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TECHNICAL NOTE DATA QUALITY
PROPORTION AND PERCENTAGES
9 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 the numerator is a subset of the denominator:
10 As an example, using estimates from Table 1, of the 496,000 children aged 0-12 years who usually attended long day care, 6.6% (19,100) were aged under 1. The RSE for 496,000 is 3.1% and the RSE for 19,100 is 13.8%. Applying the above formula, the RSE for the proportion of children under the age of 1 who attended long day care is:
11 Therefore, the SE for the proportion of children aged 0-12 years who usually attended long day care is 0.9 percentage points (=(13.4/100) x 6.6). Hence, there are about two chances in three that the proportion of children aged 0-12 years who usually attended long day care is between 5.7% and 7.5%, and 19 chances in 20 that the proportion is between 4.8% and 8.4%.
12 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or proportions). 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:
13 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.
14 A 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 above. This standard error is then used to calculate the following test statistic:
15 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.
16 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.
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