First draft — preliminary contract for discussion

Scientific project contract meeting

RDMxbCFS (Neuronenas) — Part 1

Within-participant DDM: random-dot motion vs masked-face decisions

Date: 2026-07-23

PI: L. A. Barradas-Chacón

Random-Dot-Motion × binocular Continuous Flash Suppression (full project name) · Part 1 manipulation: graded visual masking (pre-CFS) · Part 1 of N

Press → or Space to advance · ← to go back

§1 · Thesis

The one-line thesis

Goal of Part 1: stand up and validate our in-house DDM data pipeline by measuring, within the same participant, whether perceptual decisions about random-dot motion and about masked RaFD faces are governed by comparable drift-diffusion signatures.

Two very different-looking 2AFC tasks — one classically "low-level" (motion), one "high-level" (faces) — run through the same pipeline, the same participant, the same parameters (v, a, t₀, z). If the drift-diffusion signatures line up, the pipeline is validated as a reusable, domain-general tool.

Roadmap

The argument in five acts

A map of the whole deck — from the design, through stimuli and the model, to the evidence and the power decision.

ACT I

Design

One-line thesis
Two binocular 2AFC arms
Versions V1 / V2 / V3

ACT II

Stimuli & obscuring

RaFD faces
Graded Mondrian mask
Matched difficulty ladder

ACT III

DDM & four tests

DDM primer
Flagship design figure
Tests T1–T4

ACT IV

Evidence & novelty

19-paper corpus
Zero-precedent tally
Retrieved effect sizes

ACT V

Power & decisions

Four claim tiers
Decisions D1–D5 on the table
Simulated power & N

The decision for the room lands in Act V: the five explicit choices D1–D5 — design version (§3), obscuring mechanism (§4), power anchor, claim tier and equivalence margin (§6) — each argued with its cost, and backed by the simulated power distributions. Everything before it is the evidence for that call.

§1 · Honest framing

Reproduction vs. novel — stated plainly

The face arm is not a strict reproduction. Across the 19-paper face-2AFC-DDM corpus, no study combines our elements (RaFD + graded masking + strict 2AFC + full v/a/t₀/z fit) on either axis.

Reproducible

What is established

The RDM arm — Palmer, Huk & Shadlen 2005, well-established proportional-rate diffusion model
The direction of the face effect — masking lowers drift (Williams et al. 2023)

Novel

What is new

The combination: RaFD + graded masking + strict 2AFC + full v/a/t₀/z fit — 0/19 precedent for this exact bundle, on either axis

Part 1 therefore reproduces established directions and methods while being, in combination, a novel design — which is precisely where the publishable contribution sits.

§2 · Experimental structure

Two binocular 2AFC arms, within participant

Presentation is binocular (both eyes, no dichoptic rivalry) — Part 1 is deliberately the pre-CFS validation baseline.

Arm A — RDM

Binary choice: left vs right motion
Difficulty ladder: ~5 coherence levels {3.2, 6.4, 12.8, 25.6, 51.2}%
DDM prediction: drift v ↑ with coherence (µ′ = k·x, k ~ N(21,6))
Anchor: Palmer, Huk & Shadlen 2005

Arm B — Faces (RaFD)

Binary choice: see design versions V1/V2/V3
Difficulty ladder: ~5 graded binocular flashing-Mondrian mask levels
DDM prediction: drift v ↓ with obscuring (Δv ≈ −0.38 … −1.12)
Anchor: Williams et al. 2023 (RaFD, DDM)

Both arms yield choice + RT on every trial → DDM. Dependent measures are identical: v, a, t₀, z.

§4 · Arm A detail

Random-dot motion — the coherence ladder

Stimulus & task

Coherence ladder: {3.2, 6.4, 12.8, 25.6, 51.2}%
Left vs right motion, forced 2AFC
Built on the PI's own open PsychoPy RDK (abcsds/RDM, 2024)

Drift model

µ′ = k·x

Drift scales linearly with coherence proportion x; sensitivity modeled as k ~ N(21,6) between subjects (range ≈ 9–28) across observers/experiments (Palmer, Huk & Shadlen 2005, Table 2).

Anchor: Palmer, Huk & Shadlen (2005) — normalized bound A′ ≈ 0.71, non-decision time t_R ≈ 300–420 ms, threshold ratio ≈ 3.0–3.8, validating the proportional-rate model across 5 experiments.

§4 · Arm B detail

Masked faces — graded binocular Mondrian obscuring

The manipulation

~5 graded binocular flashing-Mondrian mask levels, titrating discriminability — mirrors coherence in Arm A
Mask levels degrade the RaFD face image progressively, not a single fixed occlusion

Why "pre-CFS"

Despite "CFS" in the project name, Part 1 is deliberately the pre-CFS validation baseline: the flashing Mondrians are a graded masking/degradation of a binocularly-viewed face, not interocular suppression.

No rivalry, both eyes = pre-CFS baseline.

Anchor: Williams et al. 2023 (Sci. Reports) — face-mask occlusion lowers drift rate v; two independent pre-registered studies (N=228 RaFD, N=264 RADIATE).

