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4602.0 - Environmental Issues: People's Views and Practices, Mar 2004  
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 24/11/2004   
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INTRODUCTION

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 because only a sample of dwellings was included. There are about 2 chances in 3 (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 Due to space limitations, it is impractical to print the SE of each estimate in the publication. Instead, tables of SEs are provided to enable readers to determine the SE for an estimate from the size of that estimate (see tables T1 and T2). Each SE table is derived from a mathematical model, referred to as the "SE model", which is created using the data collected in this survey. It should be noted that the SE model only gives an approximate value for the SE for any particular estimate, since there is some minor variation between SEs for different estimates of the same size.

3 This publication contains estimates for persons and households. Table T1 gives SEs for estimates of households, while SEs for estimates of persons are presented in T2. Tables containing estimates of households are found in Chapters 3 and 4, while Chapters 2 and 5 contains estimates of persons.

CALCULATION OF STANDARD ERROR

4 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Table 2.15 shows that the estimated number of persons in Australia who used signed petition as a means of registering an environmental concern was 390,700. Since this estimate is between 300,000 and 500,000, table T2 shows that the SE for Australia will lie between 18,550 and 23,550 and can be approximated by interpolation using the following general formula:
Equation: SE formula rev
5 Therefore, there are about 2 chances in 3 that the value that would have been produced if all persons had been included in the survey will fall within the range 369,900 to 411,500 and about 19 chances in 20 that the value will fall within the range 349,100 to 432,300. This example is illustrated in the diagram below.

Diagram: Published Estimate


6 Similarly, SEs are calculated for household level estimates using table T1 instead of table T2. For example, table 3.23 shows that the estimated number of households in Victoria who have mains/town water as main source of water for gardening was 1,180,500. This estimate is between 1,000,000 and 2,000,000, so the SE for this estimate will be between 16,800 and 18,100, and can be approximated using the same interpolation formula as above, with the resulting SE being 17,000 (rounded to the nearest 100).

7 Therefore, there are about 2 chances in 3 that the value that would have been produced if all households in the population had been included in the survey will fall within the range 1,163,500 to 1,197,500 and about 19 chances in 20 that the value will fall within the range 1,146,500 to 1,214,500.

8 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 so that their value for most practical purposes is unreliable. In the tables in this publication, only estimates with RSEs of 25% or less are considered reliable for most purposes. Estimates with RSEs greater than 25% are preceded by an asterisk (e.g. *1.8) to indicate they are subject to high SEs and should be used with caution.

PROPORTIONS AND PERCENTAGES

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

10 For example, in table 2.15, the estimate for the total number of persons aged 18 years and over, who registered an environmental concern in Australia was 1,090,800. The estimated number of persons who used signed petition as a means of registering that concern was 390,700, so the proportion of persons in Australia who registered an environmental concern by signed petition is 390,700/1,090,800 or 35.8%. The SE of the total number of persons in Australia registering an environmental concern may be calculated by interpolation as 33,026 or 33,000 rounded to the nearest 100. To convert this to a RSE we express the SE as a percentage of the estimate, or 33,000/1,090,800 = 3.1%. The SE for the number of persons in Australia who registerd environmental concerns by signed petition was calculated above as 20,800, which converted to a RSE is 20,800/ 390,700 = 5.3%. Applying the above formula, the RSE of the proportion is Equation: RSE example ; giving a SE for the proportion (35.8%) of 1.5 percentage points (=35.8**0.043).

11 Therefore, there are about 2 chances in 3 that the proportion of persons in Australia who registered an environmental concern by means of signed petition is between 34.3% and 37.3% and 19 chances in 20 that the proportion is within the range 32.8% to 38.8%.

12 Similarly, SEs can be calculated for household level estimates using the same formula.

DIFFERENCES

13 Published estimates may also be used to calculate the difference between two survey estimates (of numbers 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:
Equation: Differences formula


14 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.

NON-SAMPLING ERROR

15 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfect reporting by respondents, errors made in collection such as in recording and coding data, and errors made in processing the 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. It is not possible to quantify non-sampling error, but every effort is made to reduce it to a minimum. This is done by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.

T1 STANDARD ERRORS FOR HOUSEHOLD LEVEL ESTIMATES

NSW
Vic.
Qld.
SA
WA
Tas.
NT
ACT
Aust.
Size of estimate
no.
no.
no.
no.
no.
no.
no.
no.
no.

