6226.0.55.001 - Persons Not In the Labour Force, Underemployed Workers and Job Search Experience, Australia, February 2014 Quality Declaration 
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 23/02/2015  Final
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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 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, taken from Job Search Experience, is as follows. JSE table 3 shows that 249,300 unemployed females were looking for full-time work. Since this estimate is between 200,000 and 300,000, table T2 shows that the SE for Australia will lie between 6,500 and 7,700 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 within the range 242,200 to 256,400 and about 19 chances in 20 that the value will fall within the range 235,100 to 263,500. This example is illustrated in the diagram below.

Graphic: 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. *3.4) 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. **0.2), 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%. Table T3 presents the levels at which estimates have RSEs of 25% and 50%.


MEANS AND MEDIANS

6 The RSEs of means and medians are obtained by first finding the RSE of the estimate of the total number of persons contributing to the mean or median (see table T2) and then multiplying the resulting number by the following factors for Australian estimates:
  • For JSE
      • mean duration of unemployment: 1.6
      • median duration of unemployment: 2.5
  • For UEW
      • 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. JSE table 4 shows that the estimated median duration of unemployment for unemployed females in Australia was 10 weeks and shows that the number of unemployed females was estimated as 407,600. The SE of 407,600 can be calculated from table T2 (by interpolation) as 8,700. To convert this to an RSE express the SE as a percentage of the estimate or 8,700/407,600 = 2.1%.

8 The RSE of the estimate of median duration of unemployment for unemployed females is calculated by multiplying this number (2.1%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.1 x 2.5 = 5.3%. The SE of this estimate of median duration of unemployment for unemployed females is therefore 5.3% of 10 weeks, i.e. approximately one week. Therefore, there are two chances in three that the median duration of unemployment for females that would have been obtained if all dwellings had been included in the survey would have been within the range 9 to 11 weeks and about 19 chances in 20 that it would have been within the range 8 weeks to 12 weeks.

9 Table T3 represents the minimum size of estimates, based on the SE model described in paragraph 2, required to have RSEs of less than 25% and 50% respectively. For example, an estimate of median duration of unemployment for Australia based on less than 35,600 persons will have an RSE of at least 25%, and an estimate of median duration of unemployment for Australia based on less than 12,800 will have an RSE of at least 50%. For all other estimates, (i.e. those estimates based purely on number of persons in a specific category), an estimate of less than 8,800 for the Australian total will have an RSE of at least 25% and an estimate of less than 2,300 will have an RSE of at least 50%.


PROPORTIONS AND PERCENTAGES

10 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

11 Considering the example from paragraph 3, of the 249,300 unemployed females who were looking for full-time work, 51,100 or 20.5% had been unemployed for one year or more. The SE of 51,100 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 4,000/51,100 = 7.8%. The SE for 249,300 was calculated previously as 7,100, which converted to an RSE is 7,100/249,300 = 2.8%. Applying the above formula, the RSE of the proportion is:

Equation: Example calculation of relative standard errors of proportions

12 Therefore, the SE for the proportion of unemployed females looking for full-time work who had been unemployed for one year or more is 1.5 percentage points (=20.5/100) x 7.3). Therefore, there are about two chances in three that the proportion of unemployed females looking for full-time work who have been unemployed for one year or more is between 19.0% and 22.0% and 19 chances in 20 that the proportion is within the range 17.5% to 23.5%.


DIFFERENCES

13 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: Calculations of differences between estimates

14 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 (PNILF)

