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, the estimates may differ from those that would have been produced had all persons been included in the survey.
2 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 persons 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 persons had been surveyed, and about 19 chances in 20 (95%) that the difference will be less than two SEs.
3 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.
4 RSEs for all estimates 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.
5 The Excel spreadsheets (in the Downloads page of the publication) contain all the tables produced for this release and the calculated RSEs for each of the estimates. For illustrative purposes, some of the RSEs for Table 11 have been included at the end of these Technical Notes.
6 Only estimates (numbers and proportions) with RSEs less than 25% are considered sufficiently reliable for most analytical 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 are annotated to indicate they are considered too unreliable for general use. All cells in the Excel spreadsheets 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 ERRORS
7 Standard errors can be calculated using the estimates (counts or proportions) and the corresponding RSEs. For example, Table 11 shows that the estimated number of males aged 15–17 years who participated in sport or physical recreation activity at schools or educational facilities was 215,000. The RSE corresponding to this estimate is 9.3%. The SE is calculated by:
8 Therefore, there are about two chances in three that the actual number of males aged 15-17 years who participated in a sport or physical recreation activity at schools or educational facilities was in the range 195,000 to 235,000 and about 19 chances in 20 that the value was in the range 175,000 to 255,000. 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 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. This formula is only valid when the numerator is a subset of the denominator:
10 As an example, using estimates from Table 11, of the 415,100 males aged 15–17 years who participated in sport or physical recreation activity, 51.8%, that is 215,000 males, participated at schools or educational facilities. The RSE for 215,000 is 9.3%, and the RSE for 415,100 is 6.1% (see the Relative Standard Error Table at the end of these Technical Notes). Applying the above formula, the approximate RSE for the proportion of males aged 15-17 years who participated in sport or physical recreation activity at schools or educational facilities is:
11 Therefore, the SE for the proportion of males aged 15–17 years who participated in sport or physical recreation activity at schools or educational facilities is 3.6 percentage points (= 51.8 × (7.0/100)). Hence, there are about two chances in three that the percentage of males aged 15–17 years who participated in a sport or physical recreation activity at schools or educational facilities is between 48.2% and 55.4%, and 19 chances in 20 that the percentage is between 44.6% and 59.0%.
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.
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 shown above in paragraph 12. This standard error is then used to calculate 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 with respect to that characteristic.
16 Tables which show rates from 2005–06, 2009–10 and 2011–12 have been tested to determine whether changes over time are statistically significant. Significant differences have been annotated. In all other tables which do not show the results of significance testing, users should take account of RSEs when comparing estimates for different populations.
RELATIVE STANDARD ERRORS
17 Selected RSEs for Table 11 are included below:
Table 11a PARTICIPANTS, Sport and physical recreation–Facilities used, by sex and age: Relative standard error
Public playing fields and
or educational facilities
Parks or reserves
RSE OF ESTIMATE (%)
| 15–17|| |
| 35–44|| |
| 65 and over|
| Total male participants|
RSE OF PROPORTION (%)
| 65 and over|
| Total male participants|
(a) nil or rounded to zero (including null cells)