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4906.0 - Personal Safety, Australia, 2005 (Reissue)  
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 21/08/2006  Reissue
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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 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:


Equation: SE Calculations


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.

Diagram: Standard errors of an estimate


8 The smaller the estimate the higher is the relative standard error. Very small estimates are thus subject to such high standard errors (relative to the size of the estimate) as to detract seriously from their value for most reasonable uses.


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.


Equation: RSE equation 2


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.


Equation: SE equation


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:


Equation: sig test


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


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