Fisher Barnard Proposed Assumption Monotonicity Exchangeability None Pros It is sufficient to test the sharp causal null hypothesis. It is not a problem to assume exchangeability in randomized trials. No assumption is required. Cons Rejection of the sharp causal null hypothesis does not imply that the causal risk difference is not zero. Exchangeability may not hold in randomized trials with moderate to small samples.

Table 4: Assumptions and the pros and cons of the three exact tests (Fisher, Barnard, and Proposed) for the weak causal null hypothesis.