Barnard's test is appropriate here, because while the experimental design is a 2-way contingency table, only the columns (# villagers and # friars) are constrai

Barnard's test is appropriate here, because while the experimental design is a 2-way contingency table, only the columns (# villagers and # friars) are constrained, the rows (# infected/ # not infected) are not. P value was just under 0.05.