A simple statistical framework for small sample studies

Abstract

Most studies in psychology, neuroscience, and life science research make inferences about how strong an effect is on average in the population. Yet, many research questions could instead be answered by testing for the universality of the phenomenon under investigation. By using reliable experimental designs that maximise both sensitivity and specificity of individual experiments, each participant or subject can be treated as an independent replication. This approach is common in certain subfields. To date, there is however no formal approach for calculating the evidential value of such small sample studies and to define a priori evidence thresholds that must be met to draw meaningful conclusions. Here we present such a framework, based on the ratio of binomial probabilities between a model assuming the universality of the phenomenon versus the null hypothesis that any incidence of the effect is sporadic. We demonstrate the benefits of this approach, which permits strong conclusions from samples as small as 2-5 participants and the flexibility of sequential testing. This approach will enable researchers to preregister experimental designs based on small samples and thus enhance the utility and credibility of such studies.