TECHNICAL NOTE DATA QUALITY
INTRODUCTION
1 Since the estimates published in this publication are based on information obtained from occupants of a sample of dwellings, they are subject to sampling variability. That is, they may differ from those estimates that would have been produced if all dwellings had been included in the survey. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of dwellings (or occupants) was included. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all dwellings had been included, and about 19 chances in 20 (95%) that the difference will be less than two SEs.
2 Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate.
RSE% = (SE/estimate) x 100
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 freeofcharge 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 The RSEs have been derived using the Jackknife method. 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 T2 shows that the estimated number of females aged 5559 who retired from the labour force aged less than 55 years is 137,800, and the RSE for this estimate is 8.3%. The SE is:
SE of estimate
= (RSE / 100) x estimate
= 0.083 x 137,800
= 11,400 (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 126,400 to 149,200 and about 19 chances in 20 that the value will fall within the range 115,000 to 160,600. 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 RSE of a proportion is given below. This formula is only valid when x is a subset of y.
10 Considering table T2, of the 1,719,300 females who were retired from labour force, 995,700 or 57.9% were aged less than 55 years at retirement. The RSE of 995,700 is 3.1% and the RSE for 1,719,300 is 1.7% (as shown in the corresponding RSE table for T2). 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 1.5 percentage points (= (57.9/100) x 2.6). 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 56.4% and 59.4%, and 19 chances in 20 that the proportion is within the range 54.9% to 60.9%.
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). 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 (xy) 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 5559 who retired from the labour force aged less than 55 years is 137,800 and the SE is 11,400. From table T2, the estimate of females aged 6064 who retired from the labour force aged less than 55 years old is 161,600, the RSE is 7.6% and the SE is 12,300. The estimate of females aged 5564 who retired from the labour force aged less than 55 years is:
137,800 + 161,600 = 299,400
16 The SE of the estimate of females aged 5564 who retired from the labour force aged less than 55 years is:
=16,800 (rounded to the nearest 100)
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 282,600 to 316,200 and about 19 chances in 20 that the value will fall within the range 265,800 to 333,000.
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
T1: PERSONS AGED 45 YEARS AND OVER, Retirement and retirement intentions  By labour force status and sex 

       MALES  FEMALES  PERSONS 

In the labour force   '000  2 207.2  1 764.3  3 971.4 
 Employed   '000  2 153.2  1 699.4  3 852.5 
  Fulltime workers   '000  1 834.6  905.2  2 739.8 
   Intends to continue with fulltime work:   '000  508.5  246.6  755.1 
    Intends to retire from the labour force   '000  474.9  227.9  702.8 
    Did not know whether intends to retire from the labour force   '000  33.6  *18.7  52.3 
   Intends to retire from fulltime work and work parttime:   '000  715.6  384.6  1 100.2 
    Intends to retire from the labour force   '000  573.2  337.1  910.3 
    Never intends or did not know whether intends to retire from the labour force   '000  142.3  47.5  189.9 
   Did not know whether intends to take up parttime work:   '000  484.5  234.9  719.4 
    Intends to retire from the labour force   '000  401.9  194.0  595.9 
    Never intends or did not know whether intends to retire from the labour force   '000  82.6  40.9  123.5 
   Never intends to retire from fulltime work   '000  126.1  39.0  165.1 
  Parttime workers   '000  318.5  794.2  1 112.8 
   Intends to retire   '000  238.7  650.6  889.3 
   Did not know whether will retire   '000  45.2  89.5  134.7 
   Never intends to retire   '000  34.7  54.1  88.8 
 Unemployed   '000  54.0  64.9  118.9 
Not in the labour force   '000  1 532.1  2 197.7  3 729.8 
 Retired from the labour force   '000  1 362.6  1 719.3  3 081.9 
 Not retired from the labour force   '000  136.2  193.2  329.4 
  Intends to look for, or take up, fulltime work in the future   '000  83.8  121.1  204.9 
  Intends to look for, or take up, parttime work in the future   '000  52.4  72.1  124.5 
 Had never worked   '000  33.4  285.2  318.6 
Total   '000  3 739.3  3 962.0  7 701.3 
In the labour force   RSE%  1.3  1.6  1.1 
 Employed   RSE%  1.3  1.7  1.1 
  Fulltime workers   RSE%  1.5  3.9  1.6 
   Intends to continue with fulltime work:   RSE%  4.3  10.1  4.3 
    Intends to retire from the labour force   RSE%  4.3  11.4  4.6 
    Did not know whether intends to retire from the labour force   RSE%  22.4  36.9  18.1 
   Intends to retire from fulltime work and work parttime:   RSE%  4.0  4.5  3.3 
    Intends to retire from the labour force   RSE%  4.6  5.0  3.6 
    Never intends or did not know whether intends to retire from the labour force   RSE%  10.5  17.1  9.4 
   Did not know whether intends to take up parttime work:   RSE%  4.5  7.5  3.4 
    Intends to retire from the labour force   RSE%  5.6  8.1  3.4 
    Never intends or did not know whether intends to retire from the labour force   RSE%  12.9  19.3  11.2 
   Never intends to retire from fulltime work   RSE%  12.6  19.0  10.8 
  Parttime workers   RSE%  7.0  4.7  4.3 
   Intends to retire   RSE%  7.8  5.4  5.0 
   Did not know whether will retire   RSE%  16.5  11.1  9.0 
   Never intends to retire   RSE%  23.4  17.3  14.7 
 Unemployed   RSE%  18.3  15.2  11.0 
Not in the labour force   RSE%  1.9  1.2  1.2 
 Retired from the labour force   RSE%  2.1  1.7  1.4 
 Not retired from the labour force   RSE%  12.0  7.9  7.2 
  Intends to look for, or take up, fulltime work in the future   RSE%  12.9  9.3  7.2 
  Intends to look for, or take up, parttime work in the future   RSE%  18.1  15.1  12.6 
 Had never worked   RSE%  15.3  5.9  5.5 
Total   RSE%       

