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 (or 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 dwellings 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 count estimates from 2014 Environmental Issues: Energy 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 estimates obtained from these subsamples is used to estimate the sample variability surrounding the count estimate.

4 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 denominator. A formula to approximate the RSE of a proportion has been used:

5 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 6 have been included at the end of this Technical Note.

6 Only estimates (numbers and proportions) with RSEs less than 25% are considered sufficiently reliable for most purposes. Estimates with RSEs between 25% and 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

7 SEs can be calculated using the estimates (counts or proportions) and the corresponding RSEs. For example, Table 6 shows that the estimated number of households in Australia that have insulation in their dwelling was 6,142,200. The RSE table corresponding to the estimates in Table 6 (see the 'Relative Standard Error' section at the end of this Technical Note) shows the RSE for this estimate is 0.8%. The SE is calculated by:

8 Therefore, there are about two chances in three that the actual number of households that have insulation in their dwelling was in the range of 6,093,100 to 6,191,300 and about 19 chances in 20 that the value was in the range 6,044,000 to 6,240,400. This example is illustrated in the diagram below.




PROPORTIONS AND PERCENTAGES

9 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.



10 As an example, using estimates from Table 6, of the 9,013,900 households in Australia, 68.1%, that is 6,142,200 households have insulation in their dwelling. The RSE for 6,142,200 is 0.8% and the RSE for 9,013,900 is 0.4% (see 'Relative Standard Error' section at the end of this Technical Note). Applying the above formula, the approximate RSE for the proportion of households that have insulation in their dwelling is:



11 Therefore, the SE for the proportion of households that have insulation in their dwelling is 0.5 percentage points (= (0.7/100) x 68.1%). Hence, there are about two chances in three that the proportion of households that have insulation in their dwelling is between 67.6% and 68.6%, and 19 chance in 20 that the proportion is between 67.1% and 69.1%.


DIFFERENCES

12 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:



13 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

14 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 12. The standard error is then used to create the following test statistic:



15 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.


RELATIVE STANDARD ERROR

16 The estimates and RSEs for an excerpt of Table 6 are included below:

Table 6 INSULATION, Households
		NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Aust.
ESTIMATE('000)
Total of state/territory
	With insulation	1 776.2	1 681.4	1 095.8	536.7	727.5	167.2	34.4	122.9	6 142.2
	Without insulation	507.4	162.4	386.6	42.3	105.6	18.5	11.9	*8.3	1 243.3
	Did not know	560.9	406.4	339.7	109.8	136.0	23.5	21.8	19.8	1 622.5
	Total households	2 843.2	2 243.9	1 828.1	691.4	969.9	210.6	68.6	152.5	9 013.9
PROPORTION(%)
Total of state/territory
	With insulation	62.5	74.9	59.9	77.6	75.0	79.4	50.1	80.6	68.1
	Without insulation	17.8	7.2	21.1	6.1	10.9	8.8	17.4	*5.4	13.8
	Did not know	19.7	18.1	18.6	15.9	14.0	11.1	31.8	13.0	18.0
	Total households	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RSE OF ESTIMATE(%)
Total of state/territory
	With insulation	2.0	1.3	2.6	1.6	2.1	2.1	5.8	4.6	0.8
	Without insulation	4.8	7.5	6.9	13.5	11.6	11.4	13.4	30.6	2.9
	Did not know	4.7	4.8	5.3	7.3	8.2	10.3	6.5	17.7	2.4
	Total households	0.5	0.8	0.9	0.7	0.9	1.2	1.3	2.8	0.4
RSE OF PROPORTION(%)
Total of state/territory
	With insulation	2.0	1.0	2.5	1.4	1.9	1.7	5.7	3.6	0.7
	Without insulation	4.8	7.4	6.8	13.5	11.5	11.3	13.3	30.5	2.9
	Did not know	4.7	4.7	5.3	7.3	8.2	10.2	6.4	17.4	2.4
	Total households	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

Cells in this table have been randomly adjusted to avoid the release of confidential data. Discrepancies may occur between sums of the component items and totals.
* estimate has a relative standard error of 25% to 50% and should be used with caution