4602.0.55.003 - Environmental Issues: Water use and Conservation, Mar 2010 Quality Declaration 
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 19/11/2010  First Issue
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TECHNICAL NOTE DATA QUALITY


RELIABILITY OF THE ESTIMATES

1 Since the estimates in this publication are based on information obtained from a sample, 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 (or households) 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 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: RSEpercentequalsSEoverestimatetimes100

3 RSEs for estimates from 2010 Environmental Issues: Water Use and Conservation are published in 'direct' form. Previously a statistical model was produced and the information was displayed via a 'SE table'. RSEs for Environmental Issues: Water use and Conservation have been calculated for each separate estimate and published individually. The Jackknife method of variance estimation is used for this process, which involves the calculation of 30 'replicate' estimates based on 30 different subsamples of the original sample. The variability of estimates obtained from these subsamples is used to estimate the sample variability surrounding the estimate.

4 RSE tables are included in the Data Cube (spreadsheet format) available free-of-charge on the ABS web site <www.abs.gov.au>. For illustrative purposes the RSEs for Table 1 have been included at the end of these Technical Notes.

5 In this publication, only estimates (numbers and proportions) with RSEs less than 25% are considered sufficiently reliable for most purposes. Estimates with RSEs between 25% to 50% have been included and are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high sample variability and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (e.g. **2.1) to indicate that they are considered too unreliable for general use.


CALCULATION OF STANDARD ERROR

6 SEs can be calculated using the estimates (counts or proportions) and the corresponding RSEs. For example, Table 1 shows that the estimated number of households in Australia that have mains or town water as a source of water was 7,922,900. The RSE table corresponding to the estimates in Table 1 (see Relative Standard Errors in the 'Relative Standard Error' section at the end of these Technical Notes) shows the RSE for this estimate is 0.8%. The SE is calculated by:

Equation: SE_of_estimate_(rse100estimate) - 2

7 There are about two chances in three that the actual number of households using mains or town water as a source of water was in the range of 7,859,500 to 7,986,300 and about 19 chances in 20 that the value was in the range 7,796,100 to 8,049,700. This example is illustrated in the diagram below.

Diagram: CALCULATION OF STANDARD ERROR


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. The formula is only valid when the numerator is a subset of the denominator.

Equation: RSE_x_over_y

9 As an example, using estimates from Table 1, of the 8,498,300 households in Australia, 93%, that is 7,922,900 households, used mains or town water as a source of water. The RSE for 7,922,900 is 0.8% and the RSE for 8,498,300 is 0.3% (see Relative Standard Errors Table in the 'Relative Standard Error' section at the end of these Technical Notes). Applying the above formula, the RSE for the proportion of households with mains or towns water as a source of water is:

Equation: RSE_x_over_y2


DIFFERENCES

10 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or proportions). Such an estimate is also 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: SE_x_minus_y

11 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it provides a good approximation for all differences likely to be of interest in this publication.


SIGNIFICANCE TESTING

12 A statistical significance test for any comparisons between estimates can be performed to determine whether it is likely that there is a difference between two 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. The standard error is then used to create the following test statistic:

Equation: test_statistic -2

13 If the value of this test statistics is greater than 1.96 then there are 19 chances in 20 that there is a difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a difference between the populations.


