TECHNICAL NOTE DATA QUALITY


RELIABILITY OF THE ESTIMATES

1 Since the estimates in this publication are based on information obtained from a sample of persons, they are subject to sampling variability. That is, the estimates may differ from those that would have been produced had all persons been included in the survey.

2 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 (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all persons had been surveyed, and about 19 chances in 20 (95%) that the difference will be less than two SEs.

3 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.



4 RSEs for all estimates in this publication are available free-of-charge on the ABS website <www.abs.gov.au> in spreadsheet format as an attachment to the publication.

5 In the tables in this publication, only estimates (numbers or percentages) with RSEs less than 25% are considered sufficiently reliable for most analytical purposes. However, estimates with larger RSEs have been included. Those estimates with an RSE greater than 25% 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 greater than 50% are preceded by a double asterisk (e.g. **1.5) to indicate that they are considered too unreliable for general use.


CALCULATION OF STANDARD ERRORS

6 Standard errors can be calculated using the estimates (counts or percentages) and the corresponding RSEs. For example, Table 1.10 shows that the estimated number of persons who were victims of physical assault in the last 12 months was 509,500. The RSE table corresponding to the estimate in Table 1.10 (see Relative Standard Errors table at the end of this Technical Note) shows the RSE for this estimate is 4.9%. The SE is calculated by:



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 will fall within the range 484,500 to 534,500 and about 19 chances in 20 that the value will fall within the range 459,500 to 559,500. This example is illustrated in the diagram below:

PROPORTIONS AND PERCENTAGES

8 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 RSE of a proportion is given below. This formula is only valid when x is a subset of y:



9 As an example, using estimates from Table 1.10 45,900 persons were assaulted by a friend in the most recent incident of assault in the last 12 months, representing 16% of the 295,800 persons who knew the offender in the most recent incident of assault. From the RSE table at the end of this Technical Note, the RSE of the estimated number of persons who were assaulted by a friend in the most recent incident of assault is 15.1% and the RSE of the estimated number of persons who knew the offender in the most recent incident of assault is 6.3%. Applying the above formula, the RSE of the proportion is:



10 Therefore, the SE for persons who were assaulted by a friend in the most recent incident of assault, as a proportion of persons who knew their offender in the most recent incident of assault, is 2.2 percentage points (=16.0×(13.7/100)). Hence, there are about two chances in three that the proportion of persons who were assaulted by a friend in the most recent incident of assault in the last 12 months is between 13.8% and 18.2% and 19 chances in 20 that the proportion is within the range 11.6% to 20.4%.


DIFFERENCES

11 Published estimates may also be used to calculate the difference between two survey estimates (of counts or percentages). Such an estimate is subject to sampling error. 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:




SIGNIFICANCE TESTING

12 A statistical significance test for a comparison between estimates can be 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 11. This standard error is then used to calculate the following test statistic:



13 If the absolute value of this test statistic is greater than 1.96 then there is evidence, with a 95% level of confidence, of a statistically significant difference in the two estimates with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations with respect to that characteristic.

14 Tables which show rates from 2008-09 and 2009-10 have been tested to determine whether changes over time are statistically significant. Significant differences have been annotated. In all other tables which do not show the results of significance testing, users should take account of RSEs when comparing estimates for different populations.


NON-SAMPLING ERROR

15 The imprecision due to sampling variability discussed above, labelled sampling error, should not be confused with non-sampling error. Non-sampling error may occur in any collection, whether it is based on a sample or a full count such as a census. Sources of non-sampling error include non-response, errors in reporting by respondents or recording answers by interviewers and errors in coding and processing data. Every effort was made to reduce the non-sampling error by careful design and testing of the questionnaire, training and supervision of interviewers, and extensive editing and quality control procedures at all stages of data processing.


RELATIVE STANDARD ERRORS

16 Limited space does not allow the SEs and/or RSEs of all the estimates to be shown in this publication. Only RSEs for Table 1.10 are included on the following page as an example. However, RSEs for all tables are available free-of-charge on the ABS website <www.abs.gov.au>, available in spreadsheet format as an attachment to this publication.

Victims of physical assault, Characteristics of offender in most recent incident by sex - Relative Standard Errors
		Persons	RSE of persons
		'000	%
Sex of offender
	Male	407.3	6.0
	Female	67.5	11.4
	Some male, some female	32.9	14.7
	Sex unknown	**1.8	56.5
Relationship to offender(a)
	Current partner/previous partner	48.5	14.2
	Boyfriend/girlfriend/ex-boyfriend/ex-girlfriend or date	10.8	23.4
	Other family member(b)	45.1	12.4
	Friend	45.9	15.1
	Colleague/fellow school student/professional relationship	54.7	13.3
	Neighbour	16.5	17.6
	Known by sight only	47.8	14.3
	Other known person	30.7	18.6
	Total offenders known	295.8	6.3
	Stranger	213.7	6.3
Whether living with offender
	Living with offender	56.7	8.9
	Not living with offender	239.1	7.0
Total(c)		509.5	4.9
** estimate has a relative standard error greater than 50% and is considered too unreliable for general use
(a) More than one type of relationship to offender may have been specified so components may not add to total.
(b) Includes parent, child, sibling and other family members.
(c) Includes persons who did not give details of most recent incident.