6238.0 - Retirement and Retirement Intentions, Australia, Jul 2006 to Jun 2007 Quality Declaration 
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 22/01/2008   
   Page tools: Print Print Page Print all pages in this productPrint All

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 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 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 55-59 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.

Diagram: CALCULATION OF STANDARD ERROR AND RELATIVE STANDARD ERROR



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.


Equation: Calculation of relative standard errors of proportions and percentages


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:


Equation: Example calculation of relative standard errors of proportions


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 (x-y) may be calculated by the following formula:


Equation: Calculation of differences between estimates


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:


Equation: Calculation of sum of estimates


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 137,800 and the SE is 11,400. From table T2, the estimate of females aged 60-64 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 55-64 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 55-64 who retired from the labour force aged less than 55 years is:
      Equation: Example of calculation of standard error of estimate
      =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
Full-time workers '000
1 834.6
905.2
2 739.8
Intends to continue with full-time 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 full-time work and work part-time: '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 part-time 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 full-time work '000
126.1
39.0
165.1
Part-time 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, full-time work in the future '000
83.8
121.1
204.9
Intends to look for, or take up, part-time 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
Full-time workers RSE%
1.5
3.9
1.6
Intends to continue with full-time 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 full-time work and work part-time: 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 part-time 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 full-time work RSE%
12.6
19.0
10.8
Part-time 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, full-time work in the future RSE%
12.9
9.3
7.2
Intends to look for, or take up, part-time 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
55-59
60-64
65-69
70 and over
Total
Males
45-49 '000
44.3
-
-
-
-
44.3
50-54 '000
47.7
-
-
-
-
47.7
55-59 '000
73.3
30.0
-
-
-
103.4
60-64 '000
68.1
86.5
30.2
-
-
184.9
65-69 '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
45-49 '000
43.2
-
-
-
-
43.2
50-54 '000
84.6
-
-
-
-
84.6
55-59 '000
137.8
*41.0
-
-
-
178.8
60-64 '000
161.6
75.5
46.1
-
-
283.2
65-69 '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
45-49 '000
87.5
-
-
-
-
87.5
50-54 '000
132.3
-
-
-
-
132.3
55-59 '000
211.2
71.0
-
-
-
282.2
60-64 '000
229.7
162.0
76.4
-
-
468.1
65-69 '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
45-49 RSE%
16.8
-
-
-
-
16.8
50-54 RSE%
16.1
-
-
-
-
16.1
55-59 RSE%
11.6
20.1
-
-
-
10.7
60-64 RSE%
13.9
10.1
21.2
-
-
7.6
65-69 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
45-49 RSE%
16.1
-
-
-
-
16.1
50-54 RSE%
9.7
-
-
-
-
9.7
55-59 RSE%
8.3
27.1
-
-
-
9.8
60-64 RSE%
7.6
10.3
19.8
-
-
4.6
65-69 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
45-49 RSE%
10.8
-
-
-
-
10.8
50-54 RSE%
7.8
-
-
-
-
7.8
55-59 RSE%
7.0
16.4
-
-
-
7.6
60-64 RSE%
6.8
6.1
14.1
-
-
4.0
65-69 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)