• Summary
• Downloads
• Explanatory Notes
• Related Information
• Past Releases

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 households, they are subject to sampling variability; that is, they may differ from those that would have been produced if all persons 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 because only a sample of persons was included. There are about two chances in three that a sample estimate will differ by less than one SE from the number that would have been obtained if all persons had been included, and about 19 chances in 20 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 Space does not allow for the separate indication of the SEs of all estimates in this publication. A table of SEs and RSEs for estimates of numbers of persons appears at the end of these Technical Notes. These figures will not give a precise measure of the SE for a particular estimate but will provide an indication of its magnitude.

3 The size of the SE increases with the level of the estimate, so that the larger the estimate the larger is the SE. However, the larger the sample estimate, the smaller the SE will be in percentage years (that is the RSE). This means larger estimates will be relatively more reliable than smaller estimates. In the tables in this publication, only estimates with RSEs of 25% or less, and percentages based on these estimates, are considered sufficiently reliable for most purposes. Estimates with RSEs of 25% to 50% are preceded by an asterisk (e.g. *2.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded with a double asterisk (e.g. **0.1); these estimates are considered too unreliable for general use.

4 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 reduce non-sampling error to a minimum by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.

CALCULATION OF STANDARD ERRORS

Standard errors of an estimate

5 An example of the calculation and the use of SEs in relation to estimates of persons is as follows:

6 From table 22 the estimate of the number of persons who experienced physical violence by their current partner since the age of 15 is 212,100. Since this estimate is between 200,000 and 300,000 in the SE table for person estimates, the SE for Australia will be between 17,350 and 20,950 and can be approximated by interpolation using the following general formula:

7 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 falls in the range of 194,300 to 229,900 and about nineteen chances in twenty that the value will fall within the range of 176,500 to 247,700.

Standard error of a proportion

9 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the relative standard error (RSE) of a proportion is given below.

Standard error of a difference

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

11 While this formula will only be exact for differences between separate and uncorrelated (unrelated) characteristics or sub-populations, it is expected to provide a good approximation for all differences likely to be of interest.

SIGNIFICANCE TESTING

12 Statistical significance testing has been undertaken for the comparison of estimates from the 1996 Women's Safety Survey and the 2005 PSS. 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 the paragraph above. This standard error is used to calculate the following test statistic:

13 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. Users should take account of RSEs when comparing estimates for different populations.

Standard Errors on Person Estimates
	Standard Error								Australia
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Standard error	Relative standard error
Size of estimate	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	220	190	170	80	120	90	150	110	140	140.0
200	350	310	280	160	200	160	220	180	250	125.0
300	460	400	380	230	270	220	280	240	340	113.3
500	640	570	540	350	400	320	380	330	490	98.0
700	780	710	670	460	520	420	470	420	620	88.6
1,000	980	890	850	610	670	550	580	530	800	80.0
1,500	1 250	1 150	1 100	830	890	740	740	700	1 050	70.0
2,000	1 480	1 380	1 320	1 030	1 090	910	880	850	1 270	63.5
2,500	1 700	1 600	1 500	1 200	1 250	1 050	1 000	1 000	1 450	58.0
3,000	1 900	1 750	1 700	1 400	1 450	1 200	1 150	1 100	1 650	55.0
3,500	2 050	1 950	1 850	1 550	1 600	1 350	1 250	1 250	1 850	52.9
4,000	2 250	2 100	2 000	1 700	1 750	1 450	1 350	1 350	2 000	50.0
5,000	2 550	2 400	2 300	1 950	2 000	1 700	1 550	1 550	2 300	46.0
7,000	3 100	2 900	2 800	2 450	2 500	2 150	1 950	1 950	2 850	40.7
10,000	3 750	3 600	3 450	3 100	3 100	2 750	2 400	2 500	3 500	35.0
15,000	4 700	4 500	4 350	4 000	3 950	3 550	3 100	3 300	4 450	29.7
20,000	5 500	5 300	5 100	4 750	4 700	4 250	3 750	4 000	5 250	26.3
30,000	6 850	6 600	6 400	5 950	5 950	5 450	4 900	5 250	6 600	22.0
40,000	8 000	7 750	7 450	7 000	7 000	6 500	5 900	6 350	7 700	19.3
50,000	9 000	8 700	8 350	7 850	7 900	7 400	6 800	7 350	8 700	17.4
100,000	12 850	12 450	11 900	11 150	11 450	11 050	10 750	11 750	12 400	12.4
150,000	15 800	15 250	14 500	13 500	14 050	13 850	14 100	15 400	15 150	10.1
200,000	18 200	17 600	16 600	15 350	16 200	16 200	17 100	18 700	17 350	8.7
300,000	22 200	21 400	20 100	18 200	19 650	20 100	. .	24 550	20 950	7.0
500,000	28 350	27 200	25 250	22 250	24 850	26 100	. .	. .	26 300	5.3
1,000,000	39 100	37 250	34 050	28 400	33 550	. .	. .	. .	35 150	3.5
2,000,000	53 350	50 300	45 150	35 200	44 350	. .	. .	. .	46 050	2.3
5,000,000	79 100	73 350	63 900	. .	. .	. .	. .	. .	63 900	1.3
10,000,000	. .	. .	. .	. .	. .	. .	. .	. .	79 900	0.8
. . not applicable

