Australian Bureau of Statistics
4114.0 - Attendance at Selected Cultural Venues and Events, Australia, 2009-10 Quality Declaration
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 21/12/2010
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TECHNICAL NOTE DATA QUALITY
PROPORTIONS AND PERCENTAGES
7 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. The formula to approximate the RSE of a percentage is given below. The formula is only valid when x is a subset of y:
8 As an example, using estimates from Table 3, of the 405,700 females age 15-17 years, 187,600, or 46.2% attended popular music concerts in the 12 months prior to being surveyed. The RSE for 187,600 is 11.7% and the RSE for 405,700 is 5.7% (see Table 3 Relative Standard Errors in the RSE Tables section on the ABS website). Applying the above formula, the RSE for the percentage of females age 15-17 years who attended popular music concerts in the 12 months prior to being surveyed is:
9 Therefore, the SE for the percentage of females age 15-17 years who attended popular music concerts in the 12 months prior to being surveyed, is 4.7 percentage points (=10.22/100 x 46.2%). Hence, there are about two chances in three that the percentage of females age 15-17 years who attended popular music concerts in the 12 months prior to being surveyed is between 41.5% and 50.9%, and 19 chances in 20 that the percentage is between 36.8% and 55.6%.
10 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:
11 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 shown prior to this paragraph. This standard error is then used to calculate the following test statistic:
12 If the absolute value of this test statistic is greater than 1.96, there is evidence of a statistically significant difference (with a 95% level of confidence) 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.
13 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.
14 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, extensive editing and quality control procedures at all stages of data processing and follow up of initial non-respondents.
RELATIVE STANDARD ERRORS
15 Limited space does not allow the SEs and/or RSEs of all the estimates to be shown in this publication. Only RSEs for Table 1 are included below. However, RSEs for all tables are available free-of-charge on the ABS website <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication.
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This page last updated 20 December 2010