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TECHNICAL NOTE DATA QUALITY


RELIABILITY OF ESTIMATES

1 Since the estimates in this publication are based on information obtained from occupants of a sample of dwellings, they are subject to sampling variability. That is, they may differ from those estimates that would have been produced if all dwellings had been included in the survey. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance due to only a sample of dwellings being included. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all dwellings had been included, and about 19 chances in 20 (95%) that the difference will be less than two SEs. Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate.

2 In general, the size of the SE increases as the size of the estimate increases. Conversely, the RSE decreases as the size of the estimate increases. Very small estimates are thus subject to such high RSEs that their value for most practical purposes is unreliable. In this publication, only estimates with RSEs of 25% or less are considered reliable for most purposes. Estimates with RSEs greater than 25% but less than or equal to 50% are preceded by an asterisk (e.g.*2.2) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs of greater than 50%, preceded by a double asterisk (e.g.**1.5), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of 25% or less.

3 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents and recording by interviewers, and errors made in coding and processing data. Inaccuracies of this kind are referred to as non-sampling error, and they may occur in any enumeration, whether it be a full count or a sample. Every effort is made to minimise non-sampling error by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.

4 Due to space limitations, it is impractical to print the SE of each estimate in this publication. A table of SEs and RSEs is provided at the end of this Technical Note to enable readers to determine the SE for an estimate from the size of that estimate. These figures will not give a precise measure of the SE for a particular estimate but will provide an indication of its magnitude.

CALCULATION OF STANDARD ERROR

Standard error of an estimate

5 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Consider the estimate for Australia of persons aged 25-34 years who have been a victim of assault within the last 12 months, which is 187,000. Since this estimate is between 100,000 and 200,000 in the SE table for person estimates, the SE for Australia will lie between 7,221 and 9,736 and can be approximated by interpolation using the following general formula:

6 Therefore, there are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall within the range 177,600 to 196,400 and about 19 chances in 20 that the value will fall within the range 168,200 to 205,800. This example is illustrated in the diagram below.

8 Considering the example above, the 187,000 persons aged 25-34 years who had been a victim of assault within the last 12 months represent 24.3% of the 770,600 persons who were victims of assault in the last 12 months. The SE of 770,600 may be calculated by interpolation as 16,400. To convert this to a RSE we express the SE as a percentage of the estimate, or 16,400/770,600=2.1%. The SE for 187,000 was calculated previously as 9,400 which converted to a RSE is 9,400/187,000=5.0%. Applying the above formula, the RSE of the proportion is

9 Therefore, the SE for the proportion of victims of assault aged 25-34 years in the last 12 months is 1.1 percentage points (=(24.3/100)×4.5). Therefore, there are about two chances in three that the proportion of victims of assault in the last 12 months who were persons aged 25-34 years is between 23.2% and 25.4% and 19 chances in 20 that the proportion is within the range 22.1% to 26.5%.

Differences between estimates

10 The difference between two survey estimates is itself an estimate and is therefore subject to sampling variability. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:

11 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.

STATISTICAL SIGNIFICANCE TESTING

12 Where differences between data items have been noted in the Summary of Findings, they are statistically significant unless otherwise specified. In this publication a statistically significant difference is one where there are 19 chances in 20 that the difference noted reflects a true difference between population groups of interest rather than being the result of sampling variability.

13 Statistical significance testing has also been undertaken for the comparison of estimates between 2005, 2002 and 1998, included in tables 1, 2, 6 and 15. The statistical significance test for these comparisons was performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 10. This standard error is used to calculate the following test statistic:

14 If the value of the test statistic is greater than 1.96 then we may say there is good evidence of a real difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations. Tables 1, 2, 6 and 15 are annotated to indicate whether the differences between estimates which have been compared are statistically significant. In other tables, which do not show the results of significance testing, users should take account of RSEs when comparing estimates for different populations.