Person Estimates with Relative standard errors of 25% and 50%
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Aust.
Size of estimate	no.	no.	no.	no.	no.	no.	no.	no.	no.
Estimate with 25% RSE	24 795	22 776	21 096	17 419	17 218	12 800	9 081	9 963	22 362
Estimate with 50% RSE	5 181	4 501	4 117	2 242	2 599	1 403	1 454	1 194	3 971

Standard errors on Male estimates
	Standard error								Australia
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Standard error	Relative standard error
Size of estimate	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	340	470	290	80	200	70	170	80	130	130.0
200	500	620	430	150	330	150	260	150	230	115.0
300	620	750	550	220	440	220	330	220	330	110.0
500	820	940	740	360	630	360	450	360	500	100.0
700	990	1 090	900	480	790	490	570	480	660	94.3
1,000	1 200	1 290	1 100	660	1 010	680	720	670	870	87.0
1,500	1 500	1 570	1 400	950	1 330	990	950	960	1 180	78.7
2,000	1 750	1 810	1 660	1 210	1 610	1 280	1 160	1 230	1 450	72.5
2,500	2 000	2 050	1 900	1 450	1 850	1 550	1 350	1 500	1 700	68.0
3,000	2 200	2 200	2 100	1 700	2 100	1 800	1 550	1 750	1 950	65.0
3,500	2 400	2 400	2 300	1 950	2 350	2 100	1 750	2 000	2 150	61.4
4,000	2 550	2 550	2 500	2 150	2 550	2 350	1 900	2 200	2 350	58.8
5,000	2 900	2 900	2 850	2 600	3 000	2 800	2 250	2 650	2 750	55.0
7,000	3 500	3 450	3 450	3 400	3 700	3 750	2 900	3 500	3 450	49.3
10,000	4 250	4 150	4 300	4 550	4 700	5 000	3 800	4 700	4 350	43.5
15,000	5 350	5 200	5 450	6 200	6 100	6 950	5 200	6 450	5 600	37.3
20,000	6 250	6 100	6 450	7 700	7 350	8 700	6 550	8 050	6 650	33.3
30,000	7 850	7 700	8 200	10 450	9 550	11 900	9 050	10 950	8 400	28.0
40,000	9 250	9 050	9 700	12 900	11 500	14 800	11 450	13 550	9 900	24.8
50,000	10 450	10 350	11 050	15 100	13 250	17 500	13 800	15 950	11 150	22.3
100,000	15 450	15 600	16 700	24 500	20 500	28 850	24 800	26 050	16 000	16.0
150,000	19 400	20 000	21 250	32 200	26 400	38 250	35 250	34 450	19 500	13.0
200,000	22 850	23 900	25 200	38 850	31 500	46 550	45 450	41 750	22 300	11.2
300,000	28 750	30 900	32 050	50 450	40 450	60 950	65 350	54 500	26 750	8.9
500,000	38 400	42 900	43 450	69 250	55 150	84 650	104 300	. .	33 200	6.6
1,000,000	57 000	67 800	65 650	104 600	83 600	. .	. .	. .	43 400	4.3
2,000,000	84 800	108 600	99 250	154 700	125 950	. .	. .	. .	55 200	2.8
5,000,000	143 650	206 700	171 700	. .	. .	. .	. .	. .	72 700	1.5
10,000,000	. .	. .	. .	. .	. .	. .	. .	. .	86 650	0.9
. . not applicable

