Tigernut tubers are the main ingredient in the production of orxata in Valencia, a white soft sweet popular drink. In recent years, the appearance of black spots in the skin of tigernuts has led to important economic losses in orxata production because severely diseased tubers must be discarded. In this paper, we discuss three complementary statistical models to assess the disease incidence of harvested tubers from selected or treated seeds, and propose a measure of effectiveness for different treatments against the disease based on the probability of germination and the incidence of the disease. Statistical methods for these studies are approached from Bayesian reasoning and include mixed-effects models, Dirichlet-multinomial inferential processes and mixed-effects logistic regression models. Statistical analyses provide relevant information to carry out measures to palliate the black spot disease and achieve a high-quality production. For instance, the study shows that avoiding affected seeds increases the probability of harvesting asymptomatic tubers. It is also revealed that the best chemical treatment, when prioritizing germination, is disinfection with hydrochloric acid while sodium hypochlorite performs better if the priority is to have a reduced disease incidence. The reduction of the incidence of the black spots syndrome by disinfection with chemical agents supports the hypothesis that the causal agent is a pathogenic organism.