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TECHNICAL NOTE DATA QUALITY
6 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 thus subject to such high RSEs so that their value for most practical purposes is unreliable. In the tables in this publication, only estimates with RSEs of 25% or less are considered reliable for most purposes. Estimates with RSEs greater than 25% but less than or equal to 50% are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs of greater than 50%, preceded by a double asterisk (e.g. **0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of 25% or less.
PROPORTIONS AND PERCENTAGES
7 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 x is a subset of y.
8 For example, in table 1 the estimate for the total number of children aged 3 who used child care (formal and/or informal) is 175,300. The estimated number of children aged 3 who used formal care only is 81,100, so the proportion of children aged 3 who used formal care only out of those children who used child care is 81,100/175,300 or 46.3%. The SE of the total number of children aged 3 who used child care may be calculated by interpolation as 9,100 (rounded to the nearest 100). To convert this to an RSE we express the SE as a percentage of the estimate, which gives 9,100/175,300 = 5.2%. The SE for the number of children aged 3 who used formal care only was calculated above as 6,300, which converted to an RSE is 6,300/81,100 = 7.8%. Applying the above formula, the RSE of the proportion is:giving a SE for the proportion (46.3%) of 2.7 percentage points (=46.3*5.8/100).
9 Therefore, there are about two chances in three that the proportion of children aged 3 who used formal care only out of those who used child care is between 43.6% and 49.0% and 19 chances in 20 that the proportion is within the range 40.9% to 51.7%.
10 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or percentages). 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:
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.
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