T1 STANDARD ERROR OF ESTIMATES
	STANDARD ERROR									RELATIVE STANDARD ERROR
	NSW	VIC	QLD	SA	WA	TAS	NT	ACT	Aust.	Aust.
Size of estimate	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
500	505	536	469	385	361	265	312	247	440	92.2
600	567	588	520	429	402	292	347	272	492	84.9
700	624	636	567	470	441	317	379	294	540	79.1
800	678	680	611	507	476	339	408	315	585	74.4
900	729	721	653	543	510	361	435	334	628	70.4
1,000	777	760	692	576	542	380	459	353	668	67.0
1,100	823	796	729	608	572	399	482	369	707	64.1
1,200	867	831	764	638	601	416	504	386	744	61.6
1,300	910	865	798	667	629	433	524	401	779	59.3
1,400	951	897	831	694	655	449	543	415	814	57.2
1,500	990	928	862	721	681	464	561	429	847	55.4
1,600	1 029	957	893	746	706	478	578	442	879	53.7
1,700	1 066	986	922	771	729	492	595	455	910	52.2
1,800	1 102	1 014	950	795	753	505	610	468	940	50.8
1,900	1 137	1 040	978	818	775	518	625	479	970	49.5
2,000	1 171	1 067	1 005	840	797	531	639	491	999	48.3
2,100	1 205	1 092	1 031	862	818	543	653	502	1 027	47.2
2,200	1 237	1 117	1 056	883	839	554	666	513	1 054	46.2
2,300	1 269	1 141	1 081	904	859	565	679	523	1 081	45.2
2,400	1 300	1 164	1 105	924	879	576	691	533	1 107	44.3
2,500	1 330	1 187	1 129	943	898	587	703	543	1 133	43.4
3,000	1 474	1 295	1 240	1 035	989	636	757	589	1 255	39.7
3,500	1 606	1 393	1 341	1 117	1 071	680	803	630	1 366	36.8
4,000	1 728	1 484	1 434	1 193	1 147	720	844	667	1 470	34.5
4,500	1 842	1 568	1 521	1 262	1 218	756	880	701	1 567	32.6
5,000	1 949	1 647	1 603	1 327	1 284	790	912	732	1 659	30.9
6,000	2 148	1 792	1 753	1 445	1 405	850	968	788	1 830	28.2
8,000	2 495	2 044	2 015	1 647	1 616	950	1 055	883	2 131	24.4
10,000	2 796	2 262	2 239	1 817	1 796	1 033	1 120	961	2 393	21.8
20,000	3 926	3 080	3 076	2 420	2 459	1 313	1 303	1 232	3 397	15.3
30,000	4 741	3 673	3 676	2 826	2 926	1 492	1 389	1 407	4 141	12.4
40,000	5 395	4 154	4 157	3 137	3 295	1 624	1 436	1 539	4 749	10.6
50,000	5 950	4 565	4 563	3 390	3 604	1 729	1 465	1 645	5 273	9.4
100,000	7 950	6 082	6 031	4 239	4 693	2 061	1 503	1 988	7 221	6.5
200,000	10 399	8 029	7 840	5 157	5 980	2 389	1 461	2 343	9 736	4.4
300,000	12 048	9 404	9 069	5 711	6 823	2 571		2 550	11 513	3.5
400,000	13 315	10 501	10 022	6 105	7 458	2 693	. .	2 694	12 926	3.0
500,000	14 352	11 426	10 809	6 409	7 971	2 782	. .	. .	14 113	2.6
1,000,000	17 866	14 762	13 517	7 319	9 662	. .	. .	. .	18 356	1.7
2,000,000	21 770	18 897	16 625	8 133	11 461	. .	. .	. .	23 505	1.1
5,000,000	27 359	25 821	. .	. .	. .	. .	. .	. .	31 825	0.7
10,000,000	. .	. .	. .	. .	. .	. .	. .	. .	39 310	0.4
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	44 160	0.3
. . not applicable