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6203.0 - Labour Force, Australia, Mar 2002  
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 26/04/2002   
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  • Technical Note

1 A new sample for the Labour Force Survey has been phased in over the period September 1997 to April 1998. For information about the sample design see Information Paper: Labour Force Survey Sample Design (6269.0).


ESTIMATION PROCEDURE

2 The labour force estimates are derived from the population survey by use of a complex ratio estimation procedure, which ensures that the survey estimates conform to an independently estimated distribution of the population by age and sex, rather than to the age and sex distribution within the sample itself.


RELIABILITY OF THE ESTIMATES

3 Two types of error are possible in an estimate based on a sample survey: sampling error and non-sampling error. The sampling error is a measure of the variability that occurs by chance because a sample, rather than the entire population, is surveyed. Since the estimates in this publication are based on information obtained from occupants of a sample of dwellings they, and the movements derived from them, are subject to sampling variability; that is, they may differ from the estimates that would have been produced if all dwellings had been included in the surveys. One measure of the likely difference is given by the standard error, 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 that the estimate that would have been obtained if all dwellings had been included will differ by less than one standard error from a sample estimate, and about nineteen chances in twenty that the difference will be less than two standard errors. Another measure of sampling variability is the relative standard error which is obtained by expressing the standard error as a percentage of the estimate to which it refers. The relative standard error is a useful measure in that it provides an immediate indication of the percentage errors likely to have occurred due to sampling, and thus avoids the need to refer also to the size of the estimate.

4 The imprecision due to sampling variability, which is measured by the standard error, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents, errors made in collection such as in recording and coding data, and errors made in processing the data. Inaccuracies of this kind are referred to as the non-sampling error and they may occur in any enumeration, whether it be a full count or a sample. It is not possible to quantify non-sampling error, but every effort is made to reduce it to a minimum by careful design of questionnaires, intensive training and supervision of interviewers and efficient operating procedures. For the examples in paragraph 9 it is assumed to be zero. In practice, the potential for non-sampling error adds to the uncertainty of the estimates caused by sampling variability.

5 Space does not allow for the separate indication of the standard errors of all estimates in this publication. Standard errors of estimates for the latest month and of estimates of movements since the previous month are shown in table 1. Standard errors of other estimates and other monthly movements should be determined by using tables A and B.

6 The size of the standard error increases with the level of the estimate, so that the larger the estimate the larger is the standard error. However, it should be noted that the larger the sample estimate the smaller will be the standard error in percentage terms. Thus, larger sample estimates will be relatively more reliable than smaller estimates.

7 As the standard errors in table A show, the smaller the estimate the higher is the relative standard error. Very small estimates are subject to such high standard errors (relative to the size of the estimate) as to detract seriously from their value for most reasonable uses. In the tables in this publication, only estimates with relative standard errors of 25% or less, and percentages based on such estimates, are considered sufficiently reliable for most purposes. However, estimates and percentages with larger relative standard errors have been included and are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high standard errors and should be used with caution.

8 The movement in the level of an estimate is also subject to sampling variability. The standard error of the movement depends on the levels of the estimates from which the movement is obtained rather than the size of the movement. An indication of the magnitude of standard errors of monthly movements is given in table B. The estimates of standard error of monthly movements apply only to estimates of movements between two consecutive months. Movements between corresponding months of consecutive quarters (quarterly movements), corresponding months of consecutive years (annual movements) and other non-consecutive months, will generally be subject to somewhat greater sampling variability than is indicated in table B. Standard errors of quarterly movements can be obtained by multiplying the figures in table A by 1.04. Standard errors of all six monthly movements can be obtained by multiplying the figures in table A by 1.28. When using table A or table B to calculate standard errors of movements, refer to the larg
er of the two estimates from which the movement is derived.

9 Examples of the calculation and use of standard errors are given below:

  • Consider an estimate for Australia of 500,000 employed persons aged 15-19 years. By referring to table A, in the row for an estimate of 500,000 and the column for Australia, a standard error of 8,700 is obtained. There are about two chances in three that the true value (the number that would have been obtained if the whole population had been included in the survey) is within the range 491,300 to 508,700. There are about nineteen chances in twenty that the true value is in the range 482,600 to 517,400.

