Problem Statement

A new medical treatment was tested on a population of

n + m

{\displaystyle n+m}

volunteers, with each volunteer randomly assigned either to a group of

n

{\displaystyle n}

treatment subjects, or to a group of

m

{\displaystyle m}

control subjects.
Members of the treatment group were given the treatment, and members of the control group were given a placebo. The effect of the treatment or placebo on each volunteer was measured and reported in this table. Write a program that performs a permutation test to judge whether the treatment had a significantly stronger effect than the placebo.

Extremely dissimilar values are evidence of an effect not entirely due to chance, but your program need not draw any conclusions. You may assume the experimental data are known at compile time if that's easier than loading them at run time. Test your solution on the data given above.

Let's start with the solution:

fcn permutationTest(a,b){
   ab    := a.extend(b);
   tObs  := a.sum(0);
   combs := Utils.Helpers.pickNFrom(a.len(),ab);  // 92,378
   under := combs.reduce('wrap(sum,perm){ sum+(perm.sum(0) <= tObs) },0);
   100.0 * under / combs.len();
}
 
treatmentGroup := T(85, 88, 75, 66, 25, 29, 83, 39, 97);
controlGroup   := T(68, 41, 10, 49, 16, 65, 32, 92, 28, 98);
under          := permutationTest(treatmentGroup, controlGroup);
println("Under =%6.2f%%\nOver  =%6.2f%%".fmt(under, 100.0 - under));