Male estimates with relative standard errors of 25% and 50%
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	Aust.
Size of estimate	no.	no.	no.	no.	no.	no.	no.	no.	no.
Estimate with 25% RSE	33 371	31 803	37 134	93 788	58 631	159 944	94 073	114 460	38 932
Estimate with 50% RSE	6 991	6 781	6 838	6 216	8 358	10 190	3 380	7 192	6 726

Standard errors on female estimates
	Standard error								Australia
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Standard error	Relative standard error
Size of estimate	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	150	120	120	100	110	100	180	110	150	150.0
200	260	220	220	180	200	170	250	180	250	125.0
300	360	310	300	250	270	230	300	230	330	110.0
500	520	450	440	370	390	330	390	320	470	94.0
700	650	580	570	480	500	410	460	400	590	84.3
1,000	840	760	740	620	640	520	550	490	740	74.0
1,500	1 100	1 000	980	810	840	670	680	620	960	64.0
2,000	1 320	1 220	1 190	980	1 000	790	790	730	1 140	57.0
2,500	1 500	1 400	1 350	1 150	1 150	900	900	800	1 300	52.0
3,000	1 700	1 600	1 550	1 250	1 300	1 000	1 000	900	1 450	48.3
3,500	1 900	1 750	1 700	1 400	1 400	1 100	1 050	1 000	1 600	45.7
4,000	2 050	1 900	1 850	1 500	1 500	1 150	1 150	1 050	1 750	43.8
5,000	2 350	2 200	2 100	1 700	1 700	1 300	1 300	1 200	2 000	40.0
7,000	2 850	2 650	2 550	2 050	2 050	1 550	1 600	1 400	2 400	34.3
10,000	3 500	3 300	3 100	2 450	2 500	1 850	1 950	1 650	2 950	29.5
15,000	4 350	4 100	3 850	2 950	3 050	2 200	2 450	1 950	3 750	25.0
20,000	5 050	4 750	4 450	3 350	3 450	2 500	2 900	2 250	4 350	21.8
30,000	6 250	5 850	5 350	3 950	4 150	2 950	3 700	2 650	5 450	18.2
40,000	7 200	6 700	6 100	4 350	4 650	3 300	4 400	2 950	6 300	15.8
50,000	8 000	7 400	6 750	4 750	5 100	3 600	5 050	3 200	7 100	14.2
100,000	11 000	10 000	8 850	5 850	6 550	4 550	7 750	4 050	10 050	10.1
150,000	13 100	11 750	10 250	6 500	7 450	5 150	10 050	4 650	12 250	8.2
200,000	14 750	13 100	11 250	6 950	8 150	5 600	12 100	5 050	14 050	7.0
300,000	17 350	15 100	12 750	7 500	9 100	6 250	15 800	5 650	16 900	5.6
500,000	20 950	17 800	14 650	8 150	10 250	7 000	22 200	. .	21 300	4.3
1,000,000	26 550	21 650	17 150	8 700	11 700	. .	. .	. .	28 650	2.9
2,000,000	32 800	25 500	19 400	8 900	12 950	. .	. .	. .	37 950	1.9
5,000,000	41 750	30 150	21 600	. .	. .	. .	. .	. .	53 750	1.1
10,000,000	. .	. .	. .	. .	. .	. .	. .	. .	68 650	0.7
. . not applicable

Female estimates with relative standard errors of 25% and 50%
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	Aust.
Size of estimate	no.	no.	no.	no.	no.	no.	no.	no.	no.
Estimate with 25% RSE	20 539	18 023	15 738	9 435	9 915	5 475	5 540	4 439	14 795
Estimate with 50% RSE	4 192	3 517	3 206	1 902	2 023	1 113	1 231	960	2 827