TECHNICAL NOTE DATA QUALITY
INTRODUCTION
1 Since the estimates published in this publication are based on information obtained from occupants of a sample of households, they are subject to sampling variability. That is, they may differ from those estimates that would have been produced if all households 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 households (or occupants) was included.
2 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 households had been included, and about 19 chances in 20 (95%) that the difference will be less than two SEs.
3 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
4 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.
5 In the tables included with this release, 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 126,700 and the RSE for this estimate is 9.4%. The SE is:
SE of estimate
= (RSE / 100) x estimate
= 0.094 x 126,700
= 11,900 (rounded to the nearest 100)
8 Therefore, there are about two chances in three that the value that would have been produced if all households had been included in the survey will fall within the range 114,800 to 138,600 and about 19 chances in 20 that the value will fall within the range 102,900 to 150,500. 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 2,004,400 females who were retired from labour force, 1,026,100 or 51.2% were aged less than 55 years at retirement. The RSE of 1,026,100 is 3.6% and the RSE for 2,004,400 is 1.5% (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 1.7 percentage points (= (51.2/100) x 3.3). 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 49.5% and 52.9%, and 19 chances in 20 that the proportion is within the range 47.8% to 54.6%.
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 126,700 and the SE is 11,900. From table T1, the estimate of females aged 60–64 who retired from the labour force aged less than 55 years is 146,400, the RSE is 11.3% and the SE is
16,500 (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 households had been included in the survey will fall within the range 252,800 to 293,400 and about 19 chances in 20 that the value will fall within the range 232,500 to 313,700.
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
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  44.2          44.2  
 5054  57.2          57.2  
 5559  66.3  *27.9        95.5  
 6064  53.7  66.5  61.1      178.7  
 6569  59.7  84.0  108.0  98.0    355.6  
 70 and over  112.1  178.2  266.4  200.3  124.1  882.1  
 Total  391.7  370.4  430.8  291.0  124.1  1615.8  
Females         
 Age group (years)
      
 4549  62.6          62.6  
 5054  118.5          118.5  
 5559  126.7  34.2        159.7  
 6064  146.4  81.7  40.4      271.2  
 6569  156.2  89.9  112.7  41.8    393.8  
 70 and over  418.5  196.4  208.3  108.5  65.1  998.9  
 Total  1026.1  405.6  355.3  150.1  65.1  2004.4  
        
Persons         
 Age group (years)
      
 4549  117.8          117.8  
 5054  167.9          167.9  
 5559  191.8  68.4        258.8  
 6064  199.4  156.2  99.6      449.8  
 6569  218.2  176.7  216.3  141.4    746.8  
 70 and over  533.6  378.2  467.9  304.1  193.6  1881.0  
 Total  1421.4  776.9  783.9  443.2  193.6  3624.7  
        

* estimate has a relative standard error of 25% to 50% and should be used with caution
RSES OF ESTIMATES (%)

Males         
 Age group (years)
      
 4549  20.9          20.9  
 5054  21.1          21.1  
 5559  12.3  26.1        11.1  
 6064  14.3  16.2  14.7      6.0  
 6569  21.7  13.8  11.7  12.5    3.8  
 70 and over  11.6  9.6  6.4  7.3  12.9  1.0  
 Total  6.3  5.9  4.4  6.5  12.9  1.5  
        
Females         
 Age group (years)
      
 4549  13.8          13.8  
 5054  9.3          9.3  
 5559  9.4  20.5        7.0  
 6064  11.3  13.2  15.3      5.4  
 6569  7.4  11.3  9.1  23.2    3.4  
 70 and over  4.0  6.5  8.0  11.8  14.2  1.5  
 Total  3.6  4.2  6.1  10.6  14.2  1.5  
        
Persons         
 Age group (years)
      
 4549  7.5          7.5  
 5054  8.0          8.0  
 5559  6.8  13.9        5.1  
 6064  8.0  8.9  9.0      3.4  
 6569  8.0  8.0  6.7  12.9    1.8  
 70 and over  3.9  5.5  5.2  6.6  10.1  0.8  
 Total  2.9  3.6  3.3  5.9  10.1  1.0  
SIGNIFICANCE TESTING
19 A statistical test for any comparisons between estimates can be performed to determine whether it is likely that there is a significant difference between two corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 13. This standard error is then used to calculate the following test statistic:
20 If the value of this test statistic is greater than 1.96 then there is evidence, with a 95% level of confidence, of a statistically significant difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a difference between the populations with respect to that characteristic.
21 The imprecision due sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents and recording by interviewers, and errors made in coding and processing data. Inaccuracies of this kind are referred to as nonsampling error, and they occur in any enumeration, whether it be a full count or sample. Every effort is made to reduce nonsampling error to a minimum by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.
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