6285.0 - Involvement in Organised Sport and Physical Activity, Australia, Apr 2007  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 19/12/2007   
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TECHNICAL NOTE DATA QUALITY


RELIABILITY OF ESTIMATES

1 Since the estimates in this publication are based on information obtained from selected occupants of a sample of dwellings, they are subject to sampling variability; that is, they may differ from those 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 was included. There are about 2 chances in 3 (67%) that a sample estimate will vary 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. 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.


2 Space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication. However, RSEs for all of these estimates are available free-of-charge on the ABS website <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication, Involvement in Organised Sport and Physical Activity, Australia, 2007 (cat. no. 6285.0). An example table, containing the RSEs for Table 4, appears at the end of these notes.



CALCULATION OF STANDARD ERROR

3 An example of the calculation and the use of SEs in relation to estimates of persons follows. From table 4 an estimated 127,200 males had some paid involvement in organised sport and physical activity during the 12 months prior to interview. In the RSE spreadsheet table, the RSE for this estimate is shown to be 7.8%. The SE is -


Equation: Eqn1


4 Therefore there are about 2 chances in 3 that the number that would have been produced if all dwellings had been included in the survey will fall within the range 117,300 and 137,100, and about 19 chances in 20 that the value will fall within the range 107,400 and 147,000. This example is illustrated in the diagram below:

Diagram: Calculation of Standard Error


5 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 thus subject to such high RSEs that their value for most practical purposes is unreliable. In the tables in this publication, only estimates with an RSE of 25% or less are considered reliable for most purposes. Estimates with an RSE greater than 25% but less than or equal to 50% 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 of greater than 50%, preceded by a double asterisk (e.g. **0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with an RSE of 25% or less.



PROPORTIONS AND PERCENTAGES

6 Proportions and percentages formed from the ratio of two related 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:


Equation: Eqn2


7 Considering the example above, the 127,200 males who has some paid involvement in organised sport and physical activity during the 12 months prior to interview represent 14% of the 883,500 males who were involved in organised sport and physical activity. The RSE of 883,500 is given as 3.5% in the corresponding RSE spreadsheet table. Applying the above formula, the RSE of the proportion is:


Equation: Eqn3


8 This then gives an SE of the percentage (14%) of (7.0/100) x 14 =1.0%. Therefore, there are about 2 chances in 3 that the percentage of Victorian females who were involved in organised sport and physical activity was between 13% and 15% and approximately 19 chances in 20 that the percentage was in the range 12% to 16%.



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 SE's and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:


Equation: Eqn4


10 While this formula will only be exact for differences between separate and uncorrelated characteristics of sub-populations it is expected to provide a good approximation for all differences likely to be of interest in this publication.



SIGNIFICANCE TESTING

11 Where differences between data items have been noted in the Summary of Findings, they are statistically significant. In this publication a statistically significant difference is one where there are 19 chances in 20 that the difference noted reflects a true difference between population groups of interest rather than being the results of sampling variability.

PERSONS WITH NON-PLAYING INVOLVEMENT, By selected characteristics and payment status: Relative Standard Errors
Some paid involvement
Unpaid involvement only(a)
Total persons
Some paid involvement participation rate(b)
Unpaid involvement only participation rate(b)
Total non-playing involvement participation rate(b)
RSE%
RSE%
RSE%
RSE%
RSE%
RSE%
Sex
Males
7.8
3.9
3.5
7.8
3.9
3.5
Females
6.8
3.4
3.0
6.8
3.4
3.0
State or territory of usual residence
New South Wales
13.6
6.1
5.2
13.6
6.1
5.2
Victoria
9.1
4.3
4.0
9.1
4.3
4.0
Queensland
9.7
6.3
5.8
9.7
6.3
5.8
South Australia
13.7
6.1
5.8
13.7
6.1
5.8
Western Australia
12.1
4.2
4.0
12.1
4.2
4.0
Tasmania
28.6
7.3
7.4
28.6
7.3
7.4
Northern Territory(c)
33.4
15.4
13.8
33.4
15.4
13.8
Australian Capital Territory
19.3
9.5
8.1
19.3
9.5
8.1
Age group (years)
15-24
10.3
7.5
6.3
10.3
7.5
6.3
25-34
11.5
5.7
4.7
11.5
5.7
4.7
35-44
12.5
4.5
4.2
12.5
4.5
4.2
45-54
15.6
3.9
3.5
15.6
3.9
3.5
55-64
18.0
7.6
7.1
18.0
7.6
7.1
65 and over
31.2
6.9
7.2
31.2
6.9
7.2
Labour force status
Employed full-time
7.5
3.9
3.4
7.5
3.7
3.2
Employed part-time
9.2
3.8
4.0
9.1
4.0
4.1
Total employed
5.6
3.1
2.8
5.5
3.1
2.7
Unemployed
39.0
15.8
16.2
38.2
15.6
15.3
Not in the labour force
19.2
4.7
5.0
19.0
4.8
5.1
Area of usual residence
State capital city
7.2
3.4
3.0
7.2
3.4
3.0
Rest of Australia
9.4
3.4
3.0
9.4
3.4
3.0
Country of birth
Australia
5.8
3.2
3.0
5.6
3.0
2.7
Overseas
11.5
4.3
4.1
11.4
4.1
3.8
Main English speaking countries
14.7
6.5
5.7
14.5
6.1
5.2
Other than main English speaking countries
19.3
10.9
9.3
19.0
10.4
8.8
Total
5.4
2.6
2.4
5.4
2.6
2.4
(a) Includes those who did not know whether they would be paid for their involvement
(b) The number of persons involved in organised sport or physical activity expressed as a percentage of the population in the same group.
(c) Refers to mainly urban areas only. For further information refer to paragraph 4 of the Explanatory Notes.