Technical Note: Data quality
ESTIMATION PROCEDURE
1 Estimates derived from this survey were obtained by adjusting the MPS selection weights to account for the slightly lower sample size for this survey. The weights were then adjusted to ensure that the survey estimates conformed to an independently estimated distribution of the population (by number of adults and children within the household, and by part of state) rather than the distribution among respondents.
2 The estimates were then obtained by summing the weights of households within the required group. For example, an estimate of the total number of households with a gas hot water system is obtained by adding together the weight for each household in the sample with a gas hot water system.
RELIABILITY OF ESTIMATES
3 Estimates in this publication are subject to non-sampling and sampling errors.
Non-sampling errors
4 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.
5 It is difficult to measure the size of the non-sampling errors and the extent of these errors could vary considerably from survey to survey and from question to question. Every effort was made in the design of this survey and in the development of survey procedures to minimise the effect of these errors.
Sampling errors
6 Sampling error is the difference between the published estimate, calculated from a sample of dwellings, and the value that would have been produced if all dwellings had been included in the survey.
7 One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate may vary from the true value. There are about two chances in three (67%) that a survey estimate is within one SE of the figure that would have been obtained if all households had been included in the survey, and about 19 chances in 20 (95%) that the estimate lies within two SEs.
8 Due to space limitations, it is impractical to print the SE of each estimate in the publication. Instead, a table of SEs is provided to enable readers to determine the SE for an estimate based on the size of that estimate (see table T1). The SE table is derived from a mathematical model, which is created using the data collected in the survey. The figures in the SE table will not give a precise measure of the SE for a particular estimate but will provide an indication of its magnitude.
9 Linear interpolation can be used to calculate the SE of estimates falling between the sizes of estimates presented in T1, using the following general formula:
10 An example of the calculation and use of SEs is as follows. Table 8 shows that the estimated number of households in WA that had a dishwasher was 210,000. Since this estimate is between 200,000 and 300,000, table T1 shows that the SE will lie between 6,787 and 7,863. The approximate value of the SE can be interpolated as follows:
11 Therefore, there are about two chances in three that the true number of households in WA that had a dishwasher lies between 203,105 and 216,895, and there are about 19 chances in 20 that the value lies between 196,210 and 223,790. This example is illustrated in the diagram below:
12 The SE can also be expressed as a percentage of the estimate, known as the relative standard error (RSE). The RSE is calculated by dividing the SE of an estimate by the estimate, and expressing it as a percentage. That is:
13 For example, the RSE for the number of households that had a dishwasher is:
14 The RSE is a useful measure in that it provides an immediate indication of the level of error likely to have occurred due to sampling.
15 In general, the size of the SE increases as the size of the estimate increases. Conversely, the RSE decreases as the size of the estimate increases. Very small estimates are thus subject to high RSEs and are considered too unreliable for general use.
16 Only estimates with an RSE of less than 25%, and percentages based on such estimates, are considered sufficiently reliable for most purposes. Estimates with RSEs greater than or equal to 25% have been included in this publication, however, they are preceded by a single asterisk when the RSE is 25% to 50% (e.g. * 3.3) and by a double asterisk when the RSE is greater than 50% (e.g. ** 0.9). A single asterisk indicates that the estimate is subject to high sampling error and should be used with caution. A double asterisk indicates that the estimate is considered too unreliable for general use.
17 Published estimates are sometimes used to calculate the difference between two survey estimates. Such an estimate is also subject to sampling error. The sampling error of the difference between two estimates depends on the SE of each estimate and the relationship (correlation) between them. The approximate SE of the difference between two estimates (x and y) may be calculated using the following formula:
18 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.
19 For example, Table 8 shows that an estimated 457,700 households in Perth and 136,800 households in the Balance of WA had a top loading washing machine. This equates to a difference of 320,900 households. The standard error for each estimate is calculated using linear interpolation (as described above) and then the standard error on the estimate of the difference is calculated as:
20 Therefore, there are about two chances in three that the true difference between the number of households in Perth and the Balance of WA that had a top loading washing machine lies between 310,130 and 331,670, and there are about 19 chances in 20 that the value lies between 299,360 and 342,440.
T1 STANDARD ERRORS OF ESTIMATES OF WA HOUSEHOLDS |
|  |
| SE | RSE | |
Size of estimate
no. | no. | % | |
| |
| 500 | 316 | 63.2 | |
| 700 | 393 | 56.1 | |
| 1 000 | 491 | 49.1 | |
| 1 500 | 629 | 41.9 | |
| 2 000 | 746 | 37.3 | |
| 2 500 | 849 | 34.0 | |
| 3 000 | 942 | 31.4 | |
| 3 500 | 1,028 | 29.4 | |
| 4 000 | 1,107 | 27.7 | |
| 5 000 | 1,252 | 25.0 | |
| 7 000 | 1,499 | 21.4 | |
| 10 000 | 1,805 | 18.1 | |
| 15 000 | 2,213 | 14.8 | |
| 20 000 | 2,545 | 12.7 | |
| 30 000 | 3,080 | 10.3 | |
| 40 000 | 3,509 | 8.8 | |
| 50 000 | 3,873 | 7.7 | |
| 100 000 | 5,185 | 5.2 | |
| 150 000 | 6,086 | 4.1 | |
| 200 000 | 6,787 | 3.4 | |
| 300 000 | 7,863 | 2.6 | |
| 500 000 | 9,362 | 1.9 | |
| 1 000 000 | 11,634 | 1.2 | |
| |
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