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 shortterm and total movements.
APPROXIMATE STANDARD ERROR ON ESTIMATES FOR STRATIFIED SAMPLE 

 SHORTTERM ARRIVAL OR DEPARTURE OF AUSTRALIAN RESIDENT  SHORTTERM 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.  % 

5000000  11 302  0.2  7 934  0.2  9 705  0.2 
4000000  10 244  0.3  7 170  0.2  8 796  0.2 
3000000  9 021  0.3  6 292  0.2  7 746  0.3 
2000000  7 536  0.4  5 233  0.3  6 470  0.3 
1000000  5 530  0.6  3 815  0.4  4 745  0.5 
500000  4 047  0.8  2 778  0.6  3 469  0.7 
100000  1 941  1.9  1 325  1.3  1 658  1.7 
50000  1 408  2.8  962  1.9  1 201  2.4 
10000  662  6.6  455  4.6  561  5.6 
5000  476  9.5  329  6.6  402  8.0 
2000  307  15.3  214  10.7  258  12.9 
1000  219  21.9  154  15.4  184  18.4 
750  191  25.4  135  18.0  159  21.3 
500  156  31.3  111  22.3  130  26.1 
400  140  35.0  100  25.0  117  29.2 
300  122  40.5  87  29.1  101  33.7 
200  100  49.8  72  36.0  83  41.3 
100  71  70.6  52  51.8  58  58.3 

An example of the use of this table is as follows. If the estimate of the number of Australian resident departures for shortterm visits abroad is 1,000, then the standard error on this estimate is 219; i.e. there are approximately two chances in three that the actual number of Australian resident departures for shortterm visits abroad will lie between 781 and 1,219 and nineteen chances in twenty that it will lie between 562 and 1,438.
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 0.2%.
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 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 January 2004 and January 2005 are 7,500 and 10,000 respectively. The difference between the 2004 and 2005 figure is 2,500 and the standard errors on these estimates are approximately 392 and 455. The standard error on the estimate of the difference is approximately 637 (1.4 x 455); i.e. there are approximately two chances in three that the actual difference between the two years will lie between 1,863 and 3,137 and approximately nineteen chances in twenty that the actual difference between the two years will lie between 1,226 and 3,774. Care should be taken when using this interval to inform whether estimates are significantly different.
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