TECHNICAL NOTE DATA QUALITY
RELIABILITY OF ESTIMATES
1 As the estimates in this publication are based on information relating to a sample of employers and employees, rather than a full enumeration, they are subject to sampling variability, that is, they may differ from the figures that would have been produced if the data had been obtained from all employers and all employees. The difference, called sampling error, should not be confused with inaccuracy that may occur because of imperfections in reporting by respondents or in processing by the ABS. Such inaccuracy is referred to as nonsampling error and may occur in any enumeration whether it be a full count or a sample. Efforts have been made to reduce nonsampling error by careful design of questionnaires, detailed checking of returns and quality control of processing.
2 The sampling error associated with any estimate can be estimated from the sample results. One measure of sampling error is given by the standard error, which indicates the degree to which an estimate may vary from the value that would have been obtained from a full enumeration (the ‘true value'). There are about two chances in three that a sample estimate differs from the true value by less than one standard error, and about nineteen chances in twenty that the difference will be less than two standard errors.
3 An example of the use of a standard error is as follows. From table 2, the estimated average weekly total cash earnings for all male employees in Australia is $1153.90, with a standard error of $12.00 (from the table below). Then there would be about two chances in three that a full enumeration would have given an estimate in the range $1141.90 to $1165.90 and about nineteen chances in twenty that it would be in the range $1129.90 to $1177.90.
4 The difference between two survey estimates is also an estimate and it is therefore subject to sampling variability. The standard error on the difference between two survey estimates in the one time period (i.e. xy) can be calculated using the following formula:
5 The formula above will overestimate the standard error where there is a positive correlation between two estimates (e.g. male and female school teachers). While this formula will only be accurate where there is no correlation between two estimates (e.g. estimates from different states), it is expected to provide a reasonable approximation of the standard error for the difference between two survey estimates.
6 From table 2, the estimated average weekly total cash earnings for all female employees in Australia is $768.10, with a standard error of $8.60 (from the table below). The difference between the earnings of male and female employees is $385.80. The estimate of the standard error of the difference between the average weekly total earnings for male and female employees in Australia is:
7 There are about two chances in three that the true figure for the difference between male and female average weekly earnings lies in the range $371.00 to $400.60, and about nineteen chances in twenty that the figure is in the range $356.20 to $415.40.
8 The formula above can be used to estimate the standard error on a difference between estimated averages in two different years. (The movement standard error will be approximately 1.4 times the standard error on the level estimate, if the standard errors on the two level estimates are similar.)
9 Another measure of the sampling error is the relative standard error, which is obtained by expressing the standard error as a percentage of the estimate. Both the standard error and relative standard error are used to measure the reliability of estimates.
10 Relative standard errors can be calculated using the actual standard error and the survey estimate using the formula below:
RSE(estimate)=[SE(estimate)/(estimate)] * 100
11 For example, from table 2, the average weekly total cash earnings for all male employees in Australia is $1153.90, and for all female employees it is $768.10. The table below shows an estimate for the standard error on the male estimate is $12.00, and an estimate of the standard error on the female estimate is $8.60.
12 Applying the above formula the relative standard errors for the average weekly total earnings for all male employees and all female employees can be worked out as follows:
All male employees
RSE(1153.90) = [12.00/1153.90] * 100
All female employees
RSE(768.10) = [8.60/768.10] * 100
13 An asterisk appears against an estimate in this publication where the sampling variability is considered high. For the tables in this publication, estimates with relative standard errors between 25% and 50% have been labelled with a single asterisk; estimates with a relative standard error greater than 50% have been labelled with a double asterisk.
14 Standard errors can be used to construct confidence intervals around the estimated proportions. There are about two chances in three that the 'true' value is within the interval that ranges from the sample estimate minus one standard error (estimate  1xSE) to the sample estimate plus one standard error (estimate + 1xSE). There are approximately 19 chances in 20 that the 'true' value lies within the interval from the estimate minus two standard errors (estimate  2xSE) to the estimate plus two standard errors (estimate + 2xSE).
15 The above rule gives a symmetric confidence interval that is reasonably accurate when the estimated proportion is not too near 0.00 or 1.00. Where the estimated proportion is close to 0.00 or 1.00 it would be more accurate to use a confidence interval that was not symmetric around the sample estimate. If an estimate is close to 1.00, then the upper boundary of the confidence interval should be closer to the sample estimate than suggested above, while the lower boundary should be further from the sample estimate. Similarly, if an estimate is close to 0.00, then the lower boundary of the confidence interval should be closer to the sample estimate than suggested above, while the upper boundary should be further from the sample estimate. In particular, the symmetric confidence interval could include values that are not between 0.00 and 1.00. In such a case a good rule of thumb is to use a confidence interval of the same size as the symmetric one, but with the lower (or upper) boundary set to 0.00 (or 1.00).
16 The table below contains estimates of standard errors from which confidence intervals may be constructed.
STANDARD ERRORS. Average Weekly Total Cash Earnings, All employees—Sector 