§4 · Task

One trial, both arms — the timeline

Fixation → stimulus (coherence / mask) → response. Identical structure across arms; every trial yields choice + RT.

§3 · Design versions

Three design versions — flagship = V2 + V1 pilot

Version	Face binary choice	Literature anchor	Notes
V1 — Gaze	left vs right gaze direction	none no published gaze-discrimination drift estimate	Elegant structural parallel to RDM motion-direction. Highest novelty; pilot-dependent.
V2 — Emotion	angry vs happy	Williams 2023 masking→v on RaFD	Best-anchored; recommended flagship.
V3 — Factorial	gaze × emotion (2×2)	partial emotion anchored, gaze not	Richest, most publishable single study; largest N. PI leans here.

Flagship recommendation: run V2 (emotion) as the flagship and a ~10-person V1 (gaze) pilot in parallel to obtain the missing gaze drift anchor; keep V3 costed and ready as the ambitious variant.

§4 · Stimuli

RaFD, not FACES

RaFD (chosen)

Radboud Faces Database — 8040 images on disk
67 IDs (adults + children) × 8 expressions (anger, disgust, fear, happiness, sadness, surprise, contempt, neutral)
× 5 camera angles × 3 gaze directions (left / frontal / right)
Frontal camera angle used for this study
Free for academic use (Langner et al. 2010)

FACES (Ebner 2010) — not chosen

171 models across 3 age groups
6 expressions (neutrality, sadness, disgust, fear, anger, happiness)
Frontal shots only — no gaze-direction variation
Would rule out V1 (gaze) and V3 (factorial) entirely

RaFD is not novel to this corpus — our anchor paper (Williams 2023, Study 1) uses it. The choice is justified on RaFD's own validation (Langner et al. 2010) and its 3 gaze directions (needed for V1/V3), not as a zero-precedent novelty, with low-level confounds (luminance, contrast, spatial frequency) controlled per Purcell 1996, Becker 2011, Calvo 2016.

§3–4 · Stimuli

Real RaFD stimuli — the two manipulated dimensions

Gaze LEFT

Gaze RIGHT

ANGRY

HAPPY

Radboud Faces Database (RaFD), Langner et al. 2010 — academic use, kept local. Frontal camera (Rafd090), model 01.

Columns = gaze (V1), rows = emotion (V2), the 2×2 = the factorial (V3). Only gaze and expression vary. A separate in-house synthetic set is used only for pipeline tests.

§4 · Stimuli

The obscuring mechanism — graded Mondrian masking

Novel · 0/19 precedent for graded severity

Only 1 distinct corpus study masks at all (Williams 2023; Hartmann 2021 is its preprint, not an independent second study), and it is binary (masked vs. unmasked). A continuously graded mask — mirroring the coherence ladder in Arm A — has zero precedent in the face-DDM literature.

Justified from

Newsome & Paré 1988 — coherence/noise-dot fraction logic
Tsuchiya & Koch 2005 — 10 Hz Mondrian dynamics

Not justified from

Any face-DDM precedent — none exists
The RDM/CFS graded-noise tradition is the source, not the face literature

Mask levels titrate discriminability, mirroring coherence in Arm A — imported wholesale from the RDM/CFS tradition rather than replicated from a face-DDM template.

§4 · Parallel difficulty

Matched graded difficulty — coherence ↔ mask

§2 · Scientific tests

The four scientific tests, T1–T4

T1

Graded within-subject drop in v across obscuring — does obscuring lower drift?

T2

Parameter selectivity — is the effect drift-specific (v moves, a/t₀ don't)?

T3 ★

Cross-arm equivalence (TOST) — is the coherence→v slope quantitatively equivalent to the obscuring→v slope, in the same person?

T4

Individual-differences convergent validity — do motion-drift and face-drift covary across people?

T3 is the claim that certifies the pipeline as a reusable tool — quantitative equivalence between a "low-level" and a "high-level" decision would mean the DDM is reading out a domain-general accumulation process.

Background

DDM 60-second primer

Why choice + RT, not mean RT: a single mean-RT number collapses four dissociable processes into one. Tipples (2023): an emotion-DDM conclusion can flip with outlier-removal / RT-model choices — never trust mean RT alone.

The centerpiece

Flagship — the entire design at a glance

§5 · Analysis pipeline

EZ (screen) + HDDM (confirm)

EZ-diffusion

Wagenmakers 2007 — fast, closed-form per-subject baseline. 0/19 precedent — chosen from best-practices, not the corpus.

HDDM

Wiecki, Sofer & Frank 2013 — hierarchical Bayesian. Plurality choice among corpus papers naming a method (4/6).

Why HDDM is required

Simulated parameter recovery at our trial budget:

r_v = 0.99 | r_a ≈ 0.55–0.59 | r_t₀ ≈ 0.53–0.55

Drift is recovered cleanly under EZ; boundary and non-decision time are not. Any "drift-specific" (T2) claim needs HDDM and/or higher trial counts before it can be trusted.

§7 golden standards · comparison

The 19-paper corpus vs. 8 inclusion criteria

Every candidate paper is scored against 8 criteria (2AFC · face stimuli · gaze/emotion axis · graded masking · full DDM fit · within-subject · RaFD-class stimulus set · adequate trials/cell). All eight required for a strict PASS.

