The Myth of the ‘Correct’ Sample Size: Why Formula-Based Justification Misleads Researchers and Reviewers

This text does not report the results of a research study nor is it a bibliographic review. It does not conform to the standard format of Reviews or Research Articles. It is a “teaching article” whose “data” and “results” aim to show that what is commonly treated as the gold-standard criterion of any author, but rather to rigorously evaluate researcher’s reasoning and aims to show that:

a) In most cases it is arbitrary and wrong to require “scientific” proof that the “N” used in a study is appropriate.

b) It is even more erroneous to accept as correct alleged demonstrations that demonstrate nothing.

c) The formulas for estimating the appropriate sample size for each study have little usefulness in most cases, because in reality there are many sizes that are valid and there is not one in particular that is “the appropriate one.”

d) Contrary to common belief, the mathematical formulas used in this context do NOT say what N should be used, and therefore it makes no sense to ask authors to present here even a “scientific” justification of the size used.

Putting an end once and for all to this chain of misunderstandings and errors would save time, effort, and discomfort for many researchers. To do so they do not need to learn more mathematics; or implement more sophisticated procedures. Quite the opposite, the correct approach is simpler and more direct than the incorrect one.

What is correct is for the researcher to use the number of individuals that their resources allow. If the study is well conducted, that sample will provide useful information. In light of the results provided by it, it will be decided whether it is appropriate to subsequently expand the study by incorporating more individuals.

Keywords: Sample size, interval estimation, common sense