RELATIVE STANDARD ERROR

14 Relative Standard Errors for the number and proportion estimates of Table 1 are included below.

Sources of water for households, Relative standard errors - 2010
NSW
Vic.
Qld
SA
WA
Tas.
NT(a)
ACT(a)
Aust.
RSE of Number (%)
Capital city
Mains/town water
1.0
0.7
1.7
1.0
1.6
3.9
-
-
0.6
Rainwater tank(b)
8.9
5.9
6.2
5.0
13.0
36.9
-
-
2.8
Purchased bottled water
4.5
7.3
7.4
6.5
7.4
16.1
-
-
3.2
Bore/Well
22.5
36.6
33.3
41.5
9.0
73.9
-
-
7.9
River/creek/dam
72.9
41.4
35.7
np
np
71.8
-
-
35.4
Rainwater collected in other container
15.0
12.0
47.3
np
np
-
-
-
10.4
Grey water
5.7
3.5
7.1
4.4
8.0
23.6
-
-
2.5
Other(c)
47.0
48.9
-
np
np
-
-
-
33.6
Total households
0.6
0.7
1.0
0.8
1.1
1.3
-
-
0.4
Balance of state/territory
Mains/town water
3.3
5.6
3.9
9.9
6.6
6.9
-
-
2.2
Rainwater tank(b)
8.6
8.8
10.4
4.4
16.0
13.9
-
-
5.1
Purchased bottled water
5.8
7.0
6.6
19.0
14.5
10.3
-
-
2.8
Bore/Well
23.6
28.7
20.2
46.7
24.3
25.0
-
-
12.8
River/creek/dam
21.7
39.1
28.4
np
np
26.8
-
-
14.8
Rainwater collected in other container
24.4
29.0
28.5
np
np
32.3
-
-
14.3
Grey water
7.4
4.6
9.8
8.5
11.0
10.2
-
-
3.2
Other(c)
32.6
31.6
36.8
np
np
39.2
-
-
21.2
Total households
1.0
1.2
0.7
1.3
1.5
1.1
-
-
0.5
Total state/territory
Mains/town water
1.4
1.5
2.3
2.1
2.0
4.0
3.6
1.6
0.8
Rainwater tank(b)
7.4
4.8
7.3
3.6
10.3
13.0
28.5
13.1
3.1
Purchased bottled water
3.3
5.3
5.1
6.5
6.3
9.4
20.4
14.2
2.1
Bore/Well
20.1
23.6
19.5
37.1
8.6
23.4
np
np
7.5
River/creek/dam
22.0
34.8
22.8
32.8
40.5
24.9
78.6
-
13.6
Rainwater collected in other container
12.7
11.3
30.0
33.1
46.0
32.3
61.7
24.6
9.0
Grey water
4.3
3.1
6.5
4.3
5.4
10.1
20.8
8.0
2.1
Other(c)
28.4
28.4
36.8
36.1
54.3
39.2
np
np
18.5
Total households
0.6
0.6
0.6
0.7
0.9
1.0
1.4
1.6
0.3
RSE of Proportion (%)
Capital city
Mains/town water
0.8
0.4
1.4
0.4
1.1
3.4
-
-
0.4
Rainwater tank(b)
8.8
5.8
6.3
5.4
12.8
37.0
-
-
2.8
Purchased bottled water
4.7
7.1
7.4
6.4
7.3
16.2
-
-
3.2
Bore/Well
22.5
36.5
33.4
41.5
8.9
73.9
-
-
7.9
River/creek/dam
72.9
41.5
35.9
np
np
71.8
-
-
35.4
Rainwater collected in other container
15.0
12.0
47.4
np
np
-
-
-
10.5
Grey water
5.5
3.4
7.3
4.4
7.8
23.8
-
-
2.5
Other(c)
47.0
48.9
-
np
np
-
-
-
33.5
Balance of state/territory
Mains/town water
2.9
5.4
3.8
9.7
6.9
6.8
-
-
2.1
Rainwater tank(b)
8.7
8.9
10.5
4.0
15.4
13.9
-
-
5.1
Purchased bottled water
5.7
6.5
6.5
18.7
14.2
10.6
-
-
2.7
Bore/Well
23.8
28.9
20.3
46.5
24.2
24.9
-
-
12.7
River/creek/dam
21.7
39.2
28.4
np
np
26.8
-
-
14.9
Rainwater collected in other container
24.6
29.1
28.2
np
np
32.4
-
-
14.4
Grey water
7.5
4.6
9.9
8.6
10.8
10.0
-
-
3.3
Other(c)
32.5
31.6
37.0
np
np
39.5
-
-
21.3
Total state/territory
Mains/town water
1.3
1.3
2.1
2.0
1.8
3.8
3.5
-
0.7
Rainwater tank(b)
7.3
4.8
7.4
3.6
10.2
13.0
28.1
12.9
3.0
Purchased bottled water
3.4
5.2
5.0
6.4
6.4
9.6
20.8
14.2
2.1
Bore/Well
20.2
23.7
19.5
37.0
8.7
23.1
np
np
7.5
River/creek/dam
21.9
34.9
22.9
32.8
40.5
24.9
78.6
-
13.7
Rainwater collected in other container
12.8
11.3
29.8
33.1
46.1
32.4
61.5
24.8
9.0
Grey water
4.3
3.0
6.7
4.1
5.4
10.0
20.3
7.6
2.1
Other(c)
28.3
28.5
37.0
36.0
54.3
39.4
np
np
18.5
- nil or rounded to zero (including null cells)
np not available for publication but included in totals where applicable, unless otherwise indicated
(a) No regional split between capital city and balance of state/territory for NT and ACT as the sample does not support any breakdown beyond the whole territory.
(b) Excludes households that have a rainwater tank installed at the dwelling but do not use the tank as a source of water.
(c) Other includes spring and water delivered in a tanker.