100
90
50
100
90
130
60
90
70
100
200
180
100
170
170
210
110
160
140
170
300
250
150
240
230
270
160
220
190
220
500
380
250
360
330
380
240
310
280
320
700
500
340
460
420
480
310
390
350
400
1,000
650
470
590
540
590
410
490
450
500
1,500
880
670
790
700
760
540
630
570
650
2,000
1,080
850
950
840
900
650
740
680
770
2,500
1,250
1,000
1,100
950
1,000
750
850
750
900
3,000
1,450
1,150
1,250
1,050
1,150
850
900
850
1,000
3,500
1,600
1,300
1,350
1,150
1,250
900
1,000
900
1,100
4,000
1,750
1,450
1,500
1,250
1,350
1,000
1,050
1,000
1,200
5,000
2,000
1,700
1,700
1,450
1,500
1,100
1,200
1,100
1,350
7,000
2,500
2,150
2,100
1,700
1,800
1,300
1,400
1,250
1,650
10,000
3,100
2,750
2,550
2,050
2,150
1,550
1,650
1,450
2,000
15,000
3,900
3,500
3,200
2,500
2,650
1,850
1,900
1,700
2,500
20,000
4,550
4,150
3,700
2,850
3,000
2,050
2,150
1,850
2,950
30,000
5,650
5,200
4,500
3,400
3,600
2,350
2,450
2,050
3,650
40,000
6,550
6,000
5,200
3,800
4,100
2,550
2,650
2,200
4,250
50,000
7,300
6,700
5,750
4,150
4,550
2,750
2,850
2,300
4,750
100,000
9,950
9,000
7,750
5,300
6,000
3,150
3,400
2,600
6,700
150,000
11,800
10,500
9,050
6,000
7,000
3,350
3,700
2,700
8,150
200,000
13,150
11,550
10,100
6,500
7,750
3,450
3,850
2,700
9,300
300,000
15,250
13,000
11,600
7,200
8,900
3,550
-
2,750
11,200
500,000
18,100
14,750
13,650
8,050
10,500
3,550
-
-
14,000
1,000,000
22,050
16,800
16,550
9,100
12,850
-
-
-
18,650
2,000,000
26,050
18,100
19,400
9,950
15,350
-
-
-
24,500
5,000,000
30,750
18,500
22,850
-
-
-
-
-
34,200
10,000,000
-
-
-
-
-
-
-
-
43,150

- nil or rounded to zero (including null cells)
T2 STANDARD ERRORS FOR PERSON LEVEL ESTIMATES

NSW
Vic.
Qld.
SA
WA
Tas.
NT
ACT
Aust.
Size of estimate
no.
no.
no.
no.
no.
no.
no.
no.
no.

100
260
240
210
160
130
110
110
160
120
200
400
370
340
260
230
190
220
250
200
300
520
480
440
350
310
260
320
310
270
500
720
670
600
490
450
370
480
420
400
700
880
820
740
600
570
470
620
500
510
1,000
1,090
1,010
910
750
730
590
790
610
650
1,500
1,390
1,290
1,160
960
960
760
1,020
760
860
2,000
1,640
1,520
1,370
1,140
1,150
910
1,210
890
1,050
2,500
1,850
1,700
1,550
1,300
1,350
1,050
1,350
1,000
1,200
3,000
2,050
1,900
1,700
1,450
1,500
1,150
1,500
1,100
1,350
3,500
2,250
2,100
1,850
1,550
1,650
1,250
1,600
1,200
1,500
4,000
2,450
2,250
2,000
1,650
1,750
1,350
1,700
1,250
1,650
5,000
2,750
2,550
2,250
1,900
2,000
1,500
1,850
1,400
1,900
7,000
3,350
3,050
2,700
2,250
2,450
1,800
2,100
1,650
2,350
10,000
4,050
3,650
3,300
2,700
2,950
2,100
2,400
2,000
2,950
15,000
5,000
4,550
4,050
3,250
3,650
2,550
2,650
2,400
3,750
20,000
5,800
5,250
4,700
3,700
4,250
2,900
2,800
2,750
4,450
30,000
7,150
6,400
5,700
4,450
5,150
3,400
3,000
3,300
5,600
40,000
8,250
7,400
6,550
5,000
5,900
3,800
3,050
3,800
6,550
50,000
9,200
8,200
7,300
5,500
6,500
4,100
3,100
4,150
7,400
100,000
12,850
11,350
10,000
7,150
8,700
5,100
3,050
5,600
10,750
150,000
15,500
13,600
12,000
8,250
10,150
5,750
2,900
6,650
13,200
200,000
17,700
15,450
13,550
9,100
11,300
6,200
2,800
7,450
15,250
300,000
21,200
18,350
16,050
10,350
12,950
6,800
-
8,750
18,550
500,000
26,450
22,650
19,750
12,000
15,250
7,500
-
-
23,550
1,000,000
35,300
29,850
25,850
14,350
18,500
-
-
-
32,050
2,000,000
46,450
38,650
33,250
16,750
21,800
-
-
-
42,800
5,000,000
65,500
53,300
45,400
-
-
-
-
-
60,950
10,000,000
-
-
-
-
-
-
-
-
77,950

- nil or rounded to zero (including null cells)


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