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TECHNICAL NOTE DATA QUALITY 5 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 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.*3.2) 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 less than 25%. MEANS AND MEDIANS 6 The RSEs of estimates of mean duration of insufficient work, median duration of insufficient work and mean preferred number of extra hours are obtained by first finding the RSE of the estimate of the total number of persons contributing to the mean or median ( see table T1) and then multiplying the resulting number by the following factors:
7 The following is an example of the calculation of SEs where the use of a factor is required. Table 4 shows that the estimated number of male underemployed parttime workers was 288,000 with a median duration of insufficient work of 26 weeks. The SE of 288,000 can be calculated from table T1 (by interpolation) as 7,200. To convert this to an RSE we express the SE as a percentage of the estimate or 7,200/288,800 = 2.5%. 8 The RSE of the estimate of median duration of insufficient work is calculated by multiplying this number (2.5%) by the appropriate factor shown in paragraph 7 (in this case 2.5): 2.5 x 2.5 = 6.3%. The SE of this estimate of median duration of insufficient work is therefore 6.3% of 26, i.e. about 2 (rounded to the nearest whole week). Therefore, there are two chances in three that the median duration of insufficient work for males that would have been obtained if all dwellings had been included in the survey would have been within the range 2428 weeks, and about 19 chances in 20 that it would have been within the range 2230 weeks. PROPORTIONS AND PERCENTAGES 9 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. 10 Considering the example from paragraph 3, of the 445,900 female underemployed parttime workers, 179,300 or 40.0% had insufficient work for 52 weeks and over. The SE of 179,300 may be calculated by interpolation as 5,900. To convert this to an RSE we express the SE as a percentage of the estimate, or 5,900/179,300 = 3.3%. The SE for 445,900 was calculated previously as 8,700, which converted to an RSE is 8,700/445,900 = 2.0%. Applying the above formula, the RSE of the proportion is: 11 Therefore, the SE for the proportion of females who have a current period of insufficient work of 52 weeks or more is 1.0 percentage points (=(40.0/100)x2.6). Therefore, there are about two chances in three that the proportion of females who have a current period of insufficient work of 52 weeks or more was between 39.0% and 41.0% and 19 chances in 20 that the proportion is within the range 38.0% to 42.0%. DIFFERENCES 12 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 (xy) may be calculated by the following formula: 13 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. STANDARD ERRORS
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