How big should a sample be? Are 30, 50 or 80 cases enough? Let’s consider this mathematically.
No matter how carefully it is taken, no sample can ever completely reproduce every detail of the statistical population. If several samples are taken from the statistical population, it is generally seen that the measured values for the same quality differ from each other in each of the sub-groups.
But which of the measured values is correct, and/or how precisely do the values reflect the actual value?
It is clear that the quality of any statement made on the basis of a random sample can be mathematically defined. It mainly depends on the desired level of precision – the significance level – on the size of the sample and, depending on the analysed data, also on the distribution of the value or the size of the measured value. It does not, however, depend on the size of the statistical population.
Conversely, it is of course also the case that for a desired significance level, the minimum required dimensions of sampling can be clearly defined.
Depending on the given question, whether the sample is compared with the statistical population or two samples compared with each other, and whether proportional value or median values are to be interpreted, different methods of calculation are applied.