merge

Doc/library/random.rst

@@ -372,3 +372,29 @@ sample of size five::
    print(f'The sample mean of {mean(data):.1f} has a 90% confidence '
          f'interval from {means[1]:.1f} to {means[-2]:.1f}')
 
+Example of a `resampling permutation test
+<https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests>`_
+to determine the statistical significance or `p-value
+<https://en.wikipedia.org/wiki/P-value>`_ of an observed difference
+between the effects of a drug versus a placebo::
+
+    # Example from "Statistics is Easy" by Dennis Shasha and Manda Wilson
+    from statistics import mean
+    from random import shuffle
+
+    drug = [54, 73, 53, 70, 73, 68, 52, 65, 65]
+    placebo = [54, 51, 58, 44, 55, 52, 42, 47, 58, 46]
+    observed_diff = mean(drug) - mean(placebo)
+
+    n = 10000
+    count = 0
+    combined = drug + placebo
+    for i in range(n):
+        shuffle(combined)
+        new_diff = mean(combined[:len(drug)]) - mean(combined[len(drug):])
+        count += (new_diff >= observed_diff)
+
+    print(f'{n} label reshufflings produced only {count} instances with a difference')
+    print(f'at least as extreme as the observed difference of {observed_diff:.1f}.')
+    print(f'The one-sided p-value of {count / n:.4f} leads us to reject the null')
+    print(f'hypothesis that the observed difference occurred due to chance.')