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TECHNICAL NOTE DATA QUALITY
PROPORTIONS AND PERCENTAGES
8 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. A formula to approximate the RSE of a proportion is given below. The formula is only valid when x is a subset of y:
9 As an example, using estimates from Table 11, of the 3,584,800 participants residing in New South Wales, 547,800, or 15.3% used either their own home or someone else's to participate in sport or physical recreation. The RSE for 547,800 is 8.1% and the RSE for 3,584,800 is 1.4% (see Table 11 Relative Standard Errors in the 'Relative Standard Error' section at the end of this Technical Note). Applying the above formula, the RSE for the percentage of New South Wales residents who used either their own home or someone else's to participate in sport or physical recreation is:
10 Therefore, the SE for the percentage of New South Wales residents who used either their own home or someone else's to participate in sport or physical recreation in the 12 months prior to interview, is 1.2 percentage points (=8.0/100 x 15.3%). Hence, there are about two chances in three that the percentage of New South Wales residents who used either their own home or someone else's to participate in sport or physical recreation is between 14.1% and 16.5%, and 19 chances in 20 that the percentage is between 12.9% and 17.7%.
11 Published estimates may also be used to calculate the difference between two survey estimates (of counts 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 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 paragraph 11. This standard error is then used to calculate the following test statistic:
13 If the absolute value of this test statistic is greater than 1.96 then there is evidence, with a 95% level of confidence, of a statistically significant difference in the two estimates with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations with respect to that characteristic.
14 Tables which show estimates from 2005-06 and 2009-10 have been tested to determine whether changes over time are statistically significant. Significant differences have been annotated. 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.
15 The imprecision due to sampling variability, labelled sampling error, should not be confused with non-sampling error. Non-sampling error may occur in any collection, whether it is based on a sample or a full count such as a census. Sources of non-sampling error include non-response, errors in reporting by respondents or recording answers by interviewers and errors in coding and processing data. Every effort was made to reduce the non-sampling error by careful design and testing of the questionnaire, training and supervision of interviewers, and extensive editing and quality control procedures at all stages of data processing.
RELATIVE STANDARD ERRORS
16 Limited space does not allow the SEs and/or RSEs of all the estimates to be shown in this publication. Only RSEs for Table 11 are included on the following page. However, RSEs for all tables are available free-of-charge on the ABS website <www.abs.gov.au>, available in spreadsheet format as an attachment to this publication.
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