Bayesian Multilevel Single Case model (BMSC): a new approach to single case statistical analysis that allows to test the null and the alternative hypotheses

Single case studies are at the foundations of Neuropsychology. Nowadays, the gold standard for single case studies are the “Crawford tests”, allowing to test the alternative hypothesis (H1: if the single case scores are different from the control group scores) limited to specific, simple experimental designs. The objective of this research work is to develop and test a new flexible statistical approach to the single case analysis (Bayesian Multilevel Single Case model - BMSC), allowing to test H1 and the null hypothesis (H0: the single case score comes from the same statistical population of the controls’ scores), with the flexibility of multilevel methods. In order to test the resistance to false positive and false negative results, the method was compared to the Crawford dissociation test by means of a simulation approach. 1000 simulations under H0 and H1 of data concerning an experiment with 2 conditions (A and B) for a control group of 30 participants and 1 single case were analysed. Both the Crawford dissociation test and the BMSC test showed a first type error around 5%, and a second type error around 80%. Moreover, when the null hypothesis was true, BMSC showed the absence of difference between the control group and the patient in the 68% of cases. The BMSC test from these simulations is a reliable and powerful test, which is in line with the gold-standard tests, offering more opportunities and the possibility to test the null hypothesis.