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:
3 RSEs for estimates from 2013 Environmental Issues: Water Use and Conservation have been calculated using the Jackknife method of variance estimation. This involves the calculation of 30 'replicate' estimates based on 30 different subsamples of the obtained sample. The variability of the estimates obtained from these subsamples is used to estimate the sampling variability of the estimate.
4 A Data Cube (spreadsheet) containing all tables produced for this publication and the calculated RSEs for each of the estimates is available from the Downloads tab of the publication. For illustrative purposes the RSEs for Table 1 have been included at the end of this Technical Note.
5 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 annotated to indicate they are subject to high sample variability and should be used with caution. In addition, estimates with RSEs greater than 50% have also been included and annotated to indicate they are considered too unreliable for general use. All cells in the Data Cube with RSEs greater than 25% contain a comment indicating the size of the RSE. These cells can be identified by a red indicator in the corner of the cell. The comment appears when the mouse pointer hovers over the cell.
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 8,294,200. The RSE table corresponding to the estimates in Table 1 (see the 'Relative Standard Error' section at the end of this Technical Note) shows the RSE for this estimate is 0.7%. The SE is calculated by:
7 Therefore, 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 8,236,100 to 8,352,300 and about 19 chances in 20 that the value was in the range 8,178,000 to 8,410,400. This example is illustrated in the diagram below.
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. The formula is only valid when the numerator is a subset of the denominator.
9 As an example, using estimates from Table 1, of the 8,890,300 households in Australia, 93.3%, that is 8,294,200 households, used mains or town water as a source of water. The RSE for 8,294,200 is 0.7% and the RSE for 8,890,300 is 0.3% (see Relative Standard Errors table in the 'Relative Standard Error' section at the end of this Technical Note). Applying the above formula, the approximate RSE for the proportion of households with mains or towns water as a source of water is:
10 Therefore, the SE for the proportion of households who used mains or town water as a source of water is 0.6 percentage points (= (0.6/100) x 93.3%). Hence, there are about two chances in three that the proportion of households who used mains or town water as a source of water is between 92.7% and 93.9%, and 19 chance in 20 that the proportion is between 92.1% and 94.5%.
DIFFERENCES
11 Published estimates may also be used to calculate the difference between two survey estimates (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:
12 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it provides a good approximation for the differences likely to be of interest in this publication.
SIGNIFICANCE TESTING
13 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 11. The standard error is then used to create the following test statistic:
14 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
15 The RSEs for the number and proportion estimates of Table 1 are included below.
Sources of water for households, All households - 2013 |
|
 | NSW | Vic. | Qld | SA | WA | Tas. | NT | ACT | Aust. |
Estimate ('000) |
|
| Mains/town water | 2 669.8 | 2 039.0 | 1 615.8 | 657.4 | 923.9 | 179.5 | 65.7 | 143.1 | 8 294.2 |
