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 2012 Environmental Issues: Waste Management, Transport and Motor Vehicle Usage 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 Three Data Cubes (spreadsheets) 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 2.4 have been included at the end of these Technical Notes.
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 Cubes 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 2.4 shows that the estimated number of people who used public transport for convenience, comfort and less stress was 1,178,900. The RSE table corresponding to the estimate in Table 2.4 (see the 'Relative Standard Error' section at the end of these Technical Notes) shows the RSE for this estimate is 3.5%. The SE is calculated by:
7 Therefore, there are about two chances in three that the actual number of people that used public transport for convenience, comfort and less stress was in the range of 1,137,600 to 1,220,200 and about 19 chances in 20 that the value was in the range 1,096,300 to 1,261,500. This example is illustrated in the diagram below.
PROPORTIONS AND PERCENTAGES
8 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 2.4, of the 1,718,800 people who travelled to work or fulltime study in Australia, 68.6%, that is 1,178,900 people used public transport for convenience, comfort and less stress. The RSE for 1,178,900 is 3.5% and the RSE for 1,718,800 is 2.7% (see Relative Standard Errors Table in the 'Relative Standard Error' section at the end of these Technical Notes). Applying the above formula, the approximate RSE for the proportion of people that used public transport for convenience, comfort and less stress is:
10 Therefore, the SE for the proportion of people who used public transport for convenience, comfort and less stress is 1.5 percentage points (= (2.2/100) x 68.6). Hence, there are about two chances in three that the proportion of people who used public transport for convenience, comfort and less stress is between 67.1% and 70.1%, and 19 chance in 20 that the proportion is between 65.6% and 71.6%.
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 (xy) may be calculated by the following formula:
12 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, 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 statistic is greater than 1.96 then there is evidence, with a 95% level of confidence, of a statistically significant 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 with respect to that characteristic.
RELATIVE STANDARD ERROR
15 The RSEs for Table 2.4 are included below:
REASONS FOR USING PUBLIC TRANSPORT ON USUAL TRIP TO WORK OR FULLTIME STUDY, Persons who used public transport(a) 

  NSW  Vic.  Qld  SA  WA  Tas.  NT  ACT  Aust. 

Estimate ('000)          
 Convenience/comfort/less stress  584.4  304.0  131.8  51.1  91.9  *6.2  **1.1  *8.5  1 178.9 
 Public transport services near to home  208.1  92.6  52.4  *13.1  29.3    **0.7  **1.4  397.5 
 Price/cost  160.9  117.2  51.3  31.5  51.8  *4.2  **0.6  *5.8  423.4 
 Parking concerns  98.9  99.7  *28.5  *11.0  26.5  **0.5    *4.4  269.6 
 Reduced travel time  155.3  84.4  *18.6  *11.9  28.7    **0.4    299.3 
 Other(b)  285.2  192.5  91.3  16.7  58.4  *7.1  **1.8  8.0  660.8 
 Total persons(c)  753.0  472.9  234.6  83.6  144.3  *13.2  **2.7  14.4  1 718.8 
Proportion (%)          
 Convenience/comfort/less stress  77.6  64.3  56.2  61.1  63.7  *46.7  *39.5  59.2  68.6 
 Public transport services near to home  27.6  19.6  22.3  *15.6  20.3    *27.0  *9.4  23.1 
 Price/cost  21.4  24.8  21.9  37.7  35.9  *32.2  **21.7  *39.9  24.6 
 Parking concerns  13.1  21.1  *12.2  *13.1  18.4  **3.8    *30.7  15.7 
 Reduced travel time  20.6  17.8  *7.9  *14.3  19.9    **13.5    17.4 
 Other(b)  37.9  40.7  38.9  19.9  40.5  *53.5  *65.7  55.1  38.4 
RSE of estimate (%)          
 Convenience/comfort/less stress  6.5  9.3  11.7  15.1  15.4  34.3  54.9  26.4  3.5 
 Public transport services near to home  12.3  21.0  22.1  30.9  21.1    69.5  53.7  7.9 
 Price/cost  13.7  14.2  19.1  17.1  18.5  34.9  76.0  32.9  7.0 
 Parking concerns  16.7  15.7  27.8  36.4  24.3  104.1    38.2  8.7 
 Reduced travel time  15.0  13.9  30.8  31.4  20.3    101.6    7.9 
 Other(b)  12.2  10.5  11.8  23.5  16.5  38.9  68.0  24.6  5.4 
 Total persons(c)  6.3  6.0  8.8  10.5  12.6  25.2  50.9  18.3  2.7 
RSE of proportion (%)          
 Convenience/comfort/less stress  2.9  5.8  7.6  9.6  10.0  28.5  32.4  17.6  2.3 
 Public transport services near to home  11.3  18.3  18.1  29.3  14.3    41.1  48.7  7.0 
 Price/cost  10.0  12.3  16.7  15.2  12.1  25.0  70.0  26.0  5.9 
 Parking concerns  15.6  14.9  26.0  35.7  22.8  104.9    32.0  7.7 
 Reduced travel time  10.8  13.2  30.8  28.4  17.2    123.4    6.8 
 Other(b)  8.4  7.5  10.6  20.4  11.5  29.1  42.2  19.3  4.2 

* 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) 
(a) Persons aged 18 years and over whose usual main form of travel to work or fulltime study was public transport (e.g. train, bus, tram or ferry). 
(b) Other reasons include 'Cannot drive/unlicensed', 'Other household member uses car', 'Frequency of service' and 'Environmental concerns'. 
(c) Totals do not equal the sum of items in each column as more than one reason may be specified. 
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