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RELIABILITY OF THE ESTIMATES
PROPORTIONS AND PERCENTAGES
8 Proportions and percentages formed from the ratio of two estimates are also subject to sampling error. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. The formula is only valid when the numerator is a subset of the denominator:
9 As an example, using the 2009 estimates from Table 1 of Disability, Ageing and Carera, Australia: Summary of Findings (cat. no. 4430.0) , of the 4,026,200 persons who had a disability, 2,063,100 are females or 51.2%. The RSE for 2,063,100 is 1.2% and the RSE for 4,026,200 is 1.0% (see Relative Standard Errors for Table 1 in the 'Relative Standard Error' section at the end of these Technical Notes). Applying the above formula, the RSE for the proportion of females who had a disability is:
10 Therefore, the SE for the proportion of persons who had a disability and were female, is 0.4 percentage points (=0.7/100 x 51.2). Hence, there are about two chances in three that the proportion of females who had a disability is between 50.8% and 51.6%, and 19 chances in 20 that the proportion is between 50.4% and 52.0%.
11 Published estimates may also be used to calculate the difference between two s)urvey estimates (of numbers or percentages). 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:
12 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub-populations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
13 A statistical significance test for any of the comparisons between estimates can be 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 paragraph11. This standard error is then used to calculate the following test statistic:
14 If the value of this test statistic is greater than 1.96 then there is evidence of a statistically significant difference (at the 5% level) in the two estimates with respect to that characteristic. This statistic corresponds to a 95% confidence interval of the difference. Otherwise, it cannot be stated with confidence that there is a real difference between the population with respect to that characteristic.
15 The selected tables in this publication that show the results of significance testing are annotated to indicate where the estimates are significantly different from each other. 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.
16 For the publication Disability, Ageing and Carers, Australia: Summary of Findings (cat. no. 4430.0), the direct age standardisation method was used. The standard population used was the 30 June 2001 Estimated Resident Population. Estimates of age-standardised rates were calculated using the following formula:
17 The age categories used in the standardisation for this publication were 0 to 4years, 5 to 14years, 15 to 24years, 25 to 34years, 35 to 44years, 45 to 54years, then five-year groups to90years and over.
RELATIVE STANDARD ERROR
18 RSEs of all the estimates in Disability, Australia 2009 (cat. no. 44460.0) are released in spreadsheet format as attachments to the Web version of the publication.
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