6220.0 - Persons Not in the Labour Force, Australia, Sep 2007 Quality Declaration 
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 25/03/2008   
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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 people is as follows. Table 1 shows that the estimated number of people in Australia who were discouraged job seekers was 76,600. Since this estimate is between 50,000 and 100,000, table T1 shows the SE for Australia will be between 3,450 and 4,550, 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 72,600 to 80,600, and about 19 chances in 20 that the value will fall within the range 68,600 to 84,600. 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.**0.3), 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. Table T2 presents the levels at which estimates have RSEs of 25% and 50%.



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 76,600 people in Australia who were discouraged job seekers, 28,000 or 36.6% were males. The SE of 28,000 may be calculated by interpolation as 2,800. To convert this to an RSE we express the SE as a percentage of the estimate, or 2,800/28,000 = 10%. The SE for 76,600 was calculated previously as 4,000, which converted to an RSE is 4,000/76,600 = 5.2%. 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 discouraged job seekers who were male is 3.1 percentage points (=(36.6/100)x 8.5). Therefore, there are about two chances in three that the proportion of males who were discouraged job seekers is between 33.5% and 39.7% and 19 chances in 20 that the proportion is within the range 30.4% to 42.8%.



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.



STANDARD ERRORS

T1 STANDARD ERRORS OF ESTIMATES

AUST.
NSW
Vic.
Qld
SA
WA
Tas.
NT
ACT
SE
RSE
Size of estimate
(persons)
no.
no.
no.
no.
no.
no.
no.
no.
no.
%

100
150
160
130
140
130
100
140
80
100
100.0
200
240
240
210
200
200
150
190
130
180
90.0
300
320
310
270
250
250
190
220
180
240
80.0
500
440
420
370
320
330
240
290
230
350
70.0
700
530
500
460
380
400
280
340
280
440
62.9
1,000
650
610
560
450
480
320
400
320
550
55.0
1,500
810
750
700
530
580
370
490
370
710
47.3
2,000
940
860
810
610
660
410
560
400
840
42.0
2,500
1 050
950
900
650
700
450
650
400
950
38.0
3,000
1 150
1 050
1 000
700
800
450
700
450
1 050
35.0
3,500
1 250
1 100
1 050
750
850
500
750
450
1 150
32.9
4,000
1 300
1 200
1 100
800
900
500
850
500
1 250
31.3
5,000
1 450
1 300
1 250
900
950
550
950
550
1 350
27.0
7,000
1 700
1 500
1 400
1 000
1 100
650
1 250
650
1 600
22.9
10,000
1 950
1 750
1 650
1 150
1 250
800
1 650
800
1 900
19.0
15,000
2 300
2 050
1 900
1 350
1 450
1 000
2 400
1 100
2 250
15.0
20,000
2 550
2 250
2 100
1 500
1 650
1 150
3 000
1 300
2 500
12.5
30,000
2 950
2 600
2 400
1 900
2 050
1 450
4 150
1 550
2 900
9.7
40,000
3 250
2 900
2 700
2 200
2 450
1 650
. .
1 750
3 200
8.0
50,000
3 550
3 150
3 000
2 500
2 800
1 850
. .
1 900
3 450
6.9
100,000
4 950
4 600
4 450
3 550
4 100
2 550
. .
2 100
4 550
4.6
150,000
6 300
5 900
5 600
4 250
5 050
3 000
. .
. .
5 450
3.6
200,000
7 550
7 000
6 600
4 800
5 800
3 400
. .
. .
6 250
3.1
300,000
9 500
8 900
8 100
5 650
6 950
. .
. .
. .
7 600
2.5
500,000
12 300
11 900
10 250
6 800
8 600
. .
. .
. .
9 900
2.0
1,000,000
16 450
17 500
13 400
. .
. .
. .
. .
. .
14 700
1.5
2,000,000
20 450
25 350
. .
. .
. .
. .
. .
. .
21 250
1.1
5,000,000
. .
. .
. .
. .
. .
. .
. .
. .
30 650
0.6
10,000,000
. .
. .
. .
. .
. .
. .
. .
. .
36 750
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%
6 700
5 400
4 900
2 800
3 200
1 500
2 600
1 500
6 000
RSE of 50%
1 800
1 500
1 300
800
900
500
600
400
1 300

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