Principles of Sample Size Calculation
3. Sample vs Population
The key to understanding sample size calculation is to understand the underlying concepts of statistical inference, i.e. using the information from a (random) sample to draw conclusions (inferences) about the population from which the sample was taken.
Analysing the information in a sample will lead to an (observed) estimate for the treatment effect. This should help to predict the true treatment effect in the broader patient population. Every time a sample is taken, by the mere definition of a sample (at least a random one), a different estimate will be obtained. If you looked at several samples together, they will provide a clear picture of the true treatment effect and the variability (i.e. the spread of data, the measure of how far the numbers in a data set are away from the mean or median) underlying the estimation. However, in practice, only one sample is taken, i.e. the trial is run once. So, from the observed effects in samples, what can be determined about the true but unknown treatment effect in the population? This is where statistical inference comes in, more specifically through the concept of hypothesis testing and the use of confidence intervals.