4530.0 - Crime Victimisation, Australia, 2008-09 Quality Declaration 
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 18/02/2010  First Issue
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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 occupants of 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.

2 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.

Equation: Formula for calculation of RSE from Standard Error.

3 In the tables in this publication, only estimates (numbers, percentages, counts or proportions) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *2.2) to indicate they are subject to high SEs relative to their estimate 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.

4 Limited publication space does not allow for the separate indication of SEs and/or RSEs of all the estimates in this publication, only those for Table 8 have been included at the end of this Technical Note. However, RSEs were calculated for each separate estimate and are available to download free-of-charge as Excel spreadsheets from the ABS website <www.abs.gov.au> as an attachment to this publication. The Jackknife method of variance estimation is used to calculate SEs, which involves the calculation of 30 replicate estimates based on 30 different sub samples of the original sample. The variability of estimates obtained from these sub samples is used to estimate the sample variability surrounding the main estimate.


CALCULATION OF STANDARD ERROR

Standard error of an estimate

5 Standard errors can be calculated using the estimate (numbers or percentages) and the corresponding RSEs. For example, Table 8 shows the estimated number of persons who were victims of physical assault in the last 12 months was 527,400. The RSE table corresponding to the estimate in Table 8 (see VICTIMS OF PHYSICAL ASSAULT, Characteristics of most recent incident - Relative Standard Errors at the end of this Technical Note) shows the RSE for this estimate is 3.8%. The SE is calculated by:

Equation: Formula for calculation of Standard Error using RSE.

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 507,400 to 547,400 and about 19 chances in 20 that the value will fall within the range 487,400 to 567,400. This example is illustrated in the diagram below:

Diagram: Standard error of an estimate


RSES OF COMPARATIVE ESTIMATES

Proportions and percentages

7 Proportions and percentages formed from the ratio of two estimates are also subject to sampling error. 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.

Equation: Formula for calculation of RSE of a proportion.

8 As an example, using estimates from Table 8, 55,500 persons were assaulted by a friend in the most recent incident of assault in the last 12 months, representing 16.9% of the 328,200 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 12.8%, and the RSE of the estimated number of persons who knew the offender in the most recent incident of assault is 4.6%. Applying the above formula, the RSE of the proportion is:

Equation: Example of calculation of RSE of a proportion.

9 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 2.0 percentage points (=16.9(11.9/100)). Therefore, there are about two chances in three that the proportion is between 14.9% and 18.9% and 19 chances in 20 that the proportion is within the range 12.9% to 20.9%.


Differences between estimates

10 The difference between two survey estimates (numbers or percentages) is itself an estimate and is therefore 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:

Equation: Formula for calculation of Standard Error of a difference.

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 The statistical significance test for any of the comparisons between estimates was performed to determine whether, with a certain level of confidence, there is evidence of a true 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 then used to to calculate the following test statistic:

Equation: Formula for calculation of test statistic.

13 If the value of the test statistic is greater than 1.96 then there is statistical evidence (with 95% confidence) of a 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.


NON-SAMPLING ERROR

14 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 occur in any enumeration, whether it be a full count or 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.


SAMPLE TABLE WITH RSES

VICTIMS OF PHYSICAL ASSAULT, Characteristics of most recent incident - Relative Standard Errors

Persons
RSE of persons
'000
%

Relationship to offender(a)
Offender known
Family member
Current partner, boyfriend, girlfriend or date
29.1
15.9
Parent
*7.6
33.3
Child
16.8
22.1
Sibling/other family member
24.3
22.0
Total family member
75.7
11.0
Non-family member
Previous partner/ex-boyfriend/ex-girlfriend
44.4
13.6
Friend
55.5
12.8
Colleague/fellow school student/professional relationship
58.4
17.2
Neighbour
22.3
16.5
Known by sight only
53.1
12.5
Other known person(b)
21.2
18.7
Total non-family member
252.5
5.2
Total offender known
328.2
4.6
Offender not known
199.3
5.6
Location of incident
Victim's home
154.8
7.9
Other person's home
46.8
17.6
Work/place of study
93.4
10.1
In the street or other open land
107.4
8.9
Place of entertainment/recreation
67.4
9.8
In a private or public vehicle
20.9
21.6
Shopping centre
*17.2
29.3
Other location
19.6
24.8
Whether weapon used
Weapon used
78.6
11.1
No weapon used
447.9
4.2
Experienced physical injury
Physically injured
242.8
5.5
Whether sought medical treatment
Medical treatment sought
104.3
8.0
Medical treatment not sought
138.5
6.2
Not physically injured
283.6
5.5
Reported incident to police
Told police
235.7
6.5
Did not tell police
291.0
6.2
Total(c)
527.4
3.8

* estimate has a relative standard error of 25% to 50% and should be used with caution
(a) More than one type of relationship to offender may have been specified so components may not add to total.
(b) Includes persons who did not give details of relationship to offender.
(c) Includes persons who did not give details of most recent incident.