**TECHNICAL NOTE** **DATA QUALITY**

**ESTIMATION PROCEDURE**

**1 **Estimates of children are derived using a ratio estimation procedure which ensures that estimates conform to an independently estimated state by age by sex distribution of children in the population, rather than to the state by age by sex distribution within the sample itself. Estimates of families conform to an independently estimated state by household composition distribution in the population, where household composition was defined by the number of adults and children within a household.

**RELIABILITY OF ESTIMATES**

**2 **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 estimates 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 (67%) 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 (95%) that the difference will be less than two SEs.

**3 **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. The RSE 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 **Due to space limitations, it is impractical to present the RSE of each estimate in the publication. However, RSEs for estimates (with the exception of 1999 data) are in the spreadsheet version of the publication tables, available on the ABS web site <www.abs.gov.au> as an attachment to this publication, Childhood Education and Care, Australia, 2008 (cat. no. 4402.0).

**5 **In the tables in this publication, only estimates (numbers and proportions, means and medians) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *13.5) 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 indicate that they are considered too unreliable for general use.

**COMPARISON OF ESTIMATES**

**6 **Published estimates may also be used to calculate the difference between two survey estimates. Such an estimate is subject to sampling error. The sampling error of the difference between 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:

**7 **While the above formula will be exact only for differences between separate and uncorrelated (unrelated) characteristics of subpopulations, it is expected that it will provide a reasonable approximation for all differences likely to be of interest in this publication.

**SIGNIFICANCE TESTING**

**8 **The statistical significance test for any of the comparisons between estimates over time was performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 5. This standard error is then used to calculate the following test statistics:

**9 **If the value of this test statistic is greater than 1.96 then we may say there is good evidence of a real difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations.

**10 **The selected tables in this publication that show the results of significance testing are annotated to indicate whether or not the estimates which have been compared are significantly different from each other with respect to the test statistic. In all other tables which do not show the results of significance testing, users should take account of RSEs when comparing estimates for different populations.

**11 **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 occur in any enumeration, whether it be a full count or 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.

**CALCULATING STANDARD ERRORS FOR PROPORTIONS**

**12 **Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. For proportions where the denominator is an estimate of the number of persons in a group and the numerator is the number of persons in a sub-group of the denominator group, the formula to approximate the RSE is given by:

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