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RELIABILITY OF ESTIMATES
1 The estimates provided in this publication are based on a sample of approximately 9,200 persons who were aged 18 years and over in Queensland in October 2002. Therefore, the estimates may be subject to two types of error: sampling and non-sampling.
Sampling error
2 Sampling error is the difference which would be expected between the estimate from a sample and the corresponding figure that would have been obtained from a survey using the same questionnaire and procedures involving the entire population.
Non-sampling error
3 Non-sampling errors may arise as a result of errors in the reporting, recording or processing of the data and can occur even if there is a complete enumeration of the population. Non-sampling errors can be introduced through inadequacies in the questionnaire, non-response, inaccurate reporting by respondents, errors in the application of survey procedures, incorrect recording of answers and errors in data entry and processing.
4 It is difficult to measure the size of the non-sampling errors. The extent of these errors could vary considerably from survey to survey and from question to question. Every effort is made in the design of the survey and development of survey procedures to minimise the effect of these errors.
ESTIMATES OF SAMPLING ERROR
5 One measure of the variability of estimates which occurs as a result of surveying only a sample of the population is the standard error (SE).
6 There are about two chances in three (67%) that a survey estimate is within one standard error of the figure that would have been obtained if all households/persons had been included in the survey. There are about nineteen chances in twenty (95%) that the estimate will lie within two standard errors.
7 The standard error can also be expressed as a percentage of the estimate. This is known as the relative standard error (RSE). The RSE is determined by dividing the standard error of an 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.
8 Table T1 gives approximate RSEs for this survey, for general application to estimates. These figures will not give a precise measure of the SE of a particular estimate, but they will provide an indication of its magnitude.
9 Linear interpolation is used to calculate the standard error of estimates falling between the sizes of estimates listed in the table.
10 Proportions of a total and percentages formed from the ratio of two estimates are also subject to sampling error. The size of the error depends on the accuracy of both the numerator and the denominator. The formula for the relative standard error of a proportion or percentage is:
RSE (x/y) = square root sign [[RSE (x) ]2 - [RSE(y) ]2]
11 Estimates derived from very small sample sizes are subject to such high RSEs as to detract seriously from their value for most reasonable uses. Only estimates with an RSE less than 25% are considered sufficiently reliable for most purposes. In this survey, estimates between 4,582 and 1,300 have a RSE between 25% and 50% and have been indicated with the symbol '*'. Estimates smaller than 1,300 have a RSE greater than 50% and have been indicated with the symbol '**'. Any estimate preceded by '*' or '**' symbol should be used with caution.
T1 STANDARD ERRORS OF ESTIMATES OF QUEENSLAND PERSONS, OCTOBER 2002 |
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Size of estimate
(persons) | Standard error
no. | Relative standard error
% |
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500 | 420 | 83.7 |
700 | 490 | 69.9 |
1,000 | 580 | 57.6 |
1,500 | 690 | 46.3 |
2,000 | 790 | 39.5 |
2,500 | 850 | 35.0 |
3,000 | 950 | 31.6 |
3,500 | 1,000 | 29.0 |
4,000 | 1,100 | 27.0 |
5,000 | 1,200 | 23.8 |
7,000 | 1,400 | 19.7 |
10,000 | 1,600 | 16.1 |
15,000 | 1,900 | 12.8 |
20,000 | 2,200 | 10.9 |
30,000 | 2,600 | 8.6 |
40,000 | 2,900 | 7.3 |
50,000 | 3,200 | 6.4 |
100,000 | 4,250 | 4.3 |
150,000 | 5,050 | 3.4 |
200,000 | 5,650 | 2.8 |
300,000 | 6,650 | 2.2 |
500,000 | 8,150 | 1.6 |
1,000,000 | 10,700 | 1.1 |
2,000,000 | 13,950 | 0.7 |
5,000,000 | 19,650 | 0.4 |
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