TECHNICAL NOTE DATA QUALITY
RELIABILITY OF THE ESTIMATES
1 The estimates are based on information obtained from the occupants of a sample of dwellings. Therefore, the estimates are subject to sampling variability and may differ from the figures that would have been produced if information had been collected for all dwellings. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied because only a sample of dwellings was included. There are about two chances in three that the sample estimate will differ by less than one SE from the figure 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.
2 In contrast to most other ABS surveys, the 2006 ALLS estimates also include significant imputation variability, due to the use of multiple possible MTB questionnaires and the complex literacy scaling procedures. The effect of the plausible scoring methodology on the estimation can be reliably estimated and is included in the calculated SEs.
3 Together, the sampling variance and imputation variance can be added to provide a suitable measure of the total variance, and total Standard Error (SE). This SE indicates the extent to which an estimate might have varied by chance because only a sample of persons was included, and/or because of the significant imputation used in the literacy scaling procedures .
4 Another common measure used in the 2006 ALLS is the Total Relative Standard Error (RSE), which is obtained by expressing the Total SE as a percentage of the estimate to which it relates:
5 Very small estimates may be subject to such high relative standard errors as to seriously detract from their value for most reasonable purposes. Only estimates with relative standard errors less than 25% are considered sufficiently reliable for most purposes. However, estimates with relative standard errors of 25% or more are included in all 2006 ALLS output. Estimates with an RSE of 25% to 50% are preceded by the symbol * to indicate that the estimate should be used with caution. Estimates with an RSE greater than 50% are preceded by the symbol ** to indicate the estimate is considered too unreliable for most purposes.
6 More information on SEs and imputation error is available in the Adult Literacy and Life Skills, Australia: User Guide (cat. no. 4228.0.55.002).
7 Space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication. However, RSEs for all these estimates are available free-of-charge on the ABS web site <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication, Adult Literacy and Life Skills Survey: Summary Results, Australia, 2006 (cat. no. 4228.0).
COMPARISON OF ESTIMATES
8 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:
9 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
10 The statistical significance test for any of the comparisons between estimates 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 8. This standard error is then used to calculate the following test statistic:
11 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.
12 The selected tables in this publication that show the results of significance testing are annotated to indicate where 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.
13 The imprecision due to sampling variability and imputation variance, which is measured by the total 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 AND PERCENTAGES
14 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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