Lemma. Matched protocols isolate a conditional policy contrast [ftip-00DV]
Lemma. Matched protocols isolate a conditional policy contrast [ftip-00DV]
Let \(m\in \mathbb N_{\geq 1}\) and let \(Y_{1j},Y_{2j}\in \mathbb R\) for \(j=1,\ldots ,m\) be the paired scalar evaluator outcomes generated by the protocol of Definition [ftip-00DU]. Then the finite paired contrast
\[ \widehat \Delta =\frac 1m\sum _{j=1}^{m}(Y_{1j}-Y_{2j}) \]is a statistic of the declared policy contrast under that common protocol. It is not an unconditional capability effect and does not identify what would happen after changing any held-fixed coordinate.