F-tests with a rare pathology

ANOVA is routinely used to compare pathologies. Nevertheless, in many situations, the sample dimensions may not be known when planning the study. This is specially relevant when one of the pathologies is rare. Thus, the sample size for that pathology or for all pathologies must be considered as random. Sample selection for the non-rare pathologies may be carried out to increase the balance of the model. This leads to F-tests with random non-centrality parameters and random degrees of freedom for the errors. The distribution of such tests statistics is obtained.