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6265.0 - Underemployed Workers, Australia, September 2013 Quality Declaration 
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 26/02/2014   
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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 4 shows the estimated number of female underemployed part-time workers was 493,800. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 7,700 and 9,650 and can be approximated by interpolation using the following general formula:

Equation: equation 1 tech note 2013

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 484,200 to 503,400 and about 19 chances in 20 that the value will fall within the range 474,600 to 513,000. This example is illustrated in the following diagram.


Diagram: CALCULATION OF STANDARD ERROR

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%.


MEANS AND MEDIANS

6 The RSEs of estimates of mean duration of insufficient work, median duration of insufficient work and mean preferred number of extra hours are obtained by first finding the RSE of the estimate of the total number of persons contributing to the mean or median ( see table T1) and then multiplying the resulting number by the following factors:

  • mean duration of insufficient work: 1.6
  • median duration of insufficient work: 2.5
  • mean preferred number of extra hours: 0.7

7 The following is an example of the calculation of SEs where the use of a factor is required. Table 4 shows that the estimated number of male underemployed part-time workers was 323,400 with a median duration of insufficient work of 30 weeks. The SE of 323,400 can be calculated from table T1 (by interpolation) as 7,700. To convert this to an RSE we express the SE as a percentage of the estimate or 7,700/323,400 = 2.4%.

8 The RSE of this estimate of median duration of insufficient work is calculated by multiplying this number (2.4%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.5 x 2.4 = 6.0%. The SE of this estimate of median duration of insufficient work is therefore 6.0% of 30, i.e. about 2 weeks (rounded to the nearest whole week). Therefore, there are two chances in three that the median duration of insufficient work for males that would have been obtained if all dwellings had been included in the survey would have been within the range 28-32 weeks, and about 19 chances in 20 that it would have been within the range 26-34 weeks.


PROPORTIONS AND PERCENTAGES

9 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: Equation 2 tech note 2013 generic RSE

10 Considering the example from paragraph 3, of the 493,800 female underemployed part-time workers, 199,800 or 40.5% had insufficient work for 52 weeks and over. The SE of 199,800 may be calculated by interpolation as 6,500. To convert this to an RSE we express the SE as a percentage of the estimate, or 6,500/199,800 = 3.3%. The SE for 493,800 was calculated previously as 9,600, which converted to an RSE is 9,600/493,800 = 1.9%. Applying the above formula, the RSE of the proportion is:

Equation: equation 3 tech note 2013

11 Therefore, the SE for the proportion of females who have a current period of insufficient work of 52 weeks or more is 1.1 percentage points (=(40.5/100)x2.7). Therefore, there are about two chances in three that the proportion of females who have a current period of insufficient work of 52 weeks or more was between 39.4% and 41.6% and 19 chances in 20 that the proportion is within the range 38.3% and 42.7%.


DIFFERENCES

12 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: Equation 4 tech note 2013 generic SE(x-y)

13 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
360
250
250
190
240
110
50
120
130
130.0
200
480
320
360
260
320
150
80
200
220
110.0
300
570
380
440
310
380
190
100
250
310
103.3
500
700
470
560
380
460
230
130
320
440
88.0
700
810
530
650
430
530
270
150
360
560
80.0
1,000
930
610
760
490
610
310
170
400
700
70.0
1,500
1 100
710
900
580
710
350
200
430
900
60.0
2,000
1 230
800
1 010
640
790
390
220
460
1 070
53.5
2,500
1 350
850
1 100
700
850
400
250
500
1 200
48.0
3,000
1 450
950
1 200
750
900
450
250
500
1 350
45.0
3,500
1 550
1 000
1 250
800
1 000
450
250
550
1 450
41.4
4,000
1 600
1 050
1 300
850
1 050
500
300
550
1 550
38.8
5,000
1 750
1 150
1 400
900
1 100
500
300
600
1 700
34.0
7,000
2 000
1 300
1 600
1 000
1 250
600
350
700
2 000
28.6
10,000
2 300
1 450
1 800
1 150
1 450
700
450
800
2 300
23.0
15,000
2 650
1 700
2 000
1 300
1 650
850
650
1 000
2 700
18.0
20,000
2 950
1 900
2 200
1 450
1 850
950
800
1 150
3 000
15.0
30,000
3 400
2 200
2 500
1 700
2 100
1 250
1 150
1 500
3 350
11.2
40,000
3 800
2 400
2 800
1 950
2 350
1 450
1 450
1 750
3 650
9.1
50,000
4 100
2 600
3 050
2 200
2 550
1 650
1 700
2 000
3 950
7.9
100,000
5 200
3 450
4 200
3 300
3 750
2 400
3 000
2 650
4 950
5.0
150,000
6 100
4 150
5 150
4 250
4 950
2 850
4 100
3 000
5 800
3.9
200,000
7 050
4 850
6 000
4 950
5 950
3 150
5 150
3 150
6 500
3.3
300,000
8 850
6 250
7 650
6 100
7 500
3 650
7 000
3 300
7 700
2.6
500,000
12 400
8 650
10 300
7 650
9 550
4 200
. .
3 300
9 650
1.9
1,000,000
18 400
13 150
14 700
9 750
12 150
4 800
. .
. .
13 600
1.4
2,000,000
24 800
19 450
19 800
11 600
14 100
. .
. .
. .
19 750
1.0
5,000,000
31 600
31 100
26 700
13 050
14 700
. .
. .
. .
32 950
0.7
10,000,000
33 850
42 900
31 200
. .
. .
. .
. .
. .
44 000
0.4
15,000,000
. .
. .
. .
. .
. .
. .
. .
. .
49 600
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
Aust.
no.
no.
no.
no.
no.
no.
no.
no.
no.

25% RSE

Mean duration of insufficient work
18 300
9 800
13 000
5 800
9 400
2 500
1 100
3 000
19 200
Median duration of insufficient work
44 400
22 900
32 500
18 100
21 700
6 700
10 300
13 400
35 300
Mean preferred number of extra hours
5 300
3 100
3 800
2 000
2 900
1 000
400
1 100
5 000
All other estimates
8 600
4 200
6 100
3 000
4 200
1 400
500
1 800
8 800

50% RSE

Mean duration of insufficient work
6 100
3 200
4 700
2 000
3 200
900
300
1 200
6 100
Median duration of insufficient work
15 000
7 600
11 800
6 300
7 400
2 400
2 600
4 000
12 600
Mean preferred number of extra hours
1 700
1 000
1 200
600
1 000
300
100
400
1 100
All other estimates
2 800
1 400
2 000
1 000
1 400
400
100
700
2 300

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



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