Manuscript Psy03-D@1 · Psy03-D-v1.tex · proposition · 3e18951d

Proposition: Executed candidate rankings and target rankings differ

Intervention accounting and certified matching › Conditional interpolation · lines 1651–1678 · proof included or linked

Psy03-D@1#prop:targetranking

Suppose executed candidate accuracies have simultaneous allowances $r_{0}, r_{1}$ . Then

Q_{1} - Q_{0} > r_{0} + r_{1}

certifies their executed-checkpoint ranking.

To claim an exact-target ranking, additionally suppose

\abs Q_{m c_{m}} - q_{m} (d_{*}) \leq L_{m} \abs d_{m c_{m}} - d_{*} + e_{m} .

For matches within $τ$ ,

q_{1} (d_{*}) - q_{0} (d_{*}) \geq Q_{1} - Q_{0} - r_{0} - r_{1} - (L_{0} + L_{1}) τ - e_{0} - e_{1} .

Proof. Subtract the simultaneous estimate allowances and the declared target-response allowances.

Displayed formulas in this passage

unlabeled · line 1656
$Q_{1} - Q_{0} > r_{0} + r_{1}$
unlabeled · line 1662
$\abs Q_{m c_{m}} - q_{m} (d_{*}) \leq L_{m} \abs d_{m c_{m}} - d_{*} + e_{m} .$
unlabeled · line 1667
$q_{1} (d_{*}) - q_{0} (d_{*}) \geq Q_{1} - Q_{0} - r_{0} - r_{1} - (L_{0} + L_{1}) τ - e_{0} - e_{1} .$