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TECHNICAL NOTE DATA QUALITY
9 In general, the size of the SE increases as the size of the estimate increases. Conversely, the RSE decreases as the size of the estimate increases. Very small estimates are subject to such high RSEs that their value for most practical purposes is unreliable and should only be used to aggregate with other estimates to provide derived estimates with RSEs of less than 25%.
CALCULATION OF STANDARD ERROR FOR MEANS AND MEDIANS
10 This publication contains means and medians. Both are measures for locating the centre of a set of values, but each measure has its own method of calculation. The mean is the arithmetic average, whereas the median is the middle value of a set of values when the values are sorted in size order.
11 Table 5 shows that the estimated number of children who played a musical instrument was 490,200 with the median number of hours those children played a musical instrument being 3 hours in the last 2 weeks of school.
12 Standard errors can be calculated using the estimates (means or medians) and their corresponding RSEs. The RSE table corresponding to the estimates in Table 5 (see Datacubes in the Downloads tab) shows the RSE for the estimated median number of hours children played a musical instrument in the last 2 weeks of school is 8.5%. The SE is calculated by:
13 Therefore, there are about two chances in three that the value that would have been produced if all children had been included in the survey will fall within the range 2.7 and 3.3 and about 19 chances in 20 that the value will fall within the range 2.5 to 3.5. This example is illustrated in the diagram below:
14 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or proportions). Such an estimate is also 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 formula:
15 While this formula will only be exact for differences between separate and uncorrelated (unrelated) characteristics of sub-populations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
16 A statistical significance test for any comparisons between estimates can be performed to determine whether it is likely that there is a true 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:
17 If the 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 between the populations 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.
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