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Introduction


1 The estimates for New South Wales, Victoria, Queensland, South Australia and Australia are based on information gained from a sample of marriage registrations. As the whole population of New South Wales, Victoria, Queensland and South Australia are not surveyed, the estimates published for these states and Australia are subject to sampling error.


2 Sampling error occurs when only a sample of the entire population is surveyed. Sampling error is measured using the standard error, as this indicates how close the survey estimates are to the expected population values. There are approximately two chances in three that an estimate from a sample will differ by less than one standard error from the figure that would have been obtained if all marriage registrations had been included in the marriages collection, and approximately nineteen chances in twenty that the difference will be less than two standard errors.


Calculation of Standard Error


3 Due to space limitations, it is impractical to print the Standard Error (SE) of each estimate in the publication. Instead, a table of SEs is provided to enable readers to determine the SE for an estimate from the size of that estimate (see table T1). The SE table is derived from a mathematical model, referred to as the 'SE model'. It should be noted that the SE model only gives an approximate value for the SE for any particular estimate, since there is some minor variation between SEs for different estimates of the same size.


4 A table of SEs is provided to enable readers to calculate the standard error for an estimate from the size of that estimate (see Table T1). This table refers to population counts only.


5 Table 7 shows the estimated number of widows in Australia whose interval to remarriage in 2004 was 30 years or over was 47. As an example, Table 7 shows that there was an estimated 47 widows in Australia whose interval to remarriage in 2004 was 30 years or over. This estimate lies between 30 and 50 in Table T1. Therefore, the corresponding standard error will lie between 10 and 14, and can be interpolated using the following general formula:

SE of estimate




6 There are approximately two chances in three that the figure that would have been obtained if all marriage registrations had been included in the collection will fall in the range 34 to 60 (i.e. 47 + or - 13). There are approximately 19 chances in 20 that the value will fall within the range 21 to 73.


7 Generally, the size of the standard error increases as the size of the estimate increases. In contrast, the Relative Standard Error (RSE) decreases as the size of the estimate increases. The RSE is the standard error expressed as a percentage of the estimate. Small estimates are therefore subject to high RSEs such that their value is unreliable. In the tables in this publication, only estimates with RSEs of 25% or less are considered reliable for most purposes. Estimates of RSEs greater than 25% but less than or equal to 50% are preceded with an annotation that contains an asterisk (e.g. *17) to indicate they should be used with caution. Estimates with RSEs of greater than 50%, preceded by an annotation that contains a double asterisk (e.g. **9) are considered too unreliable for general use and should be aggregated with other estimates to provide derivations with RSEs of less than 25%.


Proportions and Percentages


8 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The formula to approximate the RSE of a proportion is only valid when x is a subset of y.




9 Following the previous example, the 47 widows whose interval to remarriage was 30 years or over represented 2.1% of the 2,290 widows who remarried in 2004. The standard error of 2,290 using the interpolation method is 97. To convert to a RSE, the SE is expressed as percentage of the estimate, or 97/2,290 = 4.2%. The conversion of the SE of 13 for the 47 estimate to a RSE is 13/47 = 27.7%.

The RSE of the proportion is




10 The SE for the proportion of widows whose interval to remarriage in 2004 was 30 years or over is 0.6 percentage points ((2.1/100) x 27.4). So, there are approximately two chances in three that the proportion of widows whose interval to remarriage was 30 years or more is between 1.5% and 2.7%. There are 19 chances out of 20 that the proportion lies between 0.9% and 3.3%.

Medians


11 This publication also contains estimates of median age and duration of residence. The tables provided in this technical note are not suitable for use with these estimates. The SE of each median age and duration of residence estimate provided in this publication has been calculated separately and the appropriate asterisk or double asterisk attached to estimates with RSEs greater than 25% and 50% respectively to provide an indication of reliability.


Standard Errors


T1 Standard Errors of Estimates

Size of Estimate									Australia...........
	NSW	Vic	Qld	SA	WA	Tas	NT	ACT	SE	RSE
	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
10	4	4	4	3	0	0	0	0	5	50.2
20	7	7	7	6	0	0	0	0	8	38.9
30	10	9	9	7	0	0	0	0	10	33.3
50	14	12	12	10	0	0	0	0	14	27.0
70	17	16	16	12	0	0	0	0	16	23.5
100	22	19	20	15	0	0	0	0	20	20.1
150	29	25	25	18	0	0	0	0	25	16.8
200	34	29	29	21	0	0	0	0	29	14.7
250	39	33	33	23	0	0	0	0	33	13.2
300	43	36	37	25	0	0	0	0	36	12.1
350	47	39	40	27	0	0	0	0	39	11.3
400	51	42	42	29	0	0	0	0	42	10.5
500	57	47	47	32	0	0	0	0	47	9.4
700	68	55	56	36	0	0	0	0	56	8.0
1,000	81	65	65	41	0	0	0	0	66	6.6
1,500	97	77	77	47	0	0	..	0	80	5.3
2,000	110	86	86	51	0	0	..	0	91	4.6
3,000	130	100	100	60	0	0	..	..	110	3.6
4,000	140	110	110	60	0	..	..	..	120	3.1
5,000	160	120	120	60	0	..	..	..	140	2.7
10,000	200	150	140	70	0	..	..	..	180	1.8
15,000	220	160	160	..	0	..	..	..	210	1.4
20,000	240	170	170	..	..	..	..	..	230	1.2
30,000	260	180	180	..	..	..	..	..	270	0.9
50,000	290	..	..	..	..	..	..	..	320	0.6
100,000	..	..	..	..	..	..	..	..	400	0.4
200,000	..	..	..	..	..	..	..	..	490	0.2

	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	Aust.
Percentage	no.	no.	no.	no.	no.	no.	no.	no.	no.
RSE of 25%	69	50	50	28	..	..	..	..	60
RSE of 50%	..	2	..	2	..	..	..	..	10