STANDARD ERRORS
RELIABILITY OF ESTIMATES
Estimates based on a sample are subject to sampling variability, that is, they may differ from those that would be obtained from full enumeration.
The sampling error associated with any estimate can be estimated from the sample results and one measure so derived is the standard error. Given an estimate and the standard error on that estimate, there are about two chances in three that the sample estimate will differ by less than one standard error from the figure that would have been obtained from full enumeration, and about nineteen chances in twenty that the difference will be less than two standard errors. The relative standard error is the standard error on the estimate expressed as a percentage of the estimate.
It would be impractical to publish estimates of standard errors for all figures in individual tables. However, the following table of standard errors and relative standard errors gives an indication of the magnitude of the sampling error associated with any estimate of a particular size for short-term and total movement.
APPROXIMATE STANDARD ERROR ON ESTIMATES FOR STRATIFIED SAMPLE |
| |
| Short-term arrival or departure of Australian resident
| Short-term arrival or departure of overseas visitor
| Total arrival or departure
| |
| Standard error | Relative standard error | Standard error | Relative standard error | Standard error | Relative standard error | |
Estimated number of movements | no. | % | no. | % | no. | % | |
| |
5,000,000 | 13,296 | 0.3 | 9,334 | 0.2 | 11,417 | 0.2 | |
4,000,000 | 12,052 | 0.3 | 8,436 | 0.2 | 10,349 | 0.3 | |
3,000,000 | 10,613 | 0.4 | 7,403 | 0.2 | 9,113 | 0.3 | |
2,000,000 | 8,866 | 0.4 | 6,156 | 0.3 | 7,612 | 0.4 | |
1,000,000 | 6,506 | 0.7 | 4,488 | 0.4 | 5,582 | 0.6 | |
500,000 | 4,761 | 1.0 | 3,268 | 0.7 | 4,082 | 0.8 | |
100,000 | 2,283 | 2.3 | 1,559 | 1.6 | 1,951 | 2.0 | |
50,000 | 1,656 | 3.3 | 1,131 | 2.3 | 1,413 | 2.8 | |
10,000 | 778 | 7.8 | 535 | 5.4 | 660 | 6.6 | |
5,000 | 560 | 11.2 | 387 | 7.7 | 473 | 9.5 | |
2,000 | 361 | 18.0 | 252 | 12.6 | 304 | 15.2 | |
1,000 | 258 | 25.8 | 182 | 18.2 | 216 | 21.6 | |
750 | 224 | 29.9 | 159 | 21.2 | 188 | 25.0 | |
500 | 184 | 36.8 | 131 | 26.2 | 153 | 30.7 | |
400 | 165 | 41.2 | 118 | 29.5 | 137 | 34.3 | |
300 | 143 | 47.7 | 103 | 34.3 | 119 | 39.7 | |
200 | 117 | 58.6 | 85 | 42.4 | 97 | 48.6 | |
100 | 83 | 83.0 | 61 | 61.0 | 69 | 68.5 | |
| |
An example of the use of this table is as follows. If the estimate of the number of Australian resident departures for short-term visits abroad is 1,000, then the standard error on this estimate is 258 i.e. there are two chances in three that the actual number of Australian resident departures for short-term visits abroad will lie between 742 and 1,258 and nineteen chances in twenty that it will lie between 484 and 1,516.
The larger the size of an estimate the smaller the relative standard error. For any estimate of greater than 5,000,000 the relative standard error will be less than 0.3%.
The estimate of the difference between an estimate in two different periods or between different estimates from the same period is also subject to sampling error. The standard error on the difference between any two estimates which are subject to sampling error can be approximated by using the larger standard error of the estimates inflated by a factor of 1.4.
An example of the use of this procedure is as follows. Assume the estimates of the number of arrivals to Australia from Germany during February 2003 and February 2004 are 7,500 and 10,000 respectively. The difference between the 2003 and 2004 figure is 2,500 and the standard errors on these estimates are approximately 461 and 535. The standard error on the difference is approximately 749 (1.4 x 535), and there are nineteen chances in twenty that the estimate of the difference between the two years will lie between 1,002 and 3,998.
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