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Table 5 All possible outcomes, p-values, and corresponding decisions for an RCT with n = 8 patients (4 per treatment arm) with Fisher’s exact test

From: A roadmap to using randomization in clinical trials

Number of responders Difference in proportions (Experimental vs. Control) Fisher’s exact test 1-sided p-value Decisiona
Experimental Control
0/4 0/4 0 1.0 F
1/4 1/4 0 0.7857 F
2/4 2/4 0 0.7571 F
3/4 3/4 0 0.7857 F
4/4 4/4 0 1.0 F
1/4 0/4 0.25 0.5 F
2/4 0/4 0.50 0.2143 F
3/4 0/4 0.75 0.0714 S
4/4 0/4 1 0.0143 S
0/4 1/4 -0.25 1.0 F
0/4 2/4 -0.50 1.0 F
0/4 3/4 -0.75 1.0 F
0/4 4/4 -1 1.0 F
2/4 1/4 0.25 0.5 F
3/4 1/4 0.50 0.2429 F
4/4 1/4 0.75 0.0714 S
1/4 2/4 -0.25 0.9286 F
1/4 3/4 -0.50 0.9857 F
1/4 4/4 -0.75 1.0 F
3/4 2/4 0.25 0.5 F
4/4 2/4 0.50 0.2143 F
2/4 3/4 -0.25 0.9286 F
2/4 4/4 -0.50 1.0 F
4/4 3/4 0.25 0.5 F
3/4 4/4 -0.25 1.0 F
  1. a F Declare study a failure, Declare study a success