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3401.0 - Overseas Arrivals and Departures, Australia, May 2004  
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 13/07/2004   
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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 ERRORS ON ESTIMATES FOR STRATIFIED SAMPLE
SHORT-TERM
DEPARTURE OR ARRIVAL
OF AUSTRALIAN RESIDENTS
SHORT-TERM
ARRIVAL OR DEPARTURE
OF OVERSEAS VISITORS
TOTAL
ARRIVALS OR
DEPARTURES



Estimated
Relative
Relative
Relative
number of
Standard
standard
Standard
standard
Standard
standard
movements
error
error
error
error
error
error
no.
%
no.
%
no.
%

10,000
550
6
490
5
550
6
5,000
450
9
330
7
410
8
2,000
280
14
230
11
250
13
1,000
200
20
150
15
170
17
750
180
24
140
19
150
20
500
130
26
110
22
125
25
400
120
30
100
25
115
29
300
110
36
84
28
97
32
200
90
45
70
35
80
40
100
63
63
49
49
56
56



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 500, then the standard error on this estimate is 130 i.e. there are two chances in three that the actual number of Australian resident departures for short-term visits abroad will lie between 370 and 630 and nineteen chances in twenty that it will lie between 240 and 760.

The larger the size of an estimate the smaller the relative standard error. For any estimate of greater than 10,000 the relative standard error will be less than 6%.

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 Taiwan during January 2002 and January 2003 are 1,500 and 750 respectively. The difference between the 2002 and 2003 figures is 750 and the standard errors on these estimates are approximately 190 and 140. The standard error on the difference is approximately 266 (1.4 x 190), and there are nineteen chances in twenty that the estimate of the difference between the two years will lie between 218 and 1,282.

ESTIMATED NUMBER OF MOVEMENTS, GREATER THAN 10,000

Currently, standard errors are provided for estimates up to 10,000. The ABS is reviewing the Standard Error table with the view of providing standard errors for movements greater than 10,000. Standard errors should be considered when comparing movements in the levels of estimates for different time periods, or in comparing estimates of various characteristics.

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