Manuscript Psy03-B@1 · Psy03-B-v1.tex · theorem · 8ca3caf9

Theorem: Checkpoint-specific effect certificate

Counterfactual sensitization and persistent vulnerability › Fresh paired assessment · lines 1461–1485 · proof included or linked

Psy03-B@1#thm:paired

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Condition on two checkpoints before a fresh assessment block. Let independent example blocks give paired correctness differences

D_{i} = C_{0, i} - C_{1, i} \in [- 1, 1], Δ = \frac{1}{n} i \sum D_{i} .

Then

P {\abs Δ - Δ > r_{D} ∣ history} \leq δ_{D}, r_{D} = \frac{2 lo g ( 2/ δ _{D} )}{n} .

A positive $Δ - r_{D}$ certifies the oriented effect at the named challenge and checkpoints.

Proof. Condition on the checkpoint history and apply Hoeffding on an interval of length two Hoeffding. This is the fresh-assessment form of the paired comparison and ranking interfaces in Psy03-A CheungPsy03A.

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unlabeled · line 1465
$D_{i} = C_{0, i} - C_{1, i} \in [- 1, 1], Δ = \frac{1}{n} i \sum D_{i} .$
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$P {\abs Δ - Δ > r_{D} ∣ history} \leq δ_{D}, r_{D} = \frac{2 lo g ( 2/ δ _{D} )}{n} .$

Theorem: Checkpoint-specific effect certificate

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