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6220.0 - Persons Not in the Labour Force, Australia, Sep 2004  
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 11/03/2005   
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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 ERRORS

3 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Table 4 shows that the estimated number of persons in Australia who were discouraged jobseekers was 82,000. Since this estimate is between 50,000 and 100,000, table T1 shows the SE for Australia will be between 4,050 and 5,300, 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 in the range 77,100 to 86,900, and about 19 chances in 20 that the value will fall within the range 72,200 to 91,800. 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.**0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of 25% or less.



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 example above, of the 82,000 persons who were discouraged jobseekers, 28,400 or 34.6% were males. The SE of 28,400 may be calculated by interpolation as 3,200. To convert this to an RSE we express the SE as a percentage of the estimate, or 3,200/28,400 = 11.3%. The SE for 82,000 was calculated previously as 4,900, which converted to an RSE is 4,900/82,000 = 6.0%. Applying the above formula, the RSE of the proportion is


Equation: Example calculation of relative standard errors of proportions


8 Therefore, the SE for the proportion of males who were discouraged jobseekers is 3.3 percentage points (=(34.6/100)x9.6). Therefore, there are about two chances in three that the proportion of males who were discouraged jobseekers is between 31.3% and 37.9% and 19 chances in 20 that the proportion is within the range 28.0% to 41.2%.



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: Calculation of differences between estimates


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.


11 SEs contained in table T1 are applicable to all estimates from this survey.



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.
%

100
100
110
200
170
180
110
110
140
90.0
90.0
200
170
190
280
230
250
150
150
170
150.0
75.0
300
240
250
340
270
300
180
180
200
210.0
70.0
500
350
360
440
340
380
220
220
230
300.0
60.0
700
450
440
510
390
440
260
260
260
380.0
54.3
1,000
570
550
600
450
520
300
290
290
490.0
49.0
1,500
740
700
720
530
620
350
350
330
630.0
42.0
2,000
880
830
820
600
700
390
390
370
760.0
38.0
2,500
1,000
950
900
650
750
450
400
400
900.0
36.0
3,000
1,100
1,050
1,000
700
850
450
450
450
1,000.0
33.3
3,500
1,250
1,100
1,050
750
900
500
500
450
1,050.0
30.0
4,000
1,300
1,200
1,100
800
950
500
500
500
1,150.0
28.8
5,000
1,500
1,350
1,250
900
1,050
550
550
500
1,300.0
26.0
7,000
1,800
1,550
1,450
1,000
1,200
650
650
600
1,600.0
22.9
10,000
2,100
1,850
1,700
1,150
1,350
750
700
700
1,900.0
19.0
15,000
2,550
2,200
2,000
1,350
1,600
850
850
800
2,350.0
15.7
20,000
2,900
2,500
2,250
1,550
1,800
950
950
900
2,700.0
13.5
30,000
3,400
2,900
2,700
1,800
2,100
1,150
1,050
1,050
3,250.0
10.8
40,000
3,800
3,250
3,050
2,050
2,350
1,250
1,200
1,200
3,700.0
9.3
50,000
4,100
3,500
3,350
2,250
2,550
1,400
1,300
1,300
4,050.0
8.1
100,000
5,100
4,400
4,450
2,950
3,300
1,800
1,650
1,750
5,300.0
5.3
150,000
5,750
5,100
5,250
3,450
3,800
2,100
1,900
2,150
6,150.0
4.1
200,000
6,350
5,700
5,900
3,900
4,200
2,300
2,100
2,450
6,800.0
3.4
300,000
7,400
6,750
6,950
4,550
4,800
2,650
2,400
2,950
7,950.0
2.7
500,000
9,200
8,500
8,500
5,550
5,700
3,200
. .
3,750
9,650.0
1.9
1,000,000
12,850
11,900
11,100
7,300
7,100
. .
. .
. .
12,650.0
1.3
2,000,000
18,850
17,300
14,500
9,550
8,800
. .
. .
. .
16,700.0
0.8
5,000,000
33,850
29,750
20,450
. .
. .
. .
. .
. .
25,600.0
0.5
10,000,000
. .
. .
. .
. .
. .
. .
. .
. .
44,850.0
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.

RSE of 25%
7,200
5,700
4,900
2,700
3,600
1,300
1,300
1,300
5,600
RSE of 50%
1,400
1,300
1,400
800
1,100
400
400
400
900

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


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