Korthals target-tracking: a robust negative result

This case shows what GazeAudit means by propagating measurement uncertainty into a scientific endpoint without turning a measurement-model interval into a population confidence interval.

Frozen estimand

The AOI is a target-centred circle with radius 1 dva. The endpoint is jumping-circle occupancy minus moving-circle occupancy. Complete matched-cell contrasts are averaged without weighting within participants and participant estimates are then averaged without weighting at study level.

The frozen grouped isotropic Gaussian gaze-error model uses validation error_avg, zero bias, 2,000 Monte Carlo draws, batch size 8, seed 20260316, and zero as the directional reference.

Korthals effect plot showing a hard effect of minus 0.09864 and a measurement-error expected effect of minus 0.07401 with a 95 percent measurement-model interval entirely below zero — **Observed frozen result.** Hard and uncertainty-propagated effects differ in magnitude but retain the same negative direction. The interval shown is induced by the prespecified measurement model.

Authoritative numbers

Quantity	Frozen result
Observations	448,336
Retained trials	999
Monte Carlo draws	2,000
Hard effect	−0.0986408756
Expected membership effect	−0.0740075674
Monte Carlo SD	0.0013013517
95% measurement-model interval	[−0.0765249127, −0.0714615962]
Probability below zero	1.0
Probability above zero	0.0
Classification	`robust_negative`

The predeclared rule assigns robust_negative when the hard effect is negative and at least 95% of measurement-error draws are below zero. All 2,000 draws were below zero.

What changed after propagating measurement uncertainty?

The estimated magnitude moved toward zero: from approximately −0.09864 under hard binary membership to −0.07401 under expected probabilistic membership. That shift is substantively useful. A stable direction does not imply that deterministic AOI assignment and uncertainty-aware assignment are numerically interchangeable.

The scientific statement is intentionally narrow:

Under the frozen paired AOI estimand, target-centred 1-dva occupancy was lower for jumping circles than for moving circles, and the negative direction remained stable under the prespecified measurement-error propagation model.

Inferential boundary. The 95% interval is a measurement-model-induced interval. It is not a population confidence interval, Bayesian posterior interval, or causal-effect interval. The Monte Carlo sign probabilities describe uncertainty induced by the frozen measurement model; they are not population p-values.

Why this matters for practice

Hard AOI membership can hide boundary uncertainty even when the final sign is stable. For a new study, the useful question is therefore not merely whether a probabilistic analysis changes significance. Ask how the endpoint moves, which observations drive uncertainty, and whether the declared scientific conclusion survives the measurement model you justified before inspecting the result.

Provenance snapshot

Scientific workflow: korthals-scientific-execution #1
Execution commit: 3312423cb43b1d9da3877914455dd471aba81174
Protocol-v2 fingerprint: 1cd4150c9341db145b8f6aee544f9634c67c46116e61e7e675ae3c50282d2d55
Artifact ID: 10306308440
ZIP SHA-256: 2eaab8171d9d5f70e138eb929554648cb6bed10b21646ab0acd7cfae4d607d11
Audit scientific fingerprint: aa4c04af9c011fe997ef107c8250b20d6a20824b180abdeb16871b5b5a2fc768

Authoritative source

This page is an explanatory view. The frozen authority is the Korthals protocol-v2 result and the validation matrix.