6278.0 - Education and Training Experience, Australia, 2001  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 31/05/2002   
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RELIABILITY OF ESTIMATES

1. Since the estimates in this publication are based on information obtained from occupants of a sample of dwellings, they are subject to sampling variability, that is, they may differ from those that would have been produced if all dwellings had been included in the survey. One measure of the likely difference is given by the standard error (SE), 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 a sample estimate will differ by less than one SE from the number that would have been obtained if all dwellings had been included, and about 19 chances in 20 that the difference will be less than two SEs. Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate.

2. Space does not allow for the separate indication of the SEs of all estimates in this publication. Tables of SEs and RSEs for estimates of numbers of persons and estimates of numbers of training courses and qualifications appear at the end of these Technical Notes. These values do not give a precise measure of the SE or RSE for a particular estimate but will provide an indication of its magnitude. SEs and RSEs for estimates of earnings, total training hours and average training hours have not been included in this publication, but are available on request.

Calculation of standard errors

3 An example of the calculation and use of SEs in relation to estimates of numbers of persons is as follows. Consider the estimate for Australia of persons aged 25 to 34 who have completed one or more non-school qualifications, which is 1,746,700. Since this estimate is between 1,000,000 and 2,000,000 in the SE table for person estimates, the SE will be between 23,650 and 32,100, and can be approximated by interpolation as 30,000. Therefore, there are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall within 30,000 persons of the survey estimate, i.e. in the range 1,716,700 to 1,776,700, and about 19 chances in 20 that the value will fall within 60,000 persons of the survey estimate, i.e. in the range 1,686,700 to 1,806,700. This example is illustrated in the diagram below.

Image - Published estimate



4. As can be seen from the first SE table at the end of this Technical Note, the smaller the estimate the higher the RSE. Very small estimates are subject to such high SEs (relative to the size of the estimate) as to detract significantly from their value for most reasonable uses. In the tables in this publication, only estimates with RSEs of less than 25%, and percentages based on such estimates, are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (e.g. **2.1) to indicatethat they are considered too unreliable for general use.

5. The SE can be calculated from the RSE and the estimate using the following formula:




PROPORTIONS AND PERCENTAGES

6. Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends of the accuracy of both the numerator and denominator. A formula to approximate the RSE of a proportion is given below:



7. Consider the example above of the number of people who have completed a non-school qualification aged 25 to 34 (1,746,700). Of these, 883,300 or 50.1% were estimated to be male. The SE of 1,746,700 is approximately 30,000 so the RSE is 1.7%. The RSE for 883,300 is 2.5%. Applying the formula above, the RSE of the proportion is 1.8%, giving a SE for the proportion (50.1%) of 0.9 percentage points. Therefore there are about two chances in three that the proportion of persons aged 25 to 34 who have completed a non-school qualification who were male is between 49.2% and 51.0%, and 19 chances in 20 the proportion is within the range 48.3% and 51.9%.

8. Published estimates may also be used to calculate the difference between two survey estimates (numbers or percentages), which are also subject to sampling error. The sampling error of the difference between the two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:



9. While this formula will only be exact for differences between separate and uncorrelated characteristics of sub-populations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.

10. The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents and recording by interviewers, and errors made in coding and processing data. Inaccuracies of this kind are referred to as non-sampling error, and they may occur in any enumeration, whether it be a full count or a sample. Every effort is made to reduce non-sampling error to a minimum by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.