
53 750
30 200
. .
. .
. .
. .
. .
41 000
0.4
15,000,000
. .
. .
. .
. .
. .
. .
. .
. .
46 250
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.

Relative Standard Error of 25%
7 100
6 100
5 800
2 900
4 000
1 600
1 300
1 600
7 800
Relative Standard Error of 50%
2 300
2 000
1 900
1 000
1 300
500
400
600
2 000

(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.