4602.0.00.002 - Community Engagement with Nature Conservation, Australia , 2011-12 Quality Declaration 
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 26/03/2013  First Issue
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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:

Image: Relative standard error equals standard error over estimate times 100

3 RSEs for estimates from Community Engagement with Nature Conservation, Australia, 2011–12 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 3 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 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 3 shows that the estimated number of people who participated in natural environment related activities for enjoyment was 11,517,000. The RSE corresponding to this estimate (see the Relative Standard Error Table section at the end of this Technical Notei) shows the RSE of the number for this estimate is 1.0%. The SE is calculated by:

Image: Standard error of estimate equals relative standard error over 100 times estimate - example

7 Therefore, there are about two chances in three that the actual number of people who participated in natural environment related activities for enjoyment was in the range of 11,401,800 and 11,632,200 and about 19 chances in 20 that the value was in the range 11,286,600 and 11,747,400. This example is illustrated below.

Image: Calculation of confidence interval - example


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:

Image: RSE of Proportion x over y equals square root of RSE x squared minus RSE y squared

9 As an example, using estimates from Table 3, of the 12,406,700 people who participated in natural environment related activities (excluding persons whose only participation in natural environment related activities was farming/farming activities), 92.8%, that is 11,517,000 people participated for enjoyment. The RSE for 11,517,000 is 1.0% and the RSE for 12,406,700 is 0.8% (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 participated in natural environment related activities for enjoyment is:

Image: Relative standard error of proportion - example

10 Therefore, the SE for the proportion of people who participated in natural environment related activities for enjoyment is 0.6 percentage points (=92.8 x (0.6/100)). Hence, there are about two chances in three that the proportion of people who participated in natural environment related activities for enjoyment is between 92.2% and 93.4% and 19 chances in 20 that the proportion is between 91.6% and 94.0%.


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:

Image: Standard error x minus y equals square root of standard error x squared plus standard error y squared

12 While this formula will only be exact for differences between separate and correlated 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:

Image: Statistical significance test statistic equals absolute value of x minus y over standard error of x minus y

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 3 are included below:

Table 3 Reasons for participation in natural environment related activities in last 12 months, Persons who have participated in natural environment related activities(a)
NSW
Vic.
Qld
SA
WA
Tas.
NT
ACT
Aust.
NUMBER ('000)
Environmental reasons
Support for local environment
518.0
537.8
409.1
128.8
204.5
62.1
14.5
34.8
1,909.6
Nature conservation
353.4
323.0
249.9
101.9
155.7
39.9
*9.2
20.0
1,253.1
Non-environmental reasons
Enjoyment
3,620.8
2,977.5
2,289.3
855.5
1,193.8
287.4
87.4
205.2
11,517.0
Social reasons
2,215.1
1,926.3
1,492.1
596.3
752.6
190.0
54.0
149.3
7,375.6
Exercise
1,763.7
1,643.1
1,218.4
514.8
555.1
166.1
34.7
122.1
6,018.0
Education or work
444.4
424.1
353.4
111.2
145.9
34.9
16.2
33.3
1,563.4
Other reasons (not specified environmental or non environmental)
63.5
69.3
53.9
25.6
28.2
8.9
*2.8
*6.0
258.2
Did not know
**6.1
*15.1
np
np
**3.2
**0.7
–
–
27.3
Total(b)
3,922.1
3,203.4
2,478.8
921.8
1,266.4
300.6
98.6
215.1
12,406.7
PROPORTION (%)
Environmental reasons
Support for local environment
13.2
16.8
16.5
14.0
16.2
20.7
14.7
16.2
15.4
Nature conservation
9.0
10.1
10.1
11.1
12.3
13.3
*9.4
9.3
10.1
Non-environmental reasons
Enjoyment
92.3
92.9
92.4
92.8
94.3
95.6
88.7
95.4
92.8
Social reasons
56.5
60.1
60.2
64.7
59.4
63.2
54.7
69.4
59.4
Exercise
45.0
51.3
49.2
55.8
43.8
55.2
35.2
56.8
48.5
Education or work
11.3
13.2
14.3
12.1
11.5
11.6
16.5
15.5
12.6
Other reasons (not specified environmental or non environmental)
1.6
2.2
2.2
2.8
2.2
3.0
*2.9
*2.8
2.1
Did not know
**0.2
*0.5
np
np
**0.3
**0.2
–
–
0.2
RSE OF NUMBER (%)
Environmental reasons
Support for local environment
7.4
7.0
6.4
7.6
6.7
9.6
17.6
15.2
3.9
Nature conservation
6.4
9.1
7.5
9.3
7.5
11.7
25.4
20.2
3.5
Non-environmental reasons
Enjoyment
1.8
1.5
1.8
2.4
1.9
1.7
3.2
2.7
1.0
Social reasons
2.9
2.8
3.5
3.2
3.3
4.2
8.1
5.3
1.4
Exercise
3.2
3.6
3.5
3.6
4.2
3.3
8.1
6.6
1.7
Education or work
8.9
8.9
9.7
9.0
11.0
14.5
12.8
14.2
4.4
Other reasons (not specified environmental or non environmental)
19.2
15.6
16.1
16.8
17.2
23.6
30.0
34.1
8.7
Did not know
64.3
35.3
np
np
65.5
55.4
–
–
24.6
Total(b)
1.5
1.3
1.2
1.9
1.6
1.7
2.5
2.7
0.8
RSE OF PROPORTION (%)
Environmental reasons
Support for local environment
7.3
6.7
6.3
6.8
6.8
8.9
17.1
15.3
3.9
Nature conservation
6.0
8.7
7.2
9.2
7.6
11.5
25.0
20.7
3.1
Non-environmental reasons
Enjoyment
0.8
0.8
1.0
1.1
0.7
0.7
2.1
0.8
0.5
Social reasons
2.3
1.9
3.5
2.5
2.5
4.2
7.6
4.1
1.1
Exercise
2.7
2.7
3.3
3.2
4.2
3.6
7.6
6.3
1.4
Education or work
8.3
8.6
9.6
9.3
11.5
14.7
13.0
14.4
4.3
Other reasons (not specified environmental or non environmental)
19.2
15.5
16.0
17.2
16.6
24.0
30.2
34.4
8.7
Did not know
64.5
35.3
np
np
66.0
55.5
–
–
24.7
*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)
npnot available for publication but included in totals where applicable, unless otherwise indicated
(a)Excludes persons whose only participation in natural environment related activities was farming/farming activities.
(b)Components may not add to total as people may have reported more than one reason.