
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 nonsampling 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 nonsampling error and they may occur in any enumeration, whether it be a full count or a sample. It is not possible to quantify nonsampling 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 nonsampling 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 nonconsecutive 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 1519 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.
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:
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 1011. 
(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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