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TECHNICAL NOTE DATA QUALITY
CALCULATION OF STANDARD ERROR FOR MEDIANS
8 This publication contains calculations of medians. The median value is the middle value of a set of values when the values are sorted in size order.
9 Standard errors can be calculated using the median and their corresponding RSE using the same formula described above for calculating SE for estimates (paragraph 6).
PROPORTION AND PERCENTAGES
10 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. This formula is only valid when the numerator is a subset of the denominator.
11 As an example, using estimates from Table 1, of the 8,536,900 males aged 15-74 years, 20.2%, or 1,725,800 had participated in formal learning. The RSE for 8,536,900 is 0.2% and the RSE for 1,725,800 is 2.2% (see Table 1 RSEs of Proportions). Applying the above formula, the RSE for the percentage of males who participated in formal learning is:
12 Therefore, the SE for the percentage of males aged 15-74 years who participated in formal learning is 0.4 percentage points ((2.2/100) x 20.2 =0.4). Hence, there are about two chances in three that the percentage of males who participated in formal learning is between 19.8% and 20.6%, and 19 chances in 20 that the percentage is between 19.4% and 21.0%.
13 Published estimates may also be used to calculate the difference between two survey estimates (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 following formula:
14 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it provides a good approximation for the differences likely to be of interest in this publication.
15 A statistical significance test for any comparisons between estimates can be performed to determine whether it is likely that there is a difference between two 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:
16 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 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.
OTHER SOURCES OF ERROR
17 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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