Math for Causal Inference
All simulators

Fisher's Exact Randomisation Test

Enumerate every possible assignment under the sharp null and read off an exact p-value — for means or ranks.

Day 37: Fisher's Exact Test & Randomisation Inference
-7.5-5-2.502.557.5statistic under all 924 assignmentsobserved 7.32
one-sided p
0.001
two-sided p
0.002
assignments
924
C(12, 6)
smallest possible p
0.0022
two-sided
13.79.74.116.17.78.74.17.73.711.5-1.010.5
Blue chips: treated workers. With n = 6 the smallest attainable two-sided p is 0.1 — no data can ever be "significant" at 5%.

Sharp null: the programme changed nobody's outcome. Then every outcome is fixed, and we can recompute the statistic under all possible assignments. The p-value is the share of assignments at least as extreme as the one that happened — exact, with no distributional assumptions.