Appendix 3—Statistical Reliability
Statistical reliability of the results
The estimates derived for this study are based on information obtained from a sample survey and are therefore subject to sampling variability. That is, they may differ from results that would be obtained if all people in Australia who have contacted government were interviewed (i.e. a Census), or if the survey was repeated with a different sample of respondents. One measure of the likelihood of any difference is the standard error (SE) which shows the extent to which an estimate might vary by chance because only a sample of people were interviewed. An alternative way of showing this is the relative standard error (RSE) which is the SE as a percentage of the estimate.
The table below shows the SE for various sample sizes and response levels. The interpretation of this table is shown in the example below.
This table can be used to assess if there are true statistically significant differences between results with in the 2009 study, or when comparing results from 2009 and previous studies.
For example:
If the sample size was 3,669, a response set of 50% for example, has a standard error of +/‑1.6 at a 95% confidence level (i.e. there are 95 chances in 100 that a repeat survey would produce a response set of between 51.6% and 48.4%).
If there were 500 respondents (i.e. n=500) to a question and 50% gave a particular response, then the standard error for that response is +/- 4.1%.
Where the relative standard error is between 30% and 49% results should be regarded as moderately reliable and where the relative standard error is 50% or higher results should be regarded as indicative estimates only.
|
Total sample & sub-sets |
|||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Survey estimate |
3669 |
3250 |
3000 |
2750 |
2500 |
2250 |
2000 |
1750 |
1500 |
1250 |
1000 |
750 |
500 |
250 |
||
|
Sample variance (+/-) 95% confidence intervals |
|||||||||||||||
10% |
1.0% |
1.0% |
1.1% |
1.1% |
1.2% |
1.2% |
1.3% |
1.4% |
1.5% |
1.7% |
1.9% |
2.1% |
2.6% |
3.7% |
||
20% |
1.3% |
1.4% |
1.4% |
1.5% |
1.6% |
1.7% |
1.8% |
1.9% |
2.0% |
2.2% |
2.5% |
2.9% |
3.5% |
5.0% |
||
30% |
1.5% |
1.6% |
1.6% |
1.7% |
1.8% |
1.9% |
2.0% |
2.1% |
2.3% |
2.5% |
2.8% |
3.3% |
4.0% |
5.7% |
||
40% |
1.6% |
1.7% |
1.8% |
1.8% |
1.9% |
2.0% |
2.1% |
2.3% |
2.5% |
2.7% |
3.0% |
3.5% |
4.3% |
6.1% |
||
50% |
1.6% |
1.7% |
1.8% |
1.9% |
2.0% |
2.1% |
2.2% |
2.3% |
2.5% |
2.8% |
3.1% |
3.6% |
4.4% |
6.2% |
||
60% |
1.6% |
1.7% |
1.8% |
1.8% |
1.9% |
2.0% |
2.1% |
2.3% |
2.5% |
2.7% |
3.0% |
3.5% |
4.3% |
6.1% |
||
70% |
1.5% |
1.6% |
1.6% |
1.7% |
1.8% |
1.9% |
2.0% |
2.1% |
2.3% |
2.5% |
2.8% |
3.3% |
4.0% |
5.7% |
||
80% |
1.3% |
1.4% |
1.4% |
1.5% |
1.6% |
1.7% |
1.8% |
1.9% |
2.0% |
2.2% |
2.5% |
2.9% |
3.5% |
5.0% |
||
90% |
1.0% |
1.0% |
1.1% |
1.1% |
1.2% |
1.2% |
1.3% |
1.4% |
1.5% |
1.7% |
1.9% |
2.1% |
2.6% |
3.7% |
||
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