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).
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 larger 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. 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.
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:
- 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
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:
- median duration of unemployment: 1.7.
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.
- 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.