6365.3 - Preferred Working Hours of Wage and Salary Earners, Queensland, Oct 2006  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 31/05/2007  First Issue
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TECHNICAL NOTE DATA RELIABILITY


RELIABILITY OF THE ESTIMATES

1 The estimates provided in this publication are based on information obtained from the occupants of a sample of dwellings and may be subject to two types of error: sampling error and non-sampling error.



NON-SAMPLING ERROR

2 Non-sampling errors may arise as a result of errors in the reporting, recording or processing of data and can occur even if there is complete enumeration of the population. Non-sampling error can be introduced through inadequacies in the questionnaire, non-response, inaccurate reporting by respondents, error in the application of survey procedures, incorrect recording of answers and errors in data entry and processing.


3 It is difficult to measure the size of the non-sampling error. The extent of these errors can vary considerably from survey to survey and even from question to question. Every effort is made during the design and development of the survey to minimise the effect of these errors.


4 The methodology employed for this survey of asking questions of one adult only within a household, who answers for all in-scope members of the household, is one possible source of non-sampling error. Every effort is made in the design of the survey and the development of survey procedures to minimise the effect of this type of error.



SAMPLING ERROR

5 This is the difference which would be expected between the estimate and the corresponding figure that would have been obtained if all dwellings in Queensland had been included in the survey, using the same questionnaires and procedures.



ESTIMATES OF SAMPLING ERROR

6 One measure of the sampling error which occurs as a result of surveying only a sample of the population is the standard error (SE) (see Table T1).


7 There are about two chances in three (67%) that the survey estimate will differ by less than one SE from the figure that would have been obtained if all persons in Queensland had been included in the survey and about nineteen chances in twenty (95%) that the difference will be less than two standard errors.


8 The standard error can also be expressed as a percentage of the estimate. This is known as the relative standard error (RSE) and is determined by dividing the standard error of the estimate SE(x) by the estimate x and expressing it as a percentage. That is: RSE(x)=100*SE(x)/x (where x is the estimate). The RSE is a measure of the percentage error likely to have occurred due to sampling.


9 The following table gives approximate SEs and RSEs for this survey, for general application to estimates of counts. These figures will not give a precise measure of the SE of a particular estimate, but will provide an indication of its magnitude.

T1: STANDARD ERRORS OF ESTIMATES

Standard Error
Relative Standard Error
Size of estimate
no.
%

100
250
250.0
200
330
165.0
300
390
130.0
500
470
94.0
700
540
77.1
1,000
620
62.0
1,500
730
48.7
2,000
810
40.5
2,500
900
36.0
3,000
950
31.7
3,500
1 000
28.6
4,000
1 050
26.3
5,000
1 150
23.0
7,000
1 300
18.6
10,000
1 500
15.0
15,000
1 750
11.7
20,000
1 950
9.8
30,000
2 300
7.7
40,000
2 550
6.4
50,000
2 800
5.6
100,000
3 600
3.6
150,000
4 350
2.9
200,000
5 200
2.6
300,000
6 800
2.3
500,000
9 300
1.9
1,000,000
13 700
1.4
2,000,000
19 350
1.0
5,000,000
28 550
0.6
10,000,000
36 450
0.4


10 Linear interpolation can be used to calculate the SE of estimates falling between the sizes of estimates listed in Table T1 above, by using the following general formula:


Equation: Linear Interpolation 1


11 Estimates derived from very small sample sizes are subject to high RSEs, which can detract seriously from their value for most reasonable uses. In this survey, estimates between 4,120 and 1,385 have a RSE between 25% and 50% and have been indicated with the symbol '*'. Estimates smaller than 1,385 have a RSE greater than 50% and have been indicated with the symbol '**'.



PROPORTIONS AND PERCENTAGES

12 Percentages formed from the ratio of two estimates of the same type (such as proportions) are also subject to sampling error. The size of the error depends on the accuracy of both the estimate used as the numerator (x) and the estimate used as the denominator (y). The formula for the relative standard error of a proportion or percentage is given below:


Equation: RSE



MEANS

13 This publication contains means. The mean is a measure for locating the centre of a set of values and is calculated by obtaining the arithmetic average of those values.


14 The RSE of an estimate of the mean number of hours usually worked can be obtained by firstly finding the RSE of the estimate of the total number of persons contributing to the mean (see Table T1), then multiplying the RSE by the relevant factor below:

  • average hours usually worked in a week: 0.74
  • average unpaid hours usually worked in week: 1.23
  • average overtime hours usually worked in week: 1.09

15 The following is an example of the calculation of RSEs where the use of a factor is required. Publication Table 5 (see page 13) shows that the estimated number of males in Queensland who usually worked unpaid hours was 164,000. Table 5 also shows that the average number of unpaid hours worked per week by males is 8.2 hours. The SE for this estimate of 164,000 males can be calculated from Table T1 by interpolation (see paragraph 10) as 4,588. To convert this to a RSE, the SE is expressed as a percentage of the estimate, or 4,588/164,000 x 100 = 2.8%.


16 Therefore, the RSE of the estimate of the mean number of unpaid hours usually worked in a week by males who usually work unpaid hours is calculated by multiplying this number (2.8%) by the appropriate factor shown in paragraph 14 (in this case 1.23): 2.8 x 1.23 = 3.4%. The SE of the estimate of the mean number of unpaid hours usually worked in a week by males is therefore 3.4% of 8.2 hours (i.e. about 0.3 hours). Therefore, if this mean estimate were obtained by a census of the population rather than a sample, then there are 2 chances in 3 that the mean number of unpaid hours usually worked in a week by males would have been within the range 7.9 hours to 8.5 hours (one standard error either side of the estimate), and about 19 chances in 20 that it would have been within the range 7.6 hours to 8.8 hours (two standard errors either side of the estimate).