Appendix D: Calculating the sample size
The sample size calculator spreadsheet enables councils to estimate how many carers they need to sample to achieve the minimum required margin of error of no more than +/-5 per cent.
As a rough guide, table 1 from the sample size calculator spreadsheet shows an example for a council with 1000 eligible carers and a predicted response rate of 40%. The table shows that for this scenario, the total number of completed questionnaires needed is 278 which implies that 696 questionnaires need to be sent out to allow for non-response.
| The Eligible Population | The anticipated response rate based on previous surveys (%) | Number of returned questionnaires needed to meet +/- 5% requirement* | Sample Size - Number of questionnaires to be sent out based on anticipated response rate | Margin of Error | Sampling interval needed to select every nth carer |
|---|---|---|---|---|---|
| 1000 | 40% | 278 | 696 | 5.0% | One in every 1.44 cases |
The spreadsheet also allows councils to consider sending more questionnaires than needed to fulfil the minimum requirement in order to increase the level of precision of their survey estimates, or in other words, to reduce the margin of error. As a rough guide, table 2 from the sample size calculator spreadsheet shows what happens if the number of questionnaires sent out is increased from 696 to 900. It can be seen that the margin of error reduces from 5.0% to 4.1%.
Table 2: Example sample size calculation – reduced error
| The Eligible Population: the number of carers the sample is drawn from | The anticipated response rate based on previous surveys (%) | Number of returned questionnaires needed to meet +/- 5% requirement* | Sample Size - Number of questionnaires need to be sent out based on anticipated response rate | Margin of Error | Sampling interval needed to select every nth carer |
|---|---|---|---|---|---|
| 1000 | 40% | 360 | 900 | 4.1% | One in every 1.11 cases |
Selecting the sample
To ensure that the results of the survey are representative of all carers, a random sample of eligible carers should be chosen. If the first 400 of a list of carers were chosen for example, then a random sample will have been selected only if the list is ordered randomly. It is more likely that this approach will yield a list of selected carers with similar characteristics, for example all living in a particular area within the council.
A common and easy way to select a random sample of carers is to take a systematic random sample. A systematic random sample is one in which, say, every 6th or 10th individual is selected.
The sample calculator spreadsheet has two additional tabs entitled Selecting the Sample-Minimum and Selecting the Sample-More. These tabs will be pre-populated based on the information already entered. The following example in Table 3 shows which carers should be selected if a council is aiming to meet the minimum requirement when selecting the sample. Each CASSR should be able to estimate how much it will have to spend on the survey by drawing on its experience of running previous surveys as well as consideration of the process outlined in the guidance.
Table 3: Selecting a random sample
| The Eligible Population | 1000 |
| Sample Size - Number of questionnaires needed to be sent out | 696 |
| Sampling interval needed to select every nth carer | 1.44 |
| Random Start | 2 |
The record that should be selected from the list of eligible carers
| Elig Pop Number | Flag |
| 1 | - |
| 1 | 1 |
| 2 | 1 |
| 3 | 1 |
| 4 | 1 |
| 5 | - |
| 6 | 2 |
| 7 | 1 |
| 8 | - |
| 9 | 1 |
| 10 | 1 |
| 11 | - |
| 12 | 1 |
| 13 | 1 |
| 14 | 1 |
| 15 | - |
| 16 | 1 |
| 17 | - |
| 18 | - |
| 19 | 1 |
| 20 | 1 |
Last edited: 23 October 2023 4:35 pm