TECHNICAL NOTE DATA QUALITY
INTRODUCTION
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 estimates that would have been produced if all occupants of all households 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 households (or occupants) 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 households 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 Environmental Issues: Waste Management and Transport Use, 2009 are published for the first time in 'direct' form. Previously a statistical model was produced that relates the size of estimates to their corresponding RSEs, and this information was displayed via an 'SE table'. RSEs for Environmental Issues: Waste Management and Transport Use, 2009 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 main estimate.
4 Limited publication space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication, only RSEs for Table 2.1 are included at the end of these Technical Notes (see Table 1 Relative Standard Errors in the section 'Relative Standard Error'). However, RSEs for all tables are available free-of-charge on the ABS website <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication Environmental Issues: Waste Management and Transport Use, 2009 (cat. no. 4602.0.55.002)
5 In the tables in this publication, only estimates (numbers and 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. *3.4) to indicate they are subject to high SEs 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 2.1 shows that the estimated number of households that recycle waste in Australia was 8,047,600. The RSE table corresponding to the estimates in Table 2.1 (see Relative Standard Errors in the 'Relative Standard Error' section at the end of these Technical Notes) shows the RSE for this estimate is 0.4%. The SE is calculated by:
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 will fall in the range 8,015,400 to 8,079,800 and about 19 chances in 20 that the value will fall within the range 7,983,200 to 8,112,000. This example is illustrated in the diagram below.
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 subject to such high RSEs that their value for most practical purposes is unreliable and should only be used to aggregate with other estimates to provide derived estimates with RSEs of less than 25%.
DIFFERENCES
9 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:
10 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
SIGNIFICANCE TESTING
11 A statistical significance test for 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 9. The standard error is then used to create the following test statistic:
12 If the value of this test statistic is greater than 1.96 then 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.
NON-SAMPLING ERROR
13 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.
RELATIVE STANDARD ERROR
14 Relative Standard Errors for Table 2.1 are included below. However, RSEs for all tables are available free-of-charge on the ABS website <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication.
Household waste recycling and reuse(a)(b), By selected characteristics |
|
 | | | | Households that recycle waste | Households that reuse waste(c) | Households that neither recycle nor reuse waste | Total households(d) |
|
| Estimate ('000) | | | | |
| Family type | | | | |
| | One family households | | | | |
| | | Couple family with dependent child(ren) | 2 169.4 | 1 951.7 | *5.5 | 2 191.4 |
| | | One parent family with dependent child(ren) | 508.2 | 452.9 | **3.7 | 517.4 |
| | | Couple only | 2 099.3 | 1 827.0 | *12.0 | 2 131.1 |
| | | Other one family households | 973.0 | 846.7 | *5.6 | 993.1 |
| | | Total one family households | 5 749.9 | 5 078.2 | 26.8 | 5 833.0 |
| | Multiple family households | | | | |
| | | Multiple family households with dependent child(ren) | 48.2 | 45.9 | - | 48.2 |
| | | Multiple family households with no dependent child(ren) | 80.4 | 73.8 | - | 81.9 |
| | | Total multiple family households | 128.6 | 119.7 | - | 130.1 |
| | Non-family households | | | | |
| | | Lone person | 1 854.2 | 1 585.5 | *26.0 | 1 927.7 |
