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TECHNICAL NOTE DATA QUALITY
RSES OF COMPARATIVE ESTIMATES
Proportions and percentages
7 Proportions and percentages formed from the ratio of two estimates are also subject to sampling error. 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 x is a subset of y.
8 As an example, using estimates from Table 8, 55,500 persons were assaulted by a friend in the most recent incident of assault in the last 12 months, representing 16.9% of the 328,200 persons who knew the offender in the most recent incident of assault. From the RSE table at the end of this Technical Note, the RSE of the estimated number of persons who were assaulted by a friend in the most recent incident of assault is 12.8%, and the RSE of the estimated number of persons who knew the offender in the most recent incident of assault is 4.6%. Applying the above formula, the RSE of the proportion is:
9 Therefore, the SE for persons who were assaulted by a friend in the most recent incident of assault as a proportion of persons who knew their offender in the most recent incident of assault is 2.0 percentage points (=16.9×(11.9/100)). Therefore, there are about two chances in three that the proportion is between 14.9% and 18.9% and 19 chances in 20 that the proportion is within the range 12.9% to 20.9%.
Differences between estimates
10 The difference between two survey estimates (numbers or percentages) is itself an estimate and is therefore 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 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
STATISTICAL SIGNIFICANCE TESTING
12 The statistical significance test for any of the comparisons between estimates was performed to determine whether, with a certain level of confidence, there is evidence of 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 in paragraph 10. This standard error is then used to to calculate the following test statistic:
13 If the value of the test statistic is greater than 1.96 then there is statistical evidence (with 95% confidence) of a 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.
14 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.
SAMPLE TABLE WITH RSES
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