Table 5:
Null hypotheses for Fisher’s, Barnard’s and Chiba’s exact tests.
Exact test
Null hypothesis
Fisher
Y
(1) =
Y
(0) for all subjects (sharp causal null hypothesis)
Barnard
Pr(
Y
= 1 |
X
= 1) = Pr(
Y
= 1 |
X
= 0)
Chiba
n
10
=
n
01
(corresponding to the weak causal null hypothesis Pr(
Y
(1) = 1) = Pr(
Y
(0) = 1))