4839.0 - Patient Experiences in Australia: Summary of Findings, 2010-11  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 25/11/2011  First Issue
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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 = the standard error divided by the estimate then multiplied by 100

3 RSEs for Patient Experiences in Australia: Summary of Findings 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 is available free-of-charge on the ABS web site <www.abs.gov.au>. The Data Cube also contains directly calculated RSEs for the 2011 estimates. For illustrative purposes the RSEs for Table 8 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.
CALCULATION OF STANDARD ERROR

6 SEs can be calculated using the estimates (counts or proportions) and the corresponding RSEs. For example, Table 8 shows that the estimated number of persons 'Born in Australia' that saw a General Practitioner (GP) in the last 12 months for their own health was 10,534,200. The RSE table corresponding to the estimates in Table 8 (see Relative Standard Errors in the 'Relative Standard Error' section at the end of these Technical Notes) shows the RSE for this estimate is 0.8%. The SE is calculated by:

Equation: standard error of estimate = relative standard error divided by 100 then multipled by the estimate

7 Therefore, there are about two chances in three that the actual number of persons 'Born in Australia' that saw a General Practitioner (GP) in the last 12 months for their own health was in the range of 10,449,900 to 10,618,500 and about 19 chances in 20 that the value was in the range 10,365,600 to 10,702,800. 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 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. The formula is only valid when the numerator is a subset of the denominator:

Equation: RSE of the proportion of x/y = square root of the RSE of x squared minus the RSE of y squared

9 As an example, using estimates from Table 8, of the 10,534,200 persons 'Born in Australia' that saw a GP in the last 12 months for their own health, 18.3%, that is 1,930,600 persons 'Born in Australia', saw a GP once in the last 12 months for their own health. The RSE for 1,930,600 is 2.3% and the RSE for 10,534,200 is 0.8% (see Relative Standard Errors Table in the 'Relative Standard Error' section at the end of these Technical Notes). Applying the above formula, the RSE for the proportion of persons 'Born in Australia' that saw a General Practitioner (GP) in the last 12 months for their own health is:

Equation: RSE of proportion example

DIFFERENCES

10 Published estimates may also be used to calculate the difference between two survey estimates (of 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: the standard error of x minus y = square root of the standard error of x squared plus the standard error of y squared

11 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

12 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 10. The standard error is then used to create the following test statistic:

Equation: test statistic = modulus of x minus y divided by the standard error of x minus y

13 If the value of this test statistic is greater than 1.96 then we may say there is good evidence of a real 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.

RELATIVE STANDARD ERROR TABLE

14 The RSEs for Table 8 are included below:

Diagram: RSEs for Table 8