6238.0 - Retirement and Retirement Intentions, Australia, July 2010 to June 2011 
Quality Declaration
Quality Declaration ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 13/12/2011
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TECHNICAL NOTE DATA QUALITY
3 RSEs for Retirement and Retirement Intentions estimates have been calculated using the Jackknife method of variance estimation. This process involves the calculation of 30 'replicate' estimates based on 30 different subsamples of the original sample. The variability of estimates obtained from these subsamples is used to estimate the sample variability surrounding the main estimate. 4 Limited publication space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication. However, RSEs for all these estimates are available free-of-charge on the ABS web site <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication, Retirement and Retirement Intentions, Australia (cat. no. 6238.0). As a guide, the population estimates and RSEs for selected data from tables 1 and 3 are presented at table T1 and table T2 in this Technical Note. 5 In the tables in this publication, only estimates (numbers, percentages, means and medians) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *13.5) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (e.g. **2.1) to indicate that they are considered too unreliable for general use. CALCULATION OF STANDARD ERROR AND RELATIVE STANDARD ERROR 6 RSEs are routinely presented as the measure of sampling error in this publication and related products. SEs can be calculated using the estimates (counts or means) and the corresponding RSEs. 7 An example of the calculation of the SE from an RSE follows. Table T1 shows that the estimated number of females aged 55-59 who retired from the labour force aged less than 55 years is 135,300, and the RSE for this estimate is 11.7%. The SE is:
= (RSE / 100) x estimate = 0.117 x 135,300 = 15,800 (rounded to the nearest 100) 8 Therefore, there are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall within the range 119,500 to 151,100 and about 19 chances in 20 that the value will fall within the range 103,700 to 166,900. This example is illustrated in the following diagram. 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 RSEs of proportions not provided in the spreadsheets is given below. This formula is only valid when x is a subset of y. 10 Considering table T1, of the 1,750,500 females who were retired from labour force, 989,100 or 56.5% were aged less than 55 years at retirement. The RSE of 989,100 is 3.5% and the RSE for 1,750,500 is 1.9% (as shown in the corresponding RSE table for T1). Applying the above formula, the RSE for the proportion of females who retired aged less than 55 years is: 11 Therefore, the SE for the proportion of females who retired from the labour force aged less than 55 years is 1.6 percentage points (= (56.5/100) x 2.9). Therefore, there are about two chances in three that the proportion of females who retired from the labour force aged less than 55 years is between 54.9% and 58.1%, and 19 chances in 20 that the proportion is within the range 53.3% to 59.7%. SUMS OR DIFFERENCES BETWEEN ESTIMATES 12 Published estimates may also be used to calculate the sum of, or difference between, two survey estimates (of numbers, means or percentages) where these are not provided in the spreadsheets. Such estimates are also subject to sampling error. 13 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: 14 The sampling error of the sum of two estimates is calculated in a similar way. An approximate SE of the sum of two estimates (x + y) may be calculated by the following formula: 15 An example follows. From paragraph 7 the estimated number of females aged 55-59 who retired from the labour force aged less than 55 years is 135,300 and the SE is 15,800. From table T1, the estimate of females aged 60-64 who retired from the labour force aged less than 55 years old is 165,200, the RSE is 9.8% and the SE is 16,200 (rounded to nearest 100). The estimate of females aged 55-64 who retired from the labour force aged less than 55 years is:
16 The SE of the estimate of females aged 55-64 who retired from the labour force aged less than 55 years is: 17 Therefore, there are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall within the range 277,900 to 323,100 and about 19 chances in 20 that the value will fall within the range 255,300 to 345,700. 18 While these formulae will only be exact for sums of, or differences between, separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all sums or differences likely to be of interest in this publication. SELECTED ESTIMATES AND RSES
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