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6220.0 - Persons Not in the Labour Force, Australia, September 2012 Quality Declaration 
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 07/03/2013   
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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 1 shows that the estimated number of people in Australia who were discouraged job seekers was 106,600. Since the estimate is between 100,000 and 150,000, table T1 shows that the SE for Australia will lie between 5,100 and 6,050 and can be approximated by interpolation using the following general formula:

Equation: Se formula and calculation

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 101,400 to 111,800 and about 19 chances in 20 that the value will fall within the range 96,200 to 117,000. This example is illustrated in the following diagram.

Diagram: Standard error from published estimate

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.**0.4), 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: RSE formula

7 Considering the example from paragraph 3, of the 106,600 people who were discouraged job seekers, 56,300 or 52.8% were females. The SE of 56,300 may be calculated by interpolation as 4,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,000/56,300=7.1%. The SE for 106,600 was calculated previously as 5,200 which converted to an RSE is 5,200/106,600=4.9%. Applying the above formula, the RSE of the proportion is:

Equation: RSE calculation

8 Therefore, the SE for the proportion of discouraged job seekers who were females is 2.7 percentage points (=(52.8/100)x5.1). Therefore, there are about two chances in three that the proportion of females who were discouraged job seekers was between 50.1% and 55.5% and 19 chances in 20 that the proportion is within the range 47.4% to 58.2%.


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: SE of difference between two estimates formula

10 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
SE
RSE
Size of Estimate (persons)
no.
no.
no.
no.
no.
no.
no.
no.
no.
%

100
160
170
150
150
160
110
90
90
110
110.0
200
270
270
240
220
240
160
130
160
200
100.0
300
350
340
310
280
310
200
150
200
270
90.0
500
470
460
430
360
410
250
190
270
390
78.0
700
580
560
520
420
490
290
230
320
490
70.0
1,000
710
680
640
490
580
340
270
370
620
62.0
1,500
880
830
800
590
700
400
330
430
790
52.7
2,000
1 030
960
930
670
800
440
380
470
930
46.5
2,500
1 150
1 050
1 050
750
900
500
450
500
1 050
42.0
3,000
1 250
1 150
1 150
800
950
500
450
500
1 150
38.3
3,500
1 350
1 250
1 200
850
1 000
550
500
550
1 250
35.7
4,000
1 450
1 350
1 300
900
1 050
550
550
550
1 350
33.8
5,000
1 600
1 450
1 400
1 000
1 150
600
650
650
1 550
31.0
7,000
1 850
1 700
1 650
1 100
1 350
700
850
750
1 800
25.7
10,000
2 150
1 950
1 900
1 250
1 500
850
1 150
950
2 100
21.0
15,000
2 500
2 300
2 200
1 500
1 750
1 050
1 600
1 250
2 500
16.7
20,000
2 800
2 550
2 400
1 700
2 000
1 250
2 050
1 500
2 800
14.0
30,000
3 200
2 900
2 750
2 100
2 500
1 550
2 800
1 850
3 250
10.8
40,000
3 550
3 200
3 150
2 450
3 000
1 750
3 450
2 050
3 550
8.9
50,000
3 850
3 550
3 500
2 750
3 400
2 000
4 000
2 200
3 850
7.7
100,000
5 400
5 100
5 100
3 900
5 000
2 700
6 250
2 500
5 100
5.1
150,000
6 850
6 550
6 450
4 700
6 150
3 250
7 850
2 500
6 050
4.0
200,000
8 200
7 800
7 600
5 350
7 050
3 650
. .
. .
6 950
3.5
300,000
10 350
9 900
9 300
6 300
8 500
4 250
. .
. .
8 450
2.8
500,000
13 350
13 300
11 800
7 550
10 500
5 050
. .
. .
11 050
2.2
1,000,000
17 850
19 600
15 450
9 400
13 600
. .
. .
. .
16 350
1.6
2,000,000
22 250
28 350
19 200
11 200
16 950
. .
. .
. .
23 700
1.2
5,000,000
26 700
45 150
23 500
. .
. .
. .
. .
. .
34 200
0.7
10,000,000
28 300
63 050
. .
. .
. .
. .
. .
. .
41 050
0.4
15,000,000
. .
. .
. .
. .
. .
. .
. .
. .
44 050
0.3

. . not applicable

T2 levels at which estimates have a relative standard errors of 25% and 50%(a)

NSW
Vic.
Qld
SA
WA
Tas.
NT
ACT
Australia
Percentage
no.
no.
no.
no.
no.
no.
no.
no.
no.

RSE of 25%
7 700
6 600
6 300
3 300
4 500
1 700
1 200
1 800
7 300
RSE of 50%
2 100
1 800
1 700
1 000
1 300
500
300
600
1 700

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



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