Seven of Eight Recovered
In a small trial, 8 patients receive a treatment and 7 of them recover; 9 patients receive a control and 2 of them recover. Apply Fisher's exact test for independence of treatment and recovery, conditioning on all margins (8 treated, 9 control, 9 recoveries in total). Define the two-sided p-value as the sum of the null probabilities of all tables whose probability is at most that of the observed table. Give the p-value as a reduced fraction.
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Source: Fisher exact test, from R. A. Fisher, The Design of Experiments (1935). Numbers and framing written for AxiomIQ. Statement written for AxiomIQ.