**TECHNICAL NOTE **- SAMPLING ERROR

**RELIABILITY OF ESTIMATES**

**1** As the estimates in this publication are based on information relating to a sample of employers, they are subject to sampling variability. That is, they may differ from the estimates that would have been produced if the information had been obtained from all employers. This difference, called **sampling error**, should not be confused with inaccuracy that may occur because of imperfections in reporting by respondents or in processing by the ABS. Such inaccuracy is referred to as **non-sampling error** and may occur in any enumeration whether it be a full count or a sample. Efforts have been made to reduce non-sampling error by careful design of questionnaires, detailed checking of returns and quality control of processing.

**2 **The sampling error associated with any estimate can be estimated from the sample results. One measure of sampling error is given by the **standard error** which indicates the degree to which an estimate may vary from the value which would have been obtained from a full enumeration (the 'true value'). There are about two chances in three that a sample estimate differs from the true value by less than one standard error, and about nineteen chances in twenty that the difference will be less than two standard errors.

**3** An example of the use of a standard error is as follows. If the estimated average earnings was $900.00 with a standard error of $7.00, then there would be about two chances in three that a full enumeration would have given an estimate in the range $893.00 to $907.00 and about nineteen chances in twenty that it would be in the range $886.00 to $914.00.

**4** An example of the use of a standard error for a quarterly change estimate is as follows. If the estimate of quarterly change between two quarters was $6.00 and the standard error on this estimate was $5.00, then there would be about two chances in three that a full enumeration would have given a quarterly change estimate in the range +$1.00 to +$11.00 and about nineteen chances in twenty that it would be in the range –$4.00 to +$16.00.

**5** Quarterly movements in estimates of average weekly earnings are considered to be statistically significant where they exceed two standard errors.

**6** Another measure of the sampling error is the **relative standard error**, which is obtained by expressing the standard error as a percentage of the estimate.