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USING THE MEASURES OF SAMPLING ERROR WITH THE ESTIMATES
10 This publication reports the relative standard error (RSE) for estimates of counts ('000) and the margin of error (MOE) for estimates of proportions (%). These measures are included in the datacubes available on the Downloads tab. In the first datacube (Tables 1-20: Education and Work), time series tables include both RSE of proportion and MOE of proportion, as do tables 21- 34. For years prior to 2018, MOE of proportion has been calculated using rounded figures and the result may have slightly less precision than the MOE of proportion calculated for 2018.
11 In the first datacube (Tables 1-20: Education and Work), estimates of proportions with a MOE greater than 10% are annotated to indicate they are subject to high sample variability and particular consideration should be given to the MOE when using these estimates. Depending on how the estimate is to be used, a MOE of greater than 10% may be considered too large to inform decisions. In addition, estimates with a corresponding standard 95% confidence interval that includes 0% or 100% are annotated to indicate they are usually considered unreliable for most purposes. In the remainder of the datacubes, estimates of proportions with high RSEs are annotated. The exception is 2017, where estimates of proportions are annotated based on the size of their MOE.
12 Only estimates with RSEs less than 25% are considered sufficiently reliable for most analytical purposes. All other estimates with RSEs between 25% and 50% are annotated to indicate they are subject to high sample variability relative to the size of the estimate and should be used with caution. In addition, estimates with RSEs greater than 50% are annotated to indicate they are usually considered unreliable for most purposes.
13 Caution needs to be applied when performing statistical tests for estimates on rare populations where the RSE is above 25%. In these instances, the small sample is more vulnerable to non-sampling error and the distribution of the sampling error is not symmetric around the estimate.
CALCULATING MEASURES OF ERROR AND DIFFERENCE
14 Proportions or percentages formed from the ratio of two count 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 (x) is a subset of the denominator (y):
15 When calculating measures of error, it may be useful to convert RSE or MOE to SE. This allows the use of standard formulas involving the SE. The SE can be obtained from RSE or MOE using the following formulas:
16 The RSE can also be used to directly calculate a MOE with a 95% confidence level:
17 The difference between two survey estimates (counts or percentages) can also be calculated from published estimates. 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:
18 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.
19 A statistical significance test for a comparison between estimates can be performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The approximate standard error of the difference between two corresponding estimates (x - y) can be calculated using the formula shown above in the Differences section. The standard error is then used to calculate the following test statistic:
20 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.
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