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 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 5559 who retired from the labour force aged less than 55 years is 136,800, and the RSE for this estimate is 9.9%. The SE is:
SE of estimate
= (RSE / 100) x estimate
= 0.099 x 136,800
= 13,500 (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 123,300 to 150,300 and about 19 chances in 20 that the value will fall within the range 109,800 to 163,800. 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 1,694,900 females who were retired from labour force, 979,900 or 57.8% were aged less than 55 years at retirement. The RSE of 979,900 is 3.4% and the RSE for 1,694,900 is 2.2% (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 1.5 percentage points (= (57.8/100) 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 56.3% and 59.3%, and 19 chances in 20 that the proportion is within the range 54.8% to 60.8%.
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 (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 136,800 and the SE is 13,500. From table T1, the estimate of females aged 6064 who retired from the labour force aged less than 55 years old is 176,200, the RSE is 6.8% and the SE is 12,000. The estimate of females aged 5564 who retired from the labour force aged less than 55 years is:
136,800 + 176,200 = 313,000
16 The SE of the estimate of females aged 5564 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 294,900 to 331,100 and about 19 chances in 20 that the value will fall within the range 276,800 to 349,200.
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 who have retired from the labour force 

   AGE AT RETIREMENT FROM THE LABOUR FORCE (YEARS)  
   Less
than 55  5559  6064  6569  70 and
over  Total 
ESTIMATES ('000) 

Males       
 Age group (years)       
  4549  40.1          40.1 
  5054  45.5          45.5 
  5559  66.8  34.4        101.2 
  6064  62.1  57.3  60.4      179.8 
  6569  52.4  55.6  95.8  43.9    247.7 
  70 and over  90.0  146.2  250.6  165.5  65.8  718.1 
Total  357.0  293.4  406.8  209.4  65.8  1 332.5 
Females       
 Age group (years)       
  4549  51.2          51.2 
  5054  93.2          93.2 
  5559  136.8  *35.4        172.3 
  6064  176.2  65.8  39.2      281.1 
  6569  141.4  63.2  75.8  24.8    305.3 
  70 and over  381.0  139.3  162.5  65.3  43.7  791.8 
Total  979.9  303.7  277.5  90.2  43.7  1 694.9 
Persons       
 Age group (years)       
  4549  91.3          91.3 
  5054  138.7          138.7 
  5559  203.7  69.8        273.5 
  6064  238.2  123.0  99.6      460.9 
  6569  193.8  118.7  171.6  68.7    553.0 
  70 and over  471.0  285.5  413.1  230.9  109.5  1 510.0 
Total  1 336.8  597.1  684.4  299.6  109.5  3 027.4 
RSES OF ESTIMATES (%) 

Males       
 Age group (years)       
  4549  22.5          22.5 
  5054  23.0          23.0 
  5559  13.2  23.6        11.8 
  6064  16.1  14.9  15.8      7.7 
  6569  16.4  17.5  10.8  19.5    6.8 
  70 and over  13.2  8.9  7.2  7.8  12.5  2.2 
Total  6.8  6.5  4.9  6.0  12.5  2.3 
Females       
 Age group (years)       
  4549  21.4          21.4 
  5054  17.2          17.2 
  5559  9.9  25.0        9.8 
  6064  6.8  13.7  19.7      4.5 
  6569  7.5  12.7  11.0  18.1    4.4 
  70 and over  3.8  10.1  9.0  13.6  16.0  1.7 
Total  3.4  7.6  6.7  9.8  16.0  2.2 
Persons       
 Age group (years)       
  4549  14.1          14.1 
  5054  13.0          13.0 
  5559  8.1  17.2        7.4 
  6064  7.2  8.1  11.8      3.7 
  6569  6.1  13.2  6.6  14.0    4.3 
  70 and over  3.9  5.9  5.5  6.4  9.5  1.3 
Total  3.3  4.7  3.9  5.0  9.5  1.8 

* 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, Retirement and retirement intentions 

     Males  Females  Persons 
ESTIMATES ('000) 

In the labour force  2 372.7  1 942.6  4 315.3 
 Employed  2 341.7  1 891.4  4 233.2 
  Fulltime workers  2 010.4  954.1  2 964.4 
   Intends to continue with fulltime work:  580.9  312.3  893.2 
    Intends to then retire from the labour force  518.3  292.6  810.9 
    Did not know whether intends to retire from the labour force  62.6  *19.7  82.3 
   Intends to retire from fulltime work and work part time:  698.8  352.9  1 051.7 
    Intends to then retire from the labour force  586.4  302.5  888.9 
    Never intends or did not know whether intends to retire from the labour force  112.4  50.4  162.8 
   Did not know whether intends to take up parttime work:  523.1  236.0  759.1 
    Intends to retire from the labour force  438.5  198.7  637.2 
    Never intends or did not know whether intends to retire from the labour force  84.5  37.3  121.8 
   Never intends to retire from fulltime work  207.6  52.9  260.5 
  Parttime workers  331.4  937.4  1 268.7 
   Intends to retire from the labour force  229.7  734.1  963.8 
   Did not know whether intends to retire from the labour force  38.9  100.7  139.6 
   Never intends to retire from the labour force  62.7  102.5  165.3 
 Unemployed  31.0  51.1  82.1 
Not in the Labour Force  1 512.0  2 186.5  3 698.6 
 Retired from the labour force  1 332.5  1 694.9  3 027.4 
 Not retired from the labour force  117.5  187.8  305.3 
 Had never worked  62.1  303.8  365.9 
Total  3 884.7  4 129.1  8 013.9 
RSES OF ESTIMATES (%) 

In the labour force  1.3  2.1  1.5 
 Employed  1.3  2.3  1.6 
  Fulltime workers  1.6  4.2  1.9 
   Intends to continue with fulltime work:  3.1  7.1  3.6 
    Intends to then retire from the labour force  3.6  7.7  3.9 
    Did not know whether intends to retire from the labour force  15.1  29.2  13.2 
   Intends to retire from fulltime work and work part time:  5.0  5.9  4.1 
    Intends to retire from the labour force  5.8  7.1  4.4 
    Never intends or did not know whether intends to retire from the labour force  10.7  18.8  10.3 
   Did not know whether intends to take up parttime work:  5.1  9.8  4.8 
    Intends to retire from the labour force  6.0  10.7  5.3 
    Never intends or did not know whether intends to retire from the labour force  12.4  22.3  9.9 
   Never intends to retire from fulltime work  15.1  18.9  12.0 
  Parttime workers  6.9  4.2  3.4 
   Intends to retire from the labour force  8.5  5.4  4.5 
   Did not know whether intends to retire from the labour force  20.9  17.0  15.1 
   Never intends to retire from the labour force  16.8  10.6  8.4 
 Unemployed  23.1  16.9  11.5 
Not in the Labour Force  2.0  1.9  1.7 
 Retired from the labour force  2.3  2.2  1.8 
 Not retired from the labour force  11.0  12.9  8.9 
 Had never worked  13.4  6.4  5.5 
Total       

* 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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