4 Sample Design
4.1 Patients eligible to be sampled for the survey were those who were registered to a Scottish GP practice at 20 October 2015 and aged 17 or over at that date. Eligible patients were identified by ISD Scotland, using an October 2015 extract from the Community Health Index ( CHI) database. All data was accessed, managed and stored in accordance with the data confidentiality protocols  .
4.2 A small number of special practices, run by NHS Boards to provide primary care services to particular small groups of patients (e.g. practices for homeless people) were excluded from the survey. A small number of patients who had requested not to be included in this or other surveys were also removed from the survey sampling frame.
Sample design and sample size calculation
4.3 Sampling was done within GP practice lists, to aim for sufficient responses to achieve a reasonably reliable result for each practice. The reliability of the result depends on the number of questionnaires returned, and also the variability of the responses.
4.4 The sample size that was calculated for each practice was based on the minimum number of responses that would be required to achieve an estimate of a percentage that has a 95 per cent confidence interval with width +/- eight percentage points, sampled from a finite population. This level of acceptable uncertainty was agreed with stakeholders.
4.5 The formula for the minimum number of responses required (M) is
M = B/(1+(B-1)/N)
- N is the number of patients in a practice on the sampling frame (i.e. the number of patients aged 17 and over)
- B = z 2p(1-p)/c 2
- p = the proportion answering in a certain way (assume 0.5 as this gives maximum variability)
- z is 1.96 for a 95 per cent confidence interval (from standard normal distribution)
- c gives maximum acceptable size of confidence interval, in this case 0.08 (8 percentage points).
Based on the above, B=150
4.6 Table 3 below shows examples of this minimum number of responses required (M) based on the assumptions above for some example practice population sizes.
Table 3 Minimum number of responses required for different practice list sizes
|Minimum sample required||86||116||131||140||146||148||149|
|Percentage of population||43%||23%||13%||7%||3%||1%||1%|
4.7 In practice, if the underlying proportion is actually higher, or lower, than 0.5, then these numbers of responses would give narrower confidence intervals (or fewer responses would be required for the same accuracy).
4.8 The minimum number of responses required is adjusted upwards to allow for assumed non-response to the survey. Estimated response rates to the 2015/16 survey were calculated using a model that took into account different factors, including age and deprivation, which had an effect on the likelihood of a person responding to the survey. The model considered response rates from the 2013/14 Health and Care Experience Survey. This provided the most efficient way of determining the sample size.
4.9 As in the 2013/14 survey, no reminders were issued because it proved to be most cost effective to send more surveys initially than to send fewer surveys and reminders.
4.10 The formula used to calculate the total sample size (S) for each practice can be simplified to
Where R is the assumed response rate for each practice.
4.11 A total of 711,159 patients were sampled for inclusion in the Health and Care Experience Survey 2015/16.
4.12 For the majority of practices in Scotland, a random sample of the required number of patients (S) from each practice was taken from the sampling frame by ISD Scotland. For some practices with very small numbers of eligible patients, all patients were included in the survey in order to meet the minimum sample size requirements identified from the calculation above. The sample was selected within SPSS software version 21.0.
4.13 Further references for this methodology are: Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.