Would you agree if N is three? On statistical inference for small N

Non-human primate studies traditionally use two or three animals. We previously used standard statistics to argue for using either one animal, for an inference about that sample, or five or more animals, for a useful inference about the population. A recently proposed framework argued for testing three animals and accepting the outcome found in the majority as the outcome that is most representative for the population. The proposal tests this framework under various assumptions about the true probability of the representative outcome in the population, i.e. its typicality. On this basis, it argues that the framework is valid across a wide range of typicalities. Here, we show (1) that the error rate of the framework depends strongly on the typicality of the representative outcome, (2) that an acceptable error rate requires this typicality to be very high (87% for a single type of outlier), which actually renders empirical testing beyond a single animal obsolete, (3) that moving from one to three animals decreases error rates mainly for typicality values of 70-90%, and much less for both lower and higher values. Furthermore, we use conjunction analysis to demonstrate that two out of three animals with a given outcome only allow to infer a lower bound to typicality of 9%, which is of limited value. Thus, the use of two or three animals does not allow a useful inference about the population, and if this option is nevertheless chosen, the inferred lower bound of typicality should be reported.