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

100
180
150
200
170
170
110
80
120
140
140.0
200
300
230
330
250
260
160
110
210
240
120.0
300
390
290
440
310
330
200
140
270
320
106.7
500
530
400
600
400
440
250
170
370
460
92.0
700
650
480
730
470
520
290
200
430
580
82.9
1,000
800
580
900
560
620
340
240
500
730
73.0
1,500
990
710
1 120
670
760
400
300
580
940
62.7
2,000
1 150
820
1 300
760
860
440
340
630
1 120
56.0
2,500
1 300
900
1 450
850
950
450
400
650
1 250
50.0
3,000
1 400
1 000
1 600
900
1 050
500
400
700
1 400
46.7
3,500
1 500
1 050
1 700
950
1 100
550
450
750
1 500
42.9
4,000
1 600
1 150
1 800
1 000
1 150
550
500
750
1 650
41.3
5,000
1 800
1 250
2 000
1 100
1 250
600
600
850
1 800
36.0
7,000
2 100
1 450
2 300
1 250
1 450
700
750
1 000
2 150
30.7
10,000
2 400
1 650
2 650
1 400
1 600
850
1 000
1 300
2 500
25.0
15,000
2 800
1 950
3 050
1 650
1 900
1 050
1 450
1 700
3 000
20.0
20,000
3 150
2 150
3 350
1 900
2 150
1 200
1 850
2 000
3 350
16.8
30,000
3 600
2 500
3 900
2 350
2 700
1 500
2 500
2 450
3 850
12.8
40,000
4 000
2 750
4 400
2 750
3 200
1 750
3 100
2 750
4 250
10.6
50,000
4 350
3 000
4 850
3 100
3 650
1 950
3 600
2 950
4 600
9.2
100,000
6 050
4 350
7 150
4 450
5 350
2 700
5 650
3 350
6 050
6.1
150,000
7 700
5 600
9 050
5 350
6 600
3 200
7 100
3 350
7 250
4.8
200,000
9 200
6 650
10 600
6 050
7 600
3 600
. .
. .
8 300
4.2
300,000
11 600
8 450
13 050
7 100
9 100
4 200
. .
. .
10 100
3.4
500,000
15 000
11 350
16 500
8 550
11 300
5 000
. .
. .
13 200
2.6
1,000,000
20 050
16 750
21 650
10 600
14 600
. .
. .
. .
19 550
2.0
2,000,000
24 950
24 200
26 850
12 650
18 250
. .
. .
. .
28 300
1.4
5,000,000
30 000
38 550
32 900
. .
. .
. .
. .
. .
40 800
0.8
10,000,000
31 800
53 850
. .
. .
. .
. .
. .
. .
49 000
0.5
15,000,000
. .
. .
. .
. .
. .
. .
. .
. .
52 550
0.4

. . not applicable

T2 STANDARD ERRORS OF ESTIMATES (UEW/JSE)

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
180
400
700
70.0
1,500
1 100
710
900
580
710
350
210
430
900
60.0
2,000
1 230
800
1 010
640
790
390
230
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
400
700
2 000
28.6
10,000
2 300
1 450
1 800
1 150
1 450
700
500
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
850
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
1 500
1 750
3 650
9.1
50,000
4 100
2 600
3 050
2 200
2 550
1 650
1 800
2 000
3 950
7.9
100,000
5 200
3 450
4 200
3 300
3 750
2 400
3 100
2 650
4 950
5.0
150,000
6 100
4 150
5 150
4 250
4 950
2 850
4 250
3 000
5 800
3.9
200,000
7 050
4 850
6 000
4 950
5 950
3 150
5 300
3 150
6 500
3.3
300,000
8 850
6 250
7 650
6 100
7 500
3 650
7 200
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

T3 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.

Persons not in the labour force

RSE of 25%
9 400
5 000
10 900
4 100
5 100
1 600
900
2 700
10 100
RSE of 50%
2 700
1 300
3 300
1 200
1 500
500
300
1 000
2 600

Underemployed Workers 25% RSE

Mean duration of insufficient work
18 300
9 800
13 000
5 800
9 400
2 500
1 200
3 000
19 200
Median duration of insufficient work
44 400
22 900
32 500
18 100
21 700
6 700
11 900
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

Underemployed Workers 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
2 700
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

Job Search Experience 25% RSE

Mean duration of unemployment
15 300
7 500
10 100
5 000
7 400
2 200
800
3 100
18 400
Median duration of unemployment
40 600
20 300
26 700
13 900
21 200
7 900
2 600
9 100
35 600
All other estimates
8 600
4 200
6 100
3 000
4 200
1 400
500
1 800
8 800

Job Search Experience 50% RSE

Mean duration of unemployment
5 100
2 500
3 600
1 700
2 500
800
200
1 200
5 800
Median duration of unemployment
13 700
6 800
9 800
4 800
7 200
2 800
900
3 000
12 800
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.