TECHNICAL NOTE DATA QUALITY
RELIABILITY OF THE ESTIMATES
1 Since the estimates 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 may have varied by chance because only a sample of dwellings 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.
3 RSEs for estimates from the 2009 Survey of Education and Training were calculated for each separate estimate and published in the 'direct' form. The Jackknife method of variance estimation is used for this process, which involves the calculation of 60 'replicate' estimates based on 60 different sub samples of the original sample. The variability of estimates obtained from these sub samples is used to estimate the sample variability surrounding the main estimate.
4 Tables 4, 10, 12 and 16 contain time series estimates from the 2009 and 2005 cycles of the SET. The spreadsheet datacubes associated with the current edition of Education and Training Experience, Australia (cat. no. 6278.0) contain 'direct' RSEs for both the 2005 and 2009 estimates. However, the RSEs published in earlier editions of Education and Training Experience (cat. no. 6278.0) were calculated using previous statistical SE models. These are detailed in Education and Training Experience, Australia, 2005 (cat. no. 6278.0) which is available on the ABS website <www.abs.gov.au>. While the direct method is more accurate, the difference between the two is usually not significant for most estimates.
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 are included and preceded by an asterisk (e.g. *15.7) 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. **2.8) to indicate that they are considered too unreliable for general use.
CALCULATION OF STANDARD ERRORS
6 Standard errors can be calculated using the estimates (counts or means) and the corresponding RSEs. For example, Table 1 shows the estimated number of persons aged 1564 years who participated in formal learning in the last 12 months and who were female was 1,905,300. The RSE Table corresponding to the estimates in Table 1 (see Table 1 Relative Standard Errors in the 'Relative Standard Error' section at the end of these Technical Notes) shows the RSE for this estimate is 1.8%. The SE is calculated by:
7 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 1,871,005 to 1,939,595 and about 19 chances in 20 that the value will fall within the range 1,836,710 to 1,973,890. This example is illustrated in the diagram below.
PROPORTIONS AND PERCENTAGES
8 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:
9 As an example, using estimates from Table 1, of the 3,786,300 persons aged 1564 years who participated in formal learning in the last 12 months, 1,905,300 are females or 50.3%. The RSE for 1,905,300 is 1.8% and the RSE for 3,786,300 is 1.3% (see Table 1 Relative Standard Errors in the 'Relative Standard Error' section at the end of these Technical Notes). Applying the above formula, the RSE for the proportion of females who participated in formal learning is:
10 Therefore, the SE for the proportion of persons aged 1564 years who participated in formal learning in the last 12 months and were female, is 0.6 percentage points (=1.2/100 x 50.3). Hence, there are about two chances in three that the proportion of females who participated in formal learning is between 49.7% and 50.9%, and 19 chances in 20 that the proportion is between 49.1% and 51.5%.
DIFFERENCES
11 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or percentages). Such an estimate is subject to sampling error. 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:
12 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
SIGNIFICANCE TESTING
13 A statistical significance test for any of the comparisons between estimates can be performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 11. This standard error is then used to calculate the following test statistic:
14 If the absolute value of this test statistic is greater than 1.96 then there is statistical evidence of a significant difference in the two populations with respect to that characteristic. This statistic corresponds to a 95% confidence interval of the difference. Otherwise, it cannot be stated with confidence that there is a real difference between the population with respect to that characteristic.
15 The selected tables in this publication that show the results of significance testing are annotated to indicate where the estimates which have been compared are significantly different from each other with respect to the test statistic. In all other tables which do not show the results of significance testing, users should take account of RSEs when comparing estimates for different populations.
16 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents, 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.
RELATIVE STANDARD ERROR
17 Limited publication space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication, only RSEs for Table 1 are included below. However, RSEs for all tables are available freeofcharge on the ABS website
<www.abs.gov.au>, released in spreadsheet format as an attachment to this publication.
TABLE 1. RELATIVE STANDARD ERRORS, Persons aged 1564 years, Selected characteristics  by type of learning participated in during the last 12 months 

   Type of learning participated in during the last 12 months(a)   
   Formal learning  Nonformal learning  Total formal and nonformal learning  Informal learning  Did not participate in learning  Total  Proportion 
   %  %  %  %  %  %  % 