| | | Group household | 269.3 | 240.2 | *7.6 | 284.6 |
| | | Total non-family households | 2 123.5 | 1 825.7 | 33.5 | 2 212.2 |
| | Could not be determined | 45.5 | 36.0 | - | 45.5 |
| Number of usual residents | | | | |
| | 1 resident | 1 884.6 | 1 613.8 | 28.3 | 1 960.4 |
| | 2 residents | 2 730.6 | 2 388.4 | 18.9 | 2 783.1 |
| | 3 residents | 1 307.6 | 1 149.0 | *6.4 | 1 329.9 |
| | 4 residents | 1 387.2 | 1 237.9 | np | 1 401.5 |
| | 5 residents | 486.0 | 443.4 | np | 491.6 |
| | 6 or more residents | 251.6 | 227.3 | - | 254.4 |
| Area of usual residence | | | | |
| | Metropolitan areas | 5 101.2 | 4 384.6 | 36.2 | 5 185.0 |
| | Ex-metropolitan areas | 2 946.4 | 2 675.1 | *24.1 | 3 035.9 |
| Remoteness index | | | | |
| | Major cities of Australia | 5 509.6 | 4 714.3 | 40.4 | 5 601.7 |
| | Inner regional Australia | 1 752.3 | 1 596.0 | *12.3 | 1 792.6 |
| | Outer regional Australia | 785.7 | 749.5 | *7.7 | 826.6 |
| | Remote Australia | - | - | - | - |
| Index of socio-economic advantage/disadvantage (SEIFA) | | | | |
| | First quintile | 1 338.6 | 1 155.5 | **16.8 | 1 384.2 |
| | Second quintile | 1 641.5 | 1 441.1 | *14.3 | 1 674.8 |
| | Third quintile | 1 654.4 | 1 445.9 | *11.5 | 1 692.0 |
| | Fourth quintile | 1 646.2 | 1 468.6 | *8.0 | 1 673.8 |
| | Fifth quintile | 1 700.5 | 1 486.4 | *8.7 | 1 725.4 |
| | Could not be determined | *66.4 | *62.2 | **1.1 | *70.7 |
| Total households | 8 047.6 | 7 059.8 | 60.4 | 8 220.9 |
| Proportion (%) | | | | |
| Family type | | | | |
| | One family households | | | | |
| | | Couple family with dependent child(ren) | 99.0 | 89.1 | *0.3 | 100.0 |
| | | One parent family with dependent child(ren) | 98.2 | 87.5 | **0.7 | 100.0 |
| | | Couple only | 98.5 | 85.7 | *0.6 | 100.0 |
| | | Other one family households | 98.0 | 85.3 | *0.6 | 100.0 |
| | | Total one family households | 98.6 | 87.1 | 0.5 | 100.0 |
| | Multiple family households | | | | |
| | | Multiple family households with dependent child(ren) | 100.0 | 95.2 | - | 100.0 |
| | | Multiple family households with no dependent child(ren) | 98.2 | 90.2 | - | 100.0 |
| | | Total multiple family households | 98.9 | 92.0 | - | 100.0 |
| | Non-family households | | | | |
| | | Lone person | 96.2 | 82.3 | *1.3 | 100.0 |
| | | Group household | 94.6 | 84.4 | *2.7 | 100.0 |
| | | Total non-family households | 96.0 | 82.5 | 1.5 | 100.0 |
| | Could not be determined | 100.0 | 79.1 | - | 100.0 |
| Number of usual residents | | | | |
| | 1 resident | 96.1 | 82.3 | 1.4 | 100.0 |
| | 2 residents | 98.1 | 85.8 | 0.7 | 100.0 |
| | 3 residents | 98.3 | 86.4 | *0.5 | 100.0 |
| | 4 residents | 99.0 | 88.3 | np | 100.0 |
| | 5 residents | 98.9 | 90.2 | np | 100.0 |
| | 6 or more residents | 98.9 | 89.4 | - | 100.0 |
| Area of usual residence | | | | |
| | Metropolitan areas | 98.4 | 84.6 | 0.7 | 100.0 |
| | Ex-metropolitan areas | 97.1 | 88.1 | *0.8 | 100.0 |
| Remoteness index | | | | |
| | Major cities of Australia | 98.4 | 84.2 | 0.7 | 100.0 |
| | Inner regional Australia | 97.8 | 89.0 | *0.7 | 100.0 |
| | Outer regional Australia | 95.1 | 90.7 | *0.9 | 100.0 |
| | Remote Australia | - | - | - | - |
| Index of socio-economic advantage/disadvantage (SEIFA) | | | | |
| | First quintile | 96.7 | 83.5 | *1.2 | 100.0 |
| | Second quintile | 98.0 | 86.0 | *0.9 | 100.0 |
| | Third quintile | 97.8 | 85.5 | *0.7 | 100.0 |
| | Fourth quintile | 98.4 | 87.7 | *0.5 | 100.0 |
| | Fifth quintile | 98.6 | 86.1 | *0.5 | 100.0 |
| | Could not be determined | 93.9 | 88.1 | **1.5 | 100.0 |
| Total households | 97.9 | 85.9 | 0.7 | 100.0 |
|
| * 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) During the 12 months prior to interview in March 2009. |
| (b) Respondents were asked about recycling and reuse of the waste items listed in table 2.4. |
| (c) Households that reused waste at home. Excludes the use of waste at home as compost or mulch which is included as recycling. |
| (d) May not add to sum of components as households may participate in both recycling and reuse. |
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