Problem

A randomized experiment assigns \(30~\text{units}\) equally to treatment and control and observes an absolute median difference of \(2.5\). Of \(2,000\) valid shuffles, \(164\) were at least as large. State the no-effect shuffle, statistic, \(p\text{-}\text{value}\), and conclusion at \(\text{alpha}~=~0.05\).

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Under no treatment effect, shuffle the 15/15 labels among the fixed outcomes and use the absolute median difference. The p-value is 164/2000 = 0.082, so the result is not significant at alpha = 0.05.

Under no treatment effect, shuffle the fixed 15/15 labels among the outcomes and use the absolute median difference. The p-value is 164/2000 = 0.082, so report a significant result at alpha = 0.05.

Under no treatment effect, shuffle the fixed 15/15 labels among the outcomes but use the signed mean difference. The p-value is 164/2000 = 0.082, so report a nonsignificant result.

Under no treatment effect, redraw the 30 outcomes and allow the two group sizes to vary; use the absolute median difference. The p-value is 164/2000 = 0.082, so report a nonsignificant result.

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