* estimate has a relative standard error of 25% to 50% and should be used with caution 
 nil or rounded to zero (including null cells) 
T2: PERSONS AGED 45 YEARS AND OVER: who have retired from the labour force 

   Age at retirement from the labour force  
   Less than 55  5559  6064  6569  70 and over  Total 

Males        
 4549  '000  44.3          44.3 
 5054  '000  47.7          47.7 
 5559  '000  73.3  30.0        103.4 
 6064  '000  68.1  86.5  30.2      184.9 
 6569  '000  50.1  75.7  86.0  48.4    260.2 
 70 and over  '000  84.2  156.1  252.6  166.4  62.9  722.2 
 Total  '000  367.8  348.4  368.8  214.7  62.9  1 362.6 
Females        
 4549  '000  43.2          43.2 
 5054  '000  84.6          84.6 
 5559  '000  137.8  *41.0        178.8 
 6064  '000  161.6  75.5  46.1      283.2 
 6569  '000  159.7  58.1  74.4  18.0    310.2 
 70 and over  '000  408.8  174.4  135.8  68.2  32.1  819.3 
 Total  '000  995.7  349.0  256.3  86.2  32.1  1 719.3 
Persons        
 4549  '000  87.5          87.5 
 5054  '000  132.3          132.3 
 5559  '000  211.2  71.0        282.2 
 6064  '000  229.7  162.0  76.4      468.1 
 6569  '000  209.8  133.8  160.4  66.4    570.4 
 70 and over  '000  493.1  330.5  388.3  234.5  95.0  1 541.4 
 Total  '000  1 363.4  697.4  625.1  300.9  95.0  3 081.9 
Males        
 4549  RSE%  16.8          16.8 
 5054  RSE%  16.1          16.1 
 5559  RSE%  11.6  20.1        10.7 
 6064  RSE%  13.9  10.1  21.2      7.6 
 6569  RSE%  18.0  14.2  14.4  15.5    4.8 
 70 and over  RSE%  10.1  9.4  5.8  8.6  13.5  1.4 
 Total  RSE%  5.9  7.5  5.9  7.3  13.5  2.1 
Females        
 4549  RSE%  16.1          16.1 
 5054  RSE%  9.7          9.7 
 5559  RSE%  8.3  27.1        9.8 
 6064  RSE%  7.6  10.3  19.8      4.6 
 6569  RSE%  6.6  15.5  11.6  23.2    3.6 
 70 and over  RSE%  4.7  6.1  8.8  16.0  23.3  1.6 
 Total  RSE%  3.1  4.7  6.3  14.3  23.3  1.7 
Persons        
 4549  RSE%  10.8          10.8 
 5054  RSE%  7.8          7.8 
 5559  RSE%  7.0  16.4        7.6 
 6064  RSE%  6.8  6.1  14.1      4.0 
 6569  RSE%  5.9  9.8  10.0  13.4    3.0 
 70 and over  RSE%  4.5  4.8  5.0  7.5  9.9  1.1 
 Total  RSE%  2.8  4.3  3.9  7.2  9.9  1.4 

* estimate has a relative standard error of 25% to 50% and should be used with caution 
 nil or rounded to zero (including null cells) 
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