Use simulation to decide whether data are consistent with a proposed model.
Match a simulation to random assignment or sampling
Problem
A randomized experiment assigns \(20~\text{units}\) equally to treatment and control and observes a treatment-minus-control mean difference of \(4.2\). Of \(1,000\) valid shuffles, \(18\) were at least as large. State the no-effect shuffle, statistic, \(p\text{-}\text{value}\), and conclusion at \(\text{alpha}~=~0.05\).
Big Picture
What this problem is really about
A randomization test must reproduce what was random in the experiment. Under a no-effect explanation, keep the observed outcomes and fixed group sizes unchanged, reshuffle only the treatment labels, and calculate the same directional statistic after every shuffle. The extreme-shuffle proportion is then compared with alpha, with any causal interpretation bounded by the randomized design and its experimental units.
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