 FULLTIME
EMPLOYEES
Adult  FULLTIME
EMPLOYEES
Total  PARTTIME
EMPLOYEES
Total  ALL
EMPLOYEES
Total 
 $  $  $  $ 
MALES 

Private sector  12.90  13.10  9.40  13.30 
Public sector  21.00  21.00  54.50  25.20 
All sectors  11.30  11.50  10.40  12.00 
FEMALES 

Private sector  9.10  9.00  6.10  8.50 
Public sector  10.80  10.80  13.40  16.40 
All sectors  8.00  8.10  6.10  8.60 
PERSONS 

Private sector  9.80  9.80  5.50  9.70 
Public sector  12.90  12.90  18.70  18.50 
All sectors  8.30  8.30  5.80  8.80 

STANDARD ERRORS. Methods of Setting Pay, All Employees—Industry 

   INDIVIDUAL ARRANGEMENT  
 Award or pay scale only  Collective agreement(a)  Registered or unregistered  Working proprietor of incorporated business  Total  All methods of setting pay 

PROPORTION OF EMPLOYEES (%) 

Mining  0.5  2.9  2.9  0.3  2.9  — 
Manufacturing  1.4  1.7  1.7  0.5  1.7  — 
Electricity, gas, water and waste services  1.7  3.1  3.0  0.2  3.0  — 
Construction  1.3  3.1  2.5  1.2  2.9  — 
Wholesale trade  1.6  1.5  2.0  0.8  2.0  — 
Retail trade  2.3  2.9  1.9  0.5  2.0  — 
Accommodation and food services  2.4  2.5  2.2  0.5  2.2  — 
Transport, postal and warehousing  2.0  2.3  2.2  0.6  2.3  — 
Information media and telecommunications  1.3  2.7  2.7  0.6  2.7  — 
Financial and insurance services  0.6  2.1  2.4  0.7  2.2  — 
Rental, hiring and real estate services  2.5  3.2  2.5  1.3  2.9  — 
Professional, scientific and technical services  1.0  1.2  1.3  0.9  1.2  — 
Administrative and support services  3.2  2.5  3.0  0.4  3.0  — 
Public administration and safety  2.5  2.6  1.3  0.1  1.3  — 
Education and training  2.5  3.0  1.9  0.2  2.0  — 
Health care and social assistance  1.9  2.0  1.3  0.3  1.4  — 
Arts and recreation services  4.2  3.3  3.1  1.0  3.6  — 
Other services  2.3  1.8  3.2  1.1  3.1  — 
All industries  0.6  0.9  0.7  0.2  0.7  — 

AVERAGE WEEKLY TOTAL CASH EARNINGS ($) 

Mining  50.10  50.00  55.80  177.40  54.20  40.80 
Manufacturing  44.50  28.00  25.50  107.30  26.00  21.90 
Electricity, gas, water and waste services  68.70  36.90  64.90  115.50  60.60  32.50 
Construction  37.70  87.80  37.20  49.70  29.70  40.10 
Wholesale trade  39.80  93.30  30.50  91.90  29.10  27.00 
Retail trade  16.60  12.50  24.80  80.10  24.30  16.70 
Accommodation and food services  15.30  34.20  34.10  96.30  32.10  15.30 
Transport, postal and warehousing  57.90  23.70  35.80  57.50  31.60  19.50 
Information media and telecommunications  60.10  49.30  65.90  72.00  62.30  48.50 
Financial and insurance services  57.10  26.60  70.70  116.70  63.40  39.50 
Rental, hiring and real estate services  32.80  110.50  92.10  74.40  79.00  59.20 
Professional, scientific and technical services  39.30  76.50  40.90  63.50  34.80  32.30 
Administrative and support services  24.90  64.80  36.40  94.40  34.90  30.00 
Public administration and safety  95.00  20.60  75.90  538.10  76.80  25.30 
Education and training  49.30  40.50  79.90  85.70  77.00  36.30 
Health care and social assistance  21.00  25.00  74.60  429.30  86.30  23.80 
Arts and recreation services  24.60  45.90  59.40  133.10  58.30  32.30 
Other services  17.60  78.60  29.10  86.80  30.50  21.40 
All industries  9.40  15.30  12.60  32.60  11.80  8.80 

— nil or rounded to zero (including null cells). 
(a) Includes registered and unregistered collective agreements. 
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