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 the 2011–12 Patient Experience Survey 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 estimate is available from the Downloads tab of the publication. For illustrative purposes the RSEs for Table 12 have been included at the end of these Technical Notes.
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 also 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 12 shows that the estimated number of people who live in 'Major cities' and saw a dental professional in the last 12 months for their own health was 6,362,900. The RSE table corresponding to the estimates in Table 12 (see the 'Relative Standard Errors' section at the end of these Technical Notes) shows the RSE for this estimate is 1.2%. The SE is calculated by:
7 Therefore, there are about two chances in three that the actual number of people who live in 'Major cities' and saw a dental professional in the last 12 months for their own health was in the range of 6,286,500 to 6,439,300 and about 19 chances in 20 that the value was in the range 6,210,100 to 6,515,700. This example is illustrated in the diagram below.
PROPORTION AND PERCENTAGES
8 Proportions and percentages formed from the ratio of two estimates are also subject to sampling error. 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 12, of the 6,362,900 people who live in 'Major cities' and saw a dental professional in the last 12 months for their own health, 43.0%, that is 2,737,900 people who live in 'Major cities', saw a dental professional once in the last 12 months for their own health. The RSE for 2,737,900 is 2.0% and the RSE for 6,362,900 is 1.2% (see 'Relative Standard Errors' section at the end of these Technical Notes). Applying the above formula, the approximate RSE for the proportion of people who live in 'Major cities' and saw a dental professional once in the last 12 months for their own health is:
10 Therefore, the SE for the proportion of people who live in 'Major cities' and saw a dental professional once in the last 12 months for their own health is 0.7 percentage points (=(1.6/100) x 43.0). Hence there are about two chances in three that the proportion of people who live in 'Major cities' and saw a dental professional once in the last 12 months for their own health is between 42.3% and 43.7%, and 19 chance in 20 that the proportion is between 41.6% and 44.4%.
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% 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 ERRORS
15 The RSEs for Table 12 are included below:
Table 12 Persons 15 years and over who had seen a dental professional, Use of dental services for own health in the last 12 months by selected characteristics: Relative standard error |
|
 | | Self-assessed health status
| Long term health conditions
| Index of disadvantage
|
| | Excellent/
very good/
good | Fair/
poor | Has LTC | No LTC | Most
disadvantage | 2nd
quintile | 3rd
quintile | 4th
quintile | Least
disadvantage |
RSE OF ESTIMATE (%)
|
| Number of dental visits in the last 12 months |
| One | 1.6 | 4.8 | 2.3 | 1.9 | 4.5 | 4.9 | 5.4 | 4.0 | 5.1 |
| 2–3 | 1.8 | 3.9 | 2.3 | 2.1 | 5.3 | 5.4 | 4.5 | 5.2 | 4.2 |
| 4 or more | 2.8 | 6.3 | 3.9 | 4.8 | 7.7 | 7.3 | 7.2 | 7.7 | 7.3 |
| Type of dental clinic most recently visited |
| Private dental clinic | 1.0 | 2.7 | 1.5 | 1.4 | 4.6 | 3.8 | 3.9 | 3.9 | 3.7 |
| Government dental clinic | 4.1 | 5.0 | 4.0 | 6.3 | 6.8 | 8.7 | 9.5 | 9.7 | 12.2 |
| Saw dental professional for urgent care | 2.4 | 5.3 | 3.1 | 3.7 | 7.9 | 5.1 | 5.8 | 7.2 | 5.0 |
| | | | | | | | | | |
| Total persons who saw a dental professional | 0.8 | 2.7 | 1.4 | 1.2 | 4.3 | 4.0 | 3.9 | 3.6 | 3.6 |
RSE OF PROPORTION (%)
|
| Number of dental visits in the last 12 months |
| One | 1.4 | 3.5 | 2.1 | 1.4 | 3.2 | 3.3 | 3.1 | 2.4 | 3.1 |
| 2–3 | 1.5 | 3.1 | 1.8 | 1.9 | 2.2 | 3.5 | 3.3 | 3.0 | 3.1 |
| 4 or more | 2.8 | 5.8 | 3.5 | 4.3 | 5.6 | 5.7 | 6.0 | 7.3 | 6.4 |
| Type of dental clinic most recently visited |
| Private dental clinic | 0.4 | 0.8 | 0.5 | 0.5 | 1.2 | 0.9 | 0.9 | 0.7 | 0.5 |
| Government dental clinic | 4.3 | 3.6 | 3.7 | 6.3 | 5.4 | 6.5 | 8.4 | 10.2 | 13.1 |
| Saw dental professional for urgent care | 2.3 | 5.0 | 2.8 | 3.7 | 7.5 | 4.6 | 5.0 | 5.5 | 4.1 |
| | | | | | | | | | |
| Total persons who saw a dental professional | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
Table 12 Persons 15 years and over who had seen a dental professional, Use of dental services for own health in the last 12 months by selected characteristics: Relative standard error - CONTINUED |
|
| | Country of birth
| Remoteness
| |
| | Born in
Australia | Born
overseas | Major
cities | Inner
regional | Outer
regional/
remote/
very remote | Total |
RSE OF ESTIMATE (%)
|
| Number of dental visits in the last 12 months |
| One | 2.0 | 3.2 | 2.0 | 4.1 | 7.3 | 1.5 |
| 2–3 | 2.1 | 2.9 | 1.8 | 4.9 | 8.4 | 1.6 |
| 4 or more | 3.5 | 5.9 | 3.4 | 7.9 | 11.5 | 2.9 |
| Type of dental clinic most recently visited |
| Private dental clinic | 1.3 | 2.0 | 1.3 | 3.3 | 7.0 | 0.9 |
| Government dental clinic | 3.4 | 6.1 | 3.9 | 7.6 | 10.3 | 2.9 |
| Saw dental professional for urgent care | 2.9 | 5.8 | 2.8 | 5.1 | 8.7 | 2.2 |
| | | | | | | |
| Total persons who saw a dental professional | 1.1 | 2.0 | 1.2 | 3.2 | 6.8 | 0.8 |
RSE OF PROPORTION (%)
|
| Number of dental visits in the last 12 months |
| One | 1.6 | 2.4 | 1.5 | 3.2 | 4.1 | 1.3 |
| 2–3 | 1.8 | 2.4 | 1.5 | 3.1 | 4.3 | 1.4 |
| 4 or more | 3.5 | 5.2 | 3.3 | 7.1 | 8.8 | 2.8 |
| Type of dental clinic most recently visited |
| Private dental clinic | 0.4 | 0.5 | 0.3 | 1.0 | 1.3 | 0.3 |
| Government dental clinic | 3.8 | 5.9 | 3.9 | 6.6 | 8.6 | 3.0 |
| Saw dental professional for urgent care | 2.7 | 6.1 | 2.8 | 5.1 | 6.0 | 2.3 |
| | | | | | | |
| Total persons who saw a dental professional | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
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