Diagram  - Published estimate

  • Consider estimates for females employed part time in Australia of 1,390,000 in one month and 1,400,000 in the next month. This represents an upward movement of 10,000. By referring to table B for the larger estimate of 1,400,000, a movement standard error of 9,200 is obtained (after applying linear interpolation and rounding). Therefore, there are about two chances in three that the true movement is in the range +800 to +19,200 and about nineteen chances in twenty that the true movement is in the range -8,400 to +28,400.

Diagram - Estimated movement


10 The relative standard errors of estimates of aggregate hours worked, average hours worked, average duration of unemployment, and median duration of unemployment are obtained by first finding the relative standard error of the estimate of the total number of persons contributing to the estimate (see table A) and then multiplying the figure so obtained by the following relevant factors:
  • aggregate hours worked: 1.4;
  • average hours worked: 0.9;
  • average duration of unemployment: 1.5; and
  • median duration of unemployment: 1.7.

The levels at which these and other labour force estimates have a relative standard error of 25% are shown in table C.

11 The following is an example of the calculation of standard errors where the use of a factor is required:
  • Consider a median duration of unemployment for Australia of 30 weeks, with an estimate of 1,000,000 persons unemployed. Table A gives the standard error as 11,350 which is 1.1% as a relative standard error. The factor of 1.7 (see paragraph 10) is applied to the relative standard error of 1.1% to obtain 1.9%. Therefore the standard error for the median duration of unemployment is 1.9% of 30 weeks, i.e. about half of one week. So there are two chances in three that the median duration of unemployment is between 29.5 and 30.5 weeks, and about nineteen chances in twenty that it is between 29 and 31 weeks.

12 Proportions and percentages (for example, unemployment rates) formed from the ratio of two estimates are also subject to sampling error. The size of the error depends on the accuracy of both the numerator and denominator. The formula for the relative standard error (RSE) of a proportion or percentage is given below:

Image - Formula for the relative standard error (RSE) of a proportion or percentage



13 Standard errors contained in tables A and B are designed to provide an average standard error applicable for all monthly Labour Force Survey estimates. Analysis of the standard errors applicable to particular survey estimates has shown that the standard errors of estimates of employment are generally 5% lower than those shown in tables A and B, while standard errors for estimates of unemployment and persons not in the labour force are both approximately 4% higher than those shown in the tables.



A. STANDARD ERRORS OF ESTIMATES FROM SEPTEMBER 1997(a)
NSW
Vic.
Qld
SA
WA
Tas.
NT
ACT
Aust.
Size of

estimate
no.
no.
no.
no.
no.
no.
no.
no.
no.
%

100
100
100
130
200
210
210
140
130
160
140
70.0
300
220
230
310
250
260
160
150
180
180
60.0
500
320
320
390
310
330
200
190
210
270
54.0
700
400
390
460
360
380
230
220
240
340
48.6
1,000
520
490
540
410
450
270
250
270
440
44.0
1,500
670
620
650
490
540
320
290
310
570
38.0
2,000
800
740
740
550
610
360
330
340
700
35.0
2,500
900
850
800
600
650
400
350
350
800
32.0
3,000
1,000
900
900
650
700
400
400
400
900
30.0
3,500
1,100
1,000
950
700
750
450
400
400
950
27.1
4,000
1,200
1,050
1,000
750
800
450
450
450
1,050
26.3
5,000
1,350
1,200
1,100
800
900
500
450
500
1,200
24.0
7,000
1,600
1,400
1,300
900
1,050
600
550
550
1,450
20.7
10,000
1,900
1,650
1,500
1,050
1,200
700
600
600
1,700
17.0
15,000
2,300
1,950
1,800
1,250
1,400
800
700
750
2,100
14.0
20,000
2,600
2,200
2,050
1,400
1,550
900
800
800
2,450
12.3
30,000
3,100
2,600
2,400
1,650
1,850
1,050
900
950
2,950
9.8
40,000
3,450
2,900
2,750
1,850
2,050
1,150
1,000
1,100
3,300
8.3
50,000
3,700
3,100
3,000
2,050
2,200
1,250
1,100
1,200
3,650
7.3
100,000
4,600
3,900
4,000
2,700
2,850
1,600
1,400
1,650
4,750
4.8
150,000
5,250
4,550
4,700
3,200
3,300
1,900
1,600
1,950
5,500
3.7
200,000
5,750
5,100
5,300
3,550
3,650
2,100
1,800
2,250
6,150
3.1
300,000
6,700
6,050
6,250
4,200
4,150
2,450
2,700
7,150
2.4
500,000
8,350
7,550
7,650
5,100
4,950
2,900
8,700
1.7
1,000,000
11,650
10,600
10,000
6,700
6,150
11,350
1.1
2,000,000
17,150
15,400
13,050
8,750
7,600
15,000
0.8
5,000,000
30,750
26,500
18,400
23,000
0.5
10,000,000
40,350
0.4

