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6220.0 - Persons Not in the Labour Force, Australia, Sep 2009 Quality Declaration 
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 24/03/2010   
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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.

3 The LFS sample size in September 2009 was approximately 9% higher than the sample size in 2008. This is due to re-instated sample that was cut from Labour Force Survey (LFS) and supplementary surveys from July 2008. In combination, the sample re-instatement is expected to decrease the standard errors for estimates from the supplementary surveys by approximately 4% at the broad aggregate level, relative to estimates from 2008 (standard errors will vary at lower aggregate levels). Detailed information about the sample reduction/re-instatement is provided in Information Paper: Labour Force Survey Sample Design, Nov 2007 (Third edition) (cat. no. 6269.0).


CALCULATION OF STANDARD ERROR

4 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 111,800. Since the estimate is between 100,000 and 150,000, table T1 shows that the SE for Australia will lie between 5,600 and 6,700 and can be approximated by interpolation using the following general formula:

Equation: Calculation of standard errors

5 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 105,900 to 117,700 and about 19 chances in 20 that the value will fall within the range 100,000 to 123,600. This example is illustrated in the following diagram.

Diagram: Confidence intervals of estimates

6 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

7 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: Example calculation of relative standard error of proportions

8 Considering the example above, of the 111,800 people who were discouraged job seekers, 59,500 or 53.2% were females. The SE of 59,500 may be calculated by interpolation as 4,500. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,500/59,500=7.6%. The SE for 111,800 was calculated previously as 5,900 which converted to an RSE is 5,900/111,800=5.3%. Applying the above formula, the RSE of the proportion is:

Equation: Calculation of relative standard  errors of proportions and percentages

9 Therefore, the SE for the proportion of discouraged job seekers who were females is 2.9 percentage points (=(53.2/100)x5.4). Therefore, there are about two chances in three that the proportion of females who were discouraged job seekers was between 50.3% and 56.1% and 19 chances in 20 that the proportion is within the range 47.4% to 59.0%.


DIFFERENCES

10 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

11 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 estimates (persons)
no.
no.
no.
no.
no.
no.
no.
no.
no.
no.

100
180
190
160
170
170
120
110
100
130
130.0
200
290
300
260
250
270
180
150
170
220
110.0
300
380
380
340
300
340
220
180
230
300
100.0
500
520
510
470
390
450
280
230
300
430
86.0
700
640
620
580
460
540
330
270
360
540
77.1
1,000
780
750
710
550
640
380
320
410
680
68.0
1,500
980
920
880
650
780
440
390
480
870
58.0
2,000
1 130
1 060
1 020
740
890
490
450
520
1 030
51.5
2,500
1 250
1 200
1 150
800
1 000
550
500
550
1 150
46.0
3,000
1 400
1 300
1 250
900
1 050
550
550
550
1 300
43.3
3,500
1 500
1 400
1 350
950
1 100
600
600
600
1 400
40.0
4,000
1 600
1 450
1 400
1 000
1 200
600
650
650
1 500
37.5
5,000
1 750
1 600
1 550
1 100
1 300
650
750
700
1 700
34.0
7,000
2 050
1 850
1 800
1 200
1 450
800
1 000
850
2 000
28.6
10,000
2 350
2 150
2 100
1 400
1 650
950
1 350
1 050
2 350
23.5
15,000
2 750
2 500
2 400
1 650
1 950
1 150
1 900
1 400
2 750
18.3
20,000
3 100
2 800
2 650
1 850
2 200
1 350
2 400
1 650
3 100
15.5
30,000
3 550
3 200
3 050
2 300
2 800
1 700
3 300
2 000
3 550
11.8
40,000
3 900
3 550
3 450
2 700
3 300
1 950
4 050
2 250
3 950
9.9
50,000
4 300
3 900
3 850
3 050
3 750
2 200
4 750
2 400
4 250
8.5
100,000
5 950
5 650
5 650
4 300
5 500
3 000
7 350
2 750
5 600
5.6
150,000
7 550
7 250
7 150
5 200
6 800
3 550
9 250
2 750
6 700
4.5
200,000
9 050
8 600
8 350
5 900
7 800
4 000
. .
. .
7 650
3.8
300,000
11 400
10 950
10 300
6 950
9 350
4 650
. .
. .
9 350
3.1
500,000
14 750
14 700
13 000
8 350
11 600
5 600
. .
. .
12 200
2.4
1,000,000
19 700
21 600
17 050
10 350
15 000
. .
. .
. .
18 050
1.8
2,000,000
24 550
31 300
21 200
12 350
18 750
. .
. .
. .
26 200
1.3
5,000,000
29 500
49 800
25 950
. .
. .
. .
. .
. .
37 750
0.8
10,000,000
31 250
69 550
. .
. .
. .
. .
. .
. .
45 300
0.5
15,000,000
. .
. .
. .
. .
. .
. .
. .
. .
48 600
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
Australia
no.
no.
no.
no.
no.
no.
no.
no.
no.

RSE of 25%
9 100
7 800
7 400
3 900
5 300
1 900
1 600
2 100
8 800
RSE of 50%
2 600
2 200
2 100
1 200
1 600
600
400
700
2 200

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



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