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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. *3.4) 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. **0.2), 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%. Table T2 presents the levels at which estimates have RSEs of 25% and 50%. MEANS AND MEDIANS 6 The RSEs of estimates of mean duration of unemployment and median duration of unemployment 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 for Australian estimates:
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 median duration of unemployment for unemployed females in Australia was 17 weeks and shows that the number of unemployed females was estimated as 271,900. The SE of 271,900 can be calculated from table T1 (by interpolation) as 6,400. To convert this to an RSE we express the SE as a percentage of the estimate or 6,400/271,900 =2.4%. 8 The RSE of the estimate of median duration of unemployment for unemployed females is calculated by multiplying this number (2.4%) by the appropriate factor shown in the previous paragraph (in this case 2.5): 2.4 x 2.5 = 6%. The SE of this estimate of median duration of unemployment for unemployed females is therefore 6% of 17 weeks, i.e. approximately one week. Therefore, there are two chances in three that the median duration of unemployment for females that would have been obtained if all dwellings had been included in the survey would have been within the range 16 to 18 weeks and about 19 chances in 20 that it would have been within the range 15 weeks to 19 weeks. 9 Table T2 represents the minimum size of estimates, based on the SE model described in paragraph 2, required to have RSEs of less than 25% and 50% respectively. For example, an estimate of median duration of unemployment for Australia based on less than 29,000 persons will have an RSE of at least 25%, and an estimate of median duration of unemployment for Australia based on less than 10,000 will have an RSE of at least 50%. For all other estimates, (i.e. those estimates based purely on number of persons in a specific category), an estimate of less than 6,800 for the Australian total will have an RSE of at least 25% and an estimate of less than 1,600 will have an RSE of at least 50%. PROPORTIONS 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 x is a subset of y: 11 Considering the example from the previous page, of the 165,200 unemployed females who were looking for fulltime work, 36,200 or 21.9% had been unemployed for one year or more. The SE of 36,200 may be calculated by interpolation as 3,100. To convert this to an RSE we express the SE as a percentage of the estimate, or 3,100/36,200 = 8.6%. The SE for 165,200 was calculated previously as 5,200, which converted to an RSE is 5,200/165,200 = 3.1%. Applying the above formula, the RSE of the proportion is: 12 Therefore, the SE for the proportion of unemployed females looking for fulltime work who had been unemployed for one year or more is 1.8 percentage points (=(21.9/100)x8.0). Therefore, there are about two chances in three that the proportion of unemployed females looking for fulltime work who have been unemployed for one year or more is between 20.1% and 23.7% and 19 chances in 20 that the proportion is within the range 18.3% to 25.5%. DIFFERENCES 13 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: 14 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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