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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:



3 RSEs for estimates from Housing Motivations and Intentions, Western Australia, October 2012 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 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 18 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% 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 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 18 shows that the estimated number of people who intend to move in 2-3 years time was 94,400. The RSE corresponding to this estimate (see the Relative Standard Error Table section at the end of this Technical Note) is 11.6%. The SE is calculated by:




7 Therefore, there are about two chances in three that the actual number of people who intend to move in 2-3 years time was in the range of 83,400 and 105,400 and about 19 chances in 20 that the value was in the range 72,400 and 116,400. This example is illustrated below.




PROPORTION 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:



9 As an example, using estimates from Table 18, of the 490,500 people who intend to move within the next three years, 19.3%, that is 94,400 people, intend to move in 2-3 years time. The RSE for 94,400 is 11.6% and the RSE for 490,500 is 3.5% (see the Relative Standard Error Table section at the end of this Technical Note). Applying the above formula, the approximate RSE for the proportion of people who intend to move in 2-3 years time is:




10 Therefore, the SE for the proportion of people who intend to move in 2-3 years time is 2.1 percentage points (= (11.1/100) x 19.3). Hence, there are about two chances in three that the proportion of people who intend to move in 2-3 years time is between 17.2% and 21.4% and 19 chances in 20 that the proportion is between 15.1% and 23.5%.


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 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 TABLE

15 The RSEs for Table 18 are included below:

Table 18 Future movers, Expected time before moving - By preferred location of future dwelling(a)

		Movers within WA(b)	Movers to interstate/over seas	Movers to an unknown location	Total
NUMBER ('000)
Expected time before moving
	Within 12 months	203.1	17.3	*6.1	226.5
	Within 2 years	108.0	14.3	*4.7	127.0
	Within 3 years	81.2	*9.0	**4.3	94.4
	Total future movers(c)	429.0	43.0	18.5	490.5
PROPORTION (%)
Expected time before moving
	Within 12 months	47.3	40.3	*32.9	46.2
	Within 2 years	25.2	33.2	*25.5	25.9
	Within 3 years	18.9	*21.0	**23.0	19.3
	Total future movers(c)	100.0	100.0	100.0	100.0
RSE OF NUMBER (%)
Expected time before moving
	Within 12 months	7.4	23.9	31.3	6.4
	Within 2 years	5.8	24.3	46.0	6.0
	Within 3 years	11.6	35.0	59.2	11.6
	Total future movers(c)	3.7	13.7	20.9	3.5
RSE OF PROPORTION (%)
Expected time before moving
	Within 12 months	5.4	19.6	25.3	4.9
	Within 2 years	6.0	23.3	44.5	5.3
	Within 3 years	11.4	30.1	52.8	11.2
	Total future movers(c)	0.0	0.0	0.0	0.0