4839.0 - Patient Experiences in Australia: Summary of Findings, 2012-13 Quality Declaration 
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 21/11/2013   
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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:

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

3 RSEs for estimates from the 2012-13 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 17 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 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 17 shows that the estimated number of people in the 15 to 24 (years) age group who visited an emergency department in the last 12 months was 454,700. The RSE table corresponding to the estimates in Table 17 (see the 'Relative Standard Errors' section at the end of this Technical Note) shows the RSE for this estimate is 5.2%. The SE is calculated by:

Equation: Standard error of estimate calculation example

7 Therefore, there are about two chances in three that the actual number of people in the 15 to 24 age group who visited an emergency department in the last 12 months was in the range of 431,100 to 478,300 and about 19 chances in 20 that the value was in the range 407,500 to 501,900. This example is illustrated in the diagram below.

Diagram: Confidence interval example


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:

Equation: 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 17, of the 454,700 people in the 15 to 24 age group who visited an emergency department in the last 12 months, 70.1%, that is 319,000 people visited an emergency department once. The RSE for 319,000 is 6.5% and the RSE for 454,700 is 5.2% (see 'Relative Standard Errors' section at the end of this Technical Note). Applying the above formula, the approximate RSE for the proportion of people in the 15 to 24 age group who visited an emergency department once in the last 12 months is:

Equation: RSE of Proportion x over y equals square root of 6.5 squared minus 5.2 squared

10 Therefore, the SE for the proportion of people in the 15 to 24 age group who visited an emergency department once in the last 12 months is 2.7 percentage points (=(3.9/100) x 70.1). Hence there are about two chances in three that the proportion of people in the 15 to 24 age group who visited an emergency department once in the last 12 months is between 67.4% and 72.8%, and 19 chances in 20 that the proportion is between 64.7% and 75.5%.


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:

Equation: 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 uncorrelated characteristics or sub populations, it provides a good approximation for the differences likely to be of interest in this publication.

13 Another measure (which is not presented in this publication) is the Margin of Error (MOE), which describes the distance from the population value of the estimate at a given confidence level, and is specified at a given level of confidence. Confidence levels typically used are 90%, 95% and 99%. For example, at the 95% confidence level the MOE indicates that there are about 19 chances in 20 that the estimate will differ by less than the specified MOE from the population value (the figure obtained if all dwellings had been enumerated). The 95% MOE is calculated as 1.96 multiplied by the SE.

14 The 95% MOE can also be calculated from the RSE by:

Equation: Margin of error y is almost equal to RSE y times y over 100 times 1.96
15 MOEs at the 95% confidence level can easily be converted to a 90% confidence level by multiplying the MOE by

Immage: Conversion of 95% Margin of Error (MOE) to 90% MOE equals MOEr times 1.645 over 1.96

or to a 99% confidence level by multiplying by a factor of

Image: Conversion of 95% Margin of Error (MOE) to 99% MOE equals MOE times 2.576 over 1.96

16 A confidence interval expresses the sampling error as a range in which the population value is expected to lie at a given level of confidence. The confidence interval can easily be constructed from the MOE of the same level of confidence by taking the estimate plus or minus the MOE of the estimate.


SIGNIFICANCE TESTING

17 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:

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

18 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

19 The estimates and RSEs for Table 17 are included below:


Table 17 Persons 15 years and over who visited an emergency department in the last 12 months, Experience of emergency department by age and sex
Age group (years)
15 - 24
25 - 34
35 - 44
45 - 54
55 - 64
65 - 74
75 - 84
85 and over
Total
ESTIMATE ('000)
Number of times visited emergency department
One
319.0
344.6
271.2
264.1
242.6
179.0
114.5
43.4
1,778.3
Two to three
102.4
108.0
86.0
80.7
67.0
67.9
46.0
16.3
574.3
Four or more
33.4
20.1
23.6
21.9
19.5
14.6
*7.1
**3.4
143.6
Total persons who visited an emergency department
454.7
472.7
380.8
366.7
329.0
261.5
167.6
63.1
2,496.2
PROPORTION (%)
Number of times visited emergency department
One
70.1
72.9
71.2
72.0
73.7
68.4
68.3
68.8
71.2
Two to three
22.5
22.9
22.6
22.0
20.3
26.0
27.4
25.9
23.0
Four or more
7.3
4.2
6.2
6.0
5.9
5.6
*4.2
**5.3
5.8
Total persons who visited an emergency department
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
RSE OF ESTIMATE (%)
Number of times visited emergency department
One
6.5
4.3
5.1
5.3
6.5
6.8
9.5
12.2
2.3
Two to three
11.9
8.7
8.8
8.8
9.3
9.0
12.2
11.9
3.7
Four or more
15.1
20.6
17.5
19.8
20.7
18.4
25.8
54.9
7.0
Total persons who visited an emergency department
5.2
3.5
4.0
4.7
5.4
5.4
8.1
9.1
1.9
RSE OF PROPORTION (%)
Number of times visited emergency department
One
3.8
2.7
2.8
2.7
2.5
3.5
3.9
5.7
1.1
Two to three
10.4
7.8
7.8
6.8
8.2
8.8
9.9
13.1
3.3
Four or more
15.0
20.4
18.0
19.8
21.4
15.6
25.9
54.2
6.9
Total persons who visited an emergency department
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

* 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