Manuscript Psy03-C@1 · Psy03-C-v1.tex · proposition · d3380b90

Proposition: A probe name does not identify a mechanism

Battery and longitudinal effect certificates › Construct identifiability · lines 1483–1507 · proof included or linked

Psy03-C@1#prop:identifiability

For two models with equal complete accessible record laws under the admitted battery, every randomized binary test satisfies

α + β = 1.

More generally,

α + β \geq 1 - d_{TV} (P_{0}, P_{1}) .

Equality of battery means is weaker than equality of complete record laws. Neither equality alone assigns a cognitive interpretation.

Proof. For a test $ψ \in [0, 1]$ ,

α + β = 1 + E_{0} ψ - E_{1} ψ .

Use total variation. Means retain only selected expectations of the complete law.

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