(a) For standard errors for earlier period, see previous issues of this publication.


B. STANDARD ERRORS OF ESTIMATES OF MONTHLY MOVEMENTS FOR OCTOBER 1997 TO NOVEMBER 1997 ONWARDS(a)
Size of
larger estimate
NSW
Vic.
Qld
SA
WA
Tas.
NT
ACT
Aust.

100
100
90
100
310
200
330
210
270
130
110
130
400
300
490
400
380
240
300
150
130
140
460
500
580
480
450
280
360
180
160
170
550
700
650
530
500
320
400
200
180
190
630
1,000
730
600
570
360
450
220
210
210
710
1,500
840
690
660
420
520
260
240
240
820
2,000
920
760
730
460
570
280
270
270
910
2,500
1,000
820
780
500
610
310
300
290
980
3,000
1,060
880
840
530
650
330
320
310
1,050
4,000
1,170
970
920
590
720
360
360
340
1,160
5,000
1,260
1,040
1,000
630
770
390
390
360
1,260
7,000
1,410
1,170
1,120
710
860
440
440
400
1,420
10,000
1,590
1,320
1,270
810
970
500
500
450
1,610
15,000
1,820
1,520
1,460
930
1,110
570
590
520
1,860
20,000
2,010
1,670
1,610
1,030
1,220
630
660
570
2,060
30,000
2,300
1,920
1,860
1,190
1,390
730
770
650
2,380
50,000
2,740
2,290
2,220
1,420
1,650
870
930
760
2,850
70,000
3,060
2,560
2,490
1,600
1,840
980
1,060
850
3,210
100,000
3,460
2,890
2,820
1,810
2,070
1,100
1,210
960
3,650
150,000
3,960
3,320
3,240
2,080
2,360
1,270
1,410
1,090
4,210
200,000
4,370
3,670
3,580
2,300
2,600
1,400
1,580
1,200
4,670
300,000
5,000
4,210
4,120
2,660
2,970
1,610
1,370
5,390
500,000
5,950
5,010
4,920
3,180
3,520
1,930
6,470
1,000,000
7,510
6,340
6,260
4,050
4,420
8,270
2,000,000
9,490
8,030
7,960
5,160
5,550
10,580
5,000,000
12,920
10,970
10,930
14,660
10,000,000
18,750

(a) For standard errors for earlier periods, see previous issues of this publication.


C. LEVELS AT WHICH LABOUR FORCE ESTIMATES HAVE A RELATIVE STANDARD ERROR OF 25%(a) FROM C SEPTEMBER 1997(b)
NSW
Vic.
Qld
SA
WA
Tas.
NT
ACT
Aust.

Estimates (c) of
Aggregate hours worked
10,600
8,200
7,200
4,000
4,800
1,800
1,500
1,800
8,700
Average hours worked
4,600
3,800
3,700
2,000
2,400
800
700
1,000
3,500
Average duration of unemployment
10,400
9,600
7,300
4,100
5,000
1,800
1,100
1,900
10,400
Median duration of unemployment
16,800
12,700
10,800
6,000
7,200
2,800
2,500
2,600
14,300
All other estimates
5,900
4,500
4,100
2,400
2,800
1,100
1,000
1,100
4,400

(a) See Technical Notes, paragraph 10-11.
(b) For standard errors for earlier periods, see previous issues of this publication.
(c) The entries in this table refer to the number of persons contributing to the estimate.


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