Feature Article: Technical report: Standard error models for the Labour Force Survey
This article was published in the October 2005 issue of Australian Labour Market Statistics (cat. no. 6105.0).
INTRODUCTION
Estimates from the Labour Force Survey (LFS) are based on information collected from people in a sample of dwellings rather than the entire population. Hence the estimates produced may differ from those that would have been produced if the entire population had been included in the survey. The most common measure of the likely difference (or 'sampling error') is the standard error. It is important to take these standard errors into consideration when using LFS estimates as they give an indication of the level of accuracy of the estimate.
The ABS has recently introduced updated standard error models which are used to calculate standard errors for estimates from the LFS. These new models are applicable to estimates from November 2002 onwards, coinciding with the introduction of the new LFS sample design based on the 2001 Census.
This article briefly describes sampling error and the standard error models designed by the ABS to simplify the calculation of standard errors for LFS estimates.
More details can be found in the publication Labour Force Survey Standard Errors (cat. no. 6298.0) released on 8 September 2005. A spreadsheet which incorporates the standard error models has been developed to allow users to quickly calculate a standard error and relative standard error for any estimate from the LFS. This spreadsheet (cat. no. 6298.0.55.001) is available free from the ABS web site.
RELIABILITY
Survey estimates are subject to two types of error: non-sampling error and sampling error.
Non-sampling error arises from imperfections in reporting, recording or processing of the data. This type of error is difficult to quantify and there are no standard measures of non-sampling error produced for ABS surveys. Every effort is made in the design and operation of the LFS to minimise non-sampling error.
Sampling error is the difference between the estimate obtained from a particular sample and the value that would be obtained if the whole population were enumerated under the same procedures. The most commonly used measure of sampling error is the standard error. The standard error of an estimate is a measure of the variation among the estimates from all possible samples, and thus a measure of the precision with which an estimate from a particular sample approximates the average over all possible samples.
STANDARD ERROR MODELS
Separate standard errors could be calculated for each individual LFS estimate for each time period. However, this would be costly; would require information on the sample design; and would require access to the unit record data. To simplify calculation of standard errors (and to save costs), models have been fitted to standard errors calculated using the group jack-knife method for estimates of employed, unemployed and not in the labour force (for a particular period). These models are then used to calculate standard errors for other periods using only information on the size and type of the estimate for which the standard error is required.
The standard error of an estimate generally increases with the size of the estimate, therefore a large standard error does not necessarily reflect poor accuracy in a relative sense. Another measure of sampling error which is often more relevant when assessing the quality of estimates of differing sizes is the relative standard error (RSE). The RSE is the standard error expressed as a proportion of the estimate, and is usually displayed as a percentage. RSEs provide an immediate indication of the percentage error likely to have occurred due to sampling, without the need to refer to the size of the estimate.
Very small estimates tend to be subject to high RSEs, which detract from their usefulness. In LFS publications, only estimates with an RSE of less than 25% are considered sufficiently reliable for most purposes. Estimates with a larger RSE are marked with an asterisk (*) to indicate that they are subject to high sampling errors and should be used with caution.
The following table displays the size of the estimates at which the RSE is 25%, as determined by the new standard error models. Any estimate of persons which is less than that displayed in the table will have an RSE greater than 25%. Estimates of hours worked or duration of unemployment with fewer persons contributing to them than displayed in the table will also have an RSE greater than 25%. All estimates with an RSE of 25% or greater would appear with an asterisk in ABS publications, and should be used with caution.
LEVELS AT WHICH LFS ESTIMATES HAVE A RELATIVE STANDARD ERROR OF 25% - November 2002 onwards(a) |
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| NSW | Vic. | Qld | SA | WA | Tas. | NT | ACT | Aust. | |
Estimates of:(b) | no. | no. | no. | no. | no. | no. | no. | no. | no. | |
| |
Aggregate hours worked(c) | 7 250 | 6 060 | 5 390 | 2 900 | 3 560 | 1 700 | 1 840 | 1 560 | 7 630 | |
Average hours worked(c) | 3 020 | 2 570 | 2 300 | 1 240 | 1 510 | 720 | 580 | 740 | 2 750 | |
Average duration of unemployment(c) | 12 400 | 10 280 | 8 830 | 5 360 | 5 710 | 3 160 | 3 070 | 3 030 | 11 310 | |
Median duration of unemployment(c) | 44 590 | 38 540 | 34 620 | 23 710 | 25 260 | 18 530 | 35 310 | 9 330 | 27 910 | |
All other estimates of employed persons | 4 870 | 3 960 | 3 710 | 1 960 | 2 340 | 1 170 | 1 350 | 1 090 | 4 830 | |
All other estimates of unemployed persons | 6 010 | 4 890 | 4 410 | 2 610 | 3 020 | 1 660 | 3 340 | 1 500 | 4 740 | |
All other estimates of persons not in the labour force | 6 030 | 4 800 | 4 410 | 2 410 | 2 990 | 1 350 | 1 760 | 1 320 | 5 130 | |
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(a) For standard errors in earlier periods, see the 2003 edition of Information Paper: Labour Force Survey Standard Errors (cat. no. 6298.0) or issues of Labour Force, Australia (cat. no. 6203.0 or cat. no. 6202.0) for the relevant period. |
(b) For estimates of persons in the labour force, use 'All other estimates of employed persons'. |
(c) The entries in this table refer to the number of persons contributing to the estimate. |
IMPROVEMENTS TO THE STANDARD ERROR MODELS
Previously, for each state, territory and Australia, a single standard error model has been prepared for level estimates, and another for monthly movement estimates. These models were used to calculate standard errors for all labour force status categories (i.e. employed, unemployed, labour force and not in the labour force). As a result of their broad basis, these models had the effect of underestimating some standard errors while overestimating others.
To improve the accuracy of the models, separate models have been created for level estimates of employed, unemployed, and persons not in the labour force, cross classified by sex, age, marital status, state, territory, capital city and balance of state, for each state, territory, and Australia. A single model for standard errors of all labour force status categories proved sufficient for LFS regions.
With the introduction of the new standard error models, some standard errors for large estimates are higher than previously published. This is not due to the standard errors of the new sample being higher than those for the previous sample; rather it reflects the improved accuracy obtained from the latest models in the estimation of standard errors, which is particularly evident for large estimates.
While the model formulae are available, their use can be time consuming. To make it easier to calculate standard errors for LFS estimates, the ABS has provided a spreadsheet, which is available free on the ABS web site <https://www.abs.gov.au> (Themes - People - Labour - LFS Standard Errors). This spreadsheet allows users to quickly calculate the standard error for any LFS level or monthly movement estimate (including rates). In addition, the spreadsheet allows users to calculate the standard error for less common estimates such as averages, aggregates and movements other than monthly. For detailed information on how to use the spreadsheet, refer to Labour Force Survey Standard Errors, 2005 (cat. no. 6298.0).
It should also be noted that these standard errors apply to original estimates only, not to seasonally adjusted or trend estimates. Work has commenced in the ABS on developing methods to produce accurate standard errors for seasonally adjusted and trend estimates. In the meantime, a reasonable approximation can be made for the standard errors of seasonally adjusted estimates (although not of trend estimates) using the standard errors for original estimates.
FURTHER INFORMATION
For further information about the new standard error models, see Labour Force Survey Standard Errors (cat. no. 6298.0) and the associated standard error calculation spreadsheet (cat. no. 6298.0.55.001) available free on the ABS web site <https://www.abs.gov.au>. Alternatively, contact the Assistant Director of Labour Household Surveys on Canberra (02) 6252 5967.
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