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.
| 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.
- For additional points, see Frequently Asked Questions.
- For a useful table to help in estimating sample sizes and sampling errors,
click here.
|
