Use randomized-experiment data and simulations to compare treatments and judge significance.
Estimate an approximate p-value from randomization simulation results
Problem
What is the approximate \(p\)-value from these simulation results: \(12~\text{of}~1000\) simulated differences at least as large?
Big Picture
What this problem is really about
Use the declared extremeness rule to identify the relevant simulated results. Divide their count by the total number of randomizations, not by the observed statistic or sample size, and convert the resulting relative frequency carefully. Because this is a finite simulation estimate, another valid run may produce a slightly different empirical p-value.
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