| Recycled or grey water | 696.6 | 760.8 | 507.5 | 229.5 | 285.4 | 55.8 | 13.2 | 35.4 | 2 584.3 |
| Rainwater tank(a) | 546.9 | 646.5 | 612.9 | 309.4 | 115.3 | 47.3 | *5.4 | 21.5 | 2 305.3 |
| Purchased bottled water | 536.1 | 439.5 | 257.4 | 120.5 | 205.1 | 25.2 | *4.0 | 12.1 | 1 600.0 |
| Bore/well | 85.0 | 49.2 | 149.9 | *13.9 | 188.1 | *6.3 | *4.8 | - | 497.2 |
| River/creek/dam | *54.2 | *46.9 | *27.7 | np | **7.7 | *8.8 | np | - | 148.5 |
| Rainwater collected in other container | 58.3 | 21.1 | *12.4 | np | *7.9 | *2.2 | - | np | 104.8 |
| Other(b) | *19.0 | *22.5 | *7.2 | np | *3.0 | *2.6 | np | - | 56.1 |
| Total households(c) | 2 827.7 | 2 194.4 | 1 809.1 | 679.4 | 955.6 | 211.0 | 69.9 | 143.1 | 8 890.3 |
Proportion (%) |
|
| Mains/town water | 94.4 | 92.9 | 89.3 | 96.8 | 96.7 | 85.1 | 94.0 | 100.0 | 93.3 |
| Recycled or grey water | 24.6 | 34.7 | 28.1 | 33.8 | 29.9 | 26.4 | 18.9 | 24.7 | 29.1 |
| Rainwater tank(a) | 19.3 | 29.5 | 33.9 | 45.5 | 12.1 | 22.4 | *7.8 | 15.0 | 25.9 |
| Purchased bottled water | 19.0 | 20.0 | 14.2 | 17.7 | 21.5 | 12.0 | *5.7 | 8.5 | 18.0 |
| Bore/well | 3.0 | 2.2 | 8.3 | *2.0 | 19.7 | *3.0 | *6.9 | - | 5.6 |
| River/creek/dam | *1.9 | *2.1 | *1.5 | np | **0.8 | *4.2 | np | - | 1.7 |
| Rainwater collected in other container | 2.1 | 1.0 | *0.7 | np | *0.8 | *1.0 | - | np | 1.2 |
| Other(b) | *0.7 | *1.0 | *0.4 | np | *0.3 | *1.2 | np | - | 0.6 |
RSE of Estimate (%) |
|
| Mains/town water | 1.4 | 1.4 | 1.9 | 1.3 | 1.9 | 4.0 | 3.6 | 1.3 | 0.7 |
| Recycled or grey water | 3.9 | 3.1 | 4.1 | 4.1 | 4.9 | 8.3 | 10.4 | 8.1 | 1.7 |
| Rainwater tank(a) | 8.6 | 3.4 | 6.6 | 3.3 | 15.2 | 15.1 | 29.9 | 14.0 | 2.9 |
| Purchased bottled water | 4.2 | 3.9 | 6.7 | 5.0 | 4.5 | 10.2 | 25.2 | 16.7 | 2.2 |
| Bore/well | 24.7 | 24.9 | 15.0 | 37.9 | 6.9 | 40.7 | 34.9 | - | 6.5 |
| River/creek/dam | 26.7 | 30.5 | 36.0 | np | 86.9 | 37.7 | np | - | 16.6 |
| Rainwater collected in other container | 9.3 | 23.5 | 33.8 | np | 27.0 | 30.6 | - | np | 9.0 |
| Other(b) | 25.7 | 30.1 | 47.6 | np | 42.1 | 34.9 | np | - | 14.7 |
| Total households(c) | 0.6 | 0.6 | 0.7 | 0.7 | 0.8 | 0.9 | 1.8 | 1.3 | 0.3 |
RSE of Proportion (%) |
|
| Mains/town water | 1.3 | 1.3 | 1.7 | 1.0 | 1.6 | 3.9 | 2.5 | - | 0.7 |
| Recycled or grey water | 3.9 | 3.1 | 4.0 | 4.2 | 4.9 | 8.2 | 10.5 | 7.8 | 1.8 |
| Rainwater tank(a) | 8.5 | 3.4 | 6.6 | 3.4 | 15.2 | 15.0 | 30.2 | 14.0 | 2.9 |
| Purchased bottled water | 4.2 | 3.9 | 6.5 | 4.9 | 4.5 | 10.1 | 25.6 | 17.1 | 2.2 |
| Bore/well | 24.7 | 24.8 | 14.9 | 38.0 | 6.8 | 40.7 | 35.3 | - | 6.5 |
| River/creek/dam | 26.6 | 30.4 | 35.9 | np | 86.9 | 37.7 | np | - | 16.6 |
| Rainwater collected in other container | 9.5 | 23.6 | 33.7 | np | 26.9 | 30.9 | - | np | 9.1 |
| Other(b) | 25.6 | 30.1 | 47.6 | np | 42.0 | 35.0 | np | - | 14.7 |
|
| * estimate has a relative standard error of 25% to 50% and should be used with caution |
| ** estimate has a relative standard error greater than 50% and is considered too unreliable for general use |
| - nil or rounded to zero (including null cells) |
| np not available for publication but included in totals where applicable, unless otherwise indicated |
| (a) Excludes households that have a rainwater tank installed at the dwelling but do not use the tank as a source of water. |
| (b) Other also includes spring and water delivered in a water cart/tanker. |
| (c) Totals do not equal the sum of items in each column as more than one source can be reported. |
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