Sample size

Choosing sample size for experiments

Choosing the sample size in a scientific experiment always involves balancing the increased information and precision that result from bigger samples and the reduced time and cost that result from smaller samples. In animal experiments where welfare is an issue, there is additional motivation to reduce the numbers of animals. We don't want unnecessarily many animals, but also need to avoid using too few so that the experiment is a waste of time. How do we choose the sample size? There are two ways of going about this. One depends on the experiment being regarded as testing for the presence of an effect or difference, the other as estimating some quantity.

Testing for an effect.

In an experiment which tests for an effect (which might show up as a difference between control and treated individuals, for example), there are three related quantities:

The size of effect we would regard as important, that we would not want to miss.
The probability that if such an effect exists, we find it. (This is the power of the test.)
The number of animals (or whatever) used in the experiment.

If any two of these are specified, the third may be determined. These calculations depend on having some idea of the variability between or within animals, as the effect is expressed relative to this variability. It can be estimated from previous experiments or intelligently guessed.

Experimental planning should involve consideration of these quantities. A statement such as `Use of 8 animals per group was chosen in order that the experiment should have 90% power to detect, at 5% significance, a difference of 9mmol, assuming between animal variability of 5mmol.' should be included in any experiment proposal.

Estimating a quantity.

In this situation, we wish to make statements like 'The effect of giving the animals an infusion of X is to increase the value of Y by 12 ± 4 mg/l compared with their baseline values.' If we know the precision we wish to achieve for the estimate, we can calculate the sample size. This precision is expressed as an SE or SED. An estimate or guess of between/within animal variability is needed. We might then say, for example: 'In order that the SE should be 4mg/l, and assuming within individual variability of 12 mg/l, 18 animals are needed'.

Doing the calculations.

Here is some help for choosing sample sizes to detect a difference or effect or to estimate a quantity.

For more information or help with making use of these pages, contact anyone in BioSS.

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