Australian Bureau of Statistics
Celebrating the International Year of Statistics 2013

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.	%
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 short-term visits abroad is 1,000, then the standard error on this estimate is 219; i.e. there are two chances in three that the actual number of Australian resident departures for short-term 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 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 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 difference is approximately 637 (1.4 x 455), and there are nineteen chances in twenty that the estimate of the difference between the two years will lie between 1,226 and 3,774.