Age group (years)        
 1524  1.8  3.1  1.5  1.6  9.7  1.1  1.1 
 2534  4.3  3.9  3.4  2.3  6.3  2.1  2.1 
 3544  4.0  3.1  2.4  1.5  5.7  1.3  1.3 
 4554  5.4  3.1  2.6  1.4  6.0  1.4  1.4 
 5564  9.5  4.1  3.7  1.9  4.6  1.6  1.6 
Sex        
 Males  2.0  2.0  1.3  0.6  4.0     
 Females  1.8  1.5  1.1  0.5  2.7     
Labour force status        
 Employed fulltime  2.8  1.9  1.5  0.8  3.8  0.7  0.7 
 Employed parttime  2.7  3.2  2.3  1.8  4.5  1.6  1.6 
 Unemployed  5.7  6.4  4.6  3.3  14.0  2.7  2.7 
 Not in the labour force  2.9  4.2  2.4  1.9  4.1  1.2  1.2 
Highest year of school completed        
 Year 12  2.1  2.2  1.4  1.2  5.4  1.1  1.1 
 Year 11  4.3  4.8  3.4  2.4  6.1  2.4  2.4 
 Year 10 or below(b)  3.0  3.1  2.3  1.8  3.4  1.3  1.3 
Main language spoken at home        
 English        
  Born in Australia  2.1  2.0  1.7  1.2  4.3  1.1  1.1 
  Born overseas  6.0  4.3  3.7  2.7  8.0  2.5  2.5 
 Other language        
  Born in Australia  9.0  8.7  7.3  6.6  15.3  6.3  6.3 
  Born overseas  5.9  5.9  4.6  4.7  8.8  4.3  4.3 
State/Territory of usual residence        
 New South Wales  2.8  3.0  2.0  1.2  5.8     
 Victoria  2.9  2.8  2.0  1.0  6.7     
 Queensland  3.5  3.9  2.5  1.2  8.4     
 South Australia  2.9  4.9  2.8  1.3  9.1     
 Western Australia  3.9  3.3  2.1  1.2  7.8     
 Tasmania  2.9  4.0  2.6  1.0  8.2     
 Northern Territory(c)  3.5  4.8  2.8  1.8  10.5     
 Australian Capital Territory  3.1  2.4  1.7  1.0  9.1     
Remoteness        
 Major Cities of Australia  1.7  1.7  1.1  0.9  3.4  0.8  0.8 
 Inner Regional Australia  5.4  5.7  4.8  4.1  9.4  4.0  4.0 
 Outer Regional Australia  8.5  7.9  7.3  7.2  12.4  6.7  6.7 
 Remote Australia  25.2  21.9  22.1  22.5  31.9  21.6  21.6 
Disability or longterm health condition        
 Has a disability  3.3  3.1  2.2  1.4  4.6  1.3  1.3 
 Does not have a disability  1.5  1.9  1.1  0.8  3.3  0.6  0.6 
Equivalised gross weekly household income(d)        
 Quintile 1 ($0$444)  5.0  6.4  4.4  3.4  5.0  2.6  2.6 
 Quintile 2 ($444$711)  5.3  4.7  4.3  3.5  5.7  3.1  3.1 
 Quintile 3 ($711$983)  4.9  4.8  3.8  3.5  7.5  3.3  3.3 
 Quintile 4 ($984$1,364)  5.4  4.8  4.1  3.7  9.3  3.7  3.7 
 Quintile 5 ($1,364$31,020)  5.7  4.9  4.8  3.6  11.5  3.7  3.7 
Total  1.3  1.3  0.9  0.4  2.5     

 nil or rounded to zero (including null cells) 
(a) Refers to all types of learning participated in during the last 12 months, therefore people may appear in more than one category. 
(b) Includes 'Never attended school'. 
(c) Refers to mainly urban areas. See paragraph 4 of the Explanatory Notes for more details. 
(d) Quintile dollar ranges are not mutually exclusive. Refer to the Glossary for more information. Excludes persons where household income was not known or not adequately reported. See paragraph 31 of the Explanatory Notes for more details. 
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