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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. **0.3), 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%. Table T2 presents the levels at which estimates have RSEs of 25% and 50%. MEANS AND MEDIANS 6 The RSEs of estimates of mean and median weekly earnings (see paragraph 20 of the Explanatory Notes) 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 5 shows an estimate of 3,046,100 parttime employees in main job and table 4 shows mean weekly earnings for the same group as $485. The SE of 3,046,100 was calculated previously as 21,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 21,000/3,046,100 = 0.7%. 8 The RSE of the estimate of mean weekly earnings is calculated by multiplying this number, 0.7%, by the appropriate factor shown in paragraph 6 (in this case 0.9): 0.7 x 0.9 = 0.63%. The approximate SE of this estimate of mean weekly earnings of parttime employees in main job is therefore 0.63% of $485, that is $3 (to the nearest dollar). Therefore, there are two chances in three that the mean weekly earnings for female parttime employees that would have been obtained if all dwellings had been included in the survey would have been within the range $482 to $488, and about 19 chances in 20 that it would have been within the range $479 to $491. 9 Mean and median estimates produced from population estimates smaller than the values in T2 have RSEs larger than 25% and should be used with caution. Table T2 also indicates the size of the population estimates that would produce mean and medians with RSEs greater than 50% which are considered too unreliable for general use. ALL OTHER ESTIMATES 10 All other estimates produced from population estimates smaller than the values in T2 have RSEs larger than 25% and should be used with caution. T2 also indicates the size of the population estimates with RSEs greater than 50% which are considered too unreliable for general use. PROPORTIONS AND PERCENTAGES 11 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. 12 Considering the example from the previous page, of the 3,046,100 parttime employees in their main job, 835,800 or 27.4% were males. The SE and RSE of 3,046,100 were calculated previously as 21,000 and 0.7% respectively. The SE for 835,800 calculated by interpolation is 10,600 which converted to a RSE is 10,600/835,800 = 1.3%. Applying the above formula, the RSE of the proportion is: 13 The SE for the proportion, 27.4%, of male parttime employees, is 0.3 percentage points, calculated as (27.4/100)x1.1. There are about two chances in three that the proportion of male parttime employees, was between 27.1% and 27.7%, and 19 chances in 20 that the proportion is within the range 26.8% to 27.4%. DIFFERENCES 14 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: 15 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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