 # Information by Design Lifestyle Survey Toolkit

## Calculating the Sample Size

The sample size of a survey depends on the following:
• The level of precision or accuracy required by the survey
• The amount of variation present in the population for the particular aspect (variable) of interest

Based on the above, there are a range of formulae that can be used to calculate the required sample size for the different sample designs available. Alternatively, if you can decide on the level of sampling error you are prepared to tolerate in your survey, you can use the following table to work out the sample size required.

 Sampling error(%) Sample size Sampling error(%) Sample size 1.0 10,000 5.5 330 1.5 4,500 6.0 277 2.0 2,500 6.5 237 2.5 1,600 7.0 204 3.0 1,100 7.5 178 3.5 816 8.0 156 4.0 625 8.5 138 4.5 494 9.0 123 5.0 400 9.5 110 10 100

The figures in the table are calculated so that you can be 95% confident that the results in the population will be the same as the sample plus or minus the sampling error (assuming that simple random sampling has been used to select the source). For example, a sample size of 4,500 will mean that you can be 95% confident that the results in the population will be the same as the sample plus or minus the sampling error, in this case, 1.5%.

Taking this a stage further, in a lifestyle survey, using a simple random sample of 1,100 residents the results might show 25% of adults smoke. Using the table, we can be reasonably confident (95% level) that the true result for the whole population will be between (25-3)% and (25+3)%, so between 22% and 28%.

Note that the above table is just for simple random sampling. If other methods of selecting the samples are used (e.g. cluster sampling), the confidence intervals will be wider.

## Sample Size and Precision

The precision of a survey estimate (how close it’s likely to be to the true population value) is measured using the sampling error. For a simple random sample, where we are estimating some percentage p, the:
 standard error = And the 95% confidence interval for p is:

 p ± 1.96 ## Example

Assuming in a large population we have undertaken a survey of 1,000 residents and found that 30% of them exercise daily.

 standard error = The 95% confidence interval is:

 0.3 ± 0.0145  = 0.2855 to 0.3155  (or 28.55% to 31.55%)
Notice in the formula above, the standard error depends on the value of p and the sample size n (n is the denominator in the formula). Sampling error decreases as the sample size increases, but not in direct proportion. The decrease is proportional to the square root of the relative increase in sample size. So increasing the sample size in your survey will bring increased precision – but doubling it will not ‘double the precision’. There is a balance

 Increase sample size ↓ Increase precision ↓ Narrower confidence intervals ↓ Increased cost

The increased costs will not be in proportion to the increase in sample size – because we should get economies of scale in doing larger surveys.  Some of these issues are illustrated in practice by clicking here.

• For illustrations of of sample sizes and response rates from a number of lifestyle surveys, click here.