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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.

• 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.

• aggregate hours worked: 1.4;

• average hours worked: 0.9;

• average duration of unemployment: 1.5; and

• median duration of unemployment: 1.7.

• 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.

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.