0

strict PASS

14

PARTIAL

5

FAIL

Headline: no paper in this set is a strict PASS on all eight criteria simultaneously. No study has run the RDM-equivalent, per-subject-calibrated, graded-masking 2AFC+DDM design on faces — our project would be the first to combine all eight elements at once, for either axis.

§7 · Key slide

The tally — where our design has zero precedent

Full combination (this design)

0/19

Graded masking (any axis)

0/19

Adaptive staircase (QUEST/Ψ)

0/19

EZ-diffusion used

0/19

Emotion as discrimination axis

12/19

Gaze as discrimination axis

2/19

Emotion outnumbers gaze 6:1 among papers that judge the face's own content — and neither of the two gaze papers combines good power with a direct gaze-2AFC-plus-DDM design. These gaps are not weaknesses to hide; they are the design's selling points.

§7 · What the corpus teaches

Best-practice lessons from the 19 papers

Each lesson is argued from a specific source paper — every paper below links to its bibliography entry and full text.

Never trust mean RT

A single mean-RT number collapses four dissociable processes. Tipples shows an angry-vs-happy conclusion can flip with outlier-removal / RT-model choice — so we pre-commit to distributional RT + DDM.

Tipples 2023bib pdf

DDM reveals what mean RT hides

The founding demonstration: a drift-rate difference (threat → v↑ in high-anxious readers) is invisible to mean RT / accuracy but recovered by the full diffusion model — the reason our readout is v,a,t₀,z, not RT.

White, Ratcliff, Vasey & McKoon 2010bib pdf

Pre-register + anchor masking→drift

Two pre-registered studies (N=228 RaFD, N=264) show occluding the expressive face region lowers v (b=−0.38…−1.12). Our masking→drift anchor and our pre-registration discipline come from here.

Williams et al. 2023bib pdf

Energy-match the controls

To prove an emotion→v effect is not a low-level artifact, Sawada contrasts expressions against energy-matched anti-expressions. Our low-level confound controls (luminance, contrast, SF) inherit this logic.

Sawada et al. 2022bib doi

Gaze cueing is a t₀ effect — a warning

Best-powered gaze DDM (N=171, 139,001 trials): the cueing effect loads on non-decision time, not drift (v inclusion 3–13%). A red flag for assuming our gaze arm (V1) will show a clean drift effect — hence the pilot.

Alister, McKay, Sewell & Evans 2023bib doi

Right task, but no DDM

The one direct left/right gaze 2AFC with parametrically graded head×eye angle — but threshold-only, no v/a/t₀ fit. It seeds our gaze stimulus calibration (cone ½-diff ≈10°), not a drift anchor.

Palmer, Caruana & Clifford 2018bib doi

Two lessons repeat across the corpus and become non-negotiable in our pre-reg: (1) distributional RT + full DDM, never mean RT (Tipples, White); (2) low-level confound control (Sawada). The gaze pair (Alister, Palmer) jointly warn that the gaze arm is the fragile one.

Effect sizes retrieved

What the literature actually reports, numerically

Williams et al. 2023 — masking → v

Collapsed-across-emotion, lower-mask vs. none: b = −0.38 [−0.41,−0.34] (Study 1, RaFD, N=228) → b = −0.65 [−0.71,−0.59] (Study 2, RADIATE, N=264). Per-emotion up to b = −1.12 (happiness/sadness).

PHS05 — coherence → v (RDM)

µ′ = k·x, sensitivity modeled as k ~ N(21,6) between subjects (range ≈ 9–28); non-decision t_R ≈ 300–420 ms.

Sawada et al. 2022 — emotion → v

GAP Paywalled — no numeric value retrievable. Direction only: v larger, t₀ shorter, a larger for normal vs. anti-expressions.

Gaze → v

GAP No drift-rate anchor exists. Alister 2023: gaze is a t₀ effect (v inclusion prob. 3–13%). Palmer/Caruana/Clifford/Seymour 2018: no DDM fit at all.

§6 · Power

The claim-tier decision matrix

Binding constraint: N is driven by participants, not trials/cell (60→150 barely moves it).

§6 · Power

The equivalence-margin trade-off

Power curves across sample size for T1, T2, T4, and T3 equivalence margins

Power curves — minimum N by test and equivalence margin (power_curves.png)

§6 · Recommendation

Sample-size recommendation + PI leaning

PI's instinct

Leans toward tiers ① (cheap validation) and ④ (full factorial) — the two ends of the ambition spectrum.

Grounded compromise path

Flagship V2 at N≈50 (tier ②, best-anchored arm)
V1 gaze pilot (~10) in parallel, to obtain the missing drift anchor
Pre-register ③ equivalence at Δ=0.3 as an honestly under-powered secondary outcome
Upgrade to ④ factorial, N≈130 in a committed follow-up

This is the decision the team makes in the room today — the tier choice determines what Part 1 can honestly claim.

§6 · The choices for the room

Decisions on the table

Five explicit decisions. For each: the question, every option with its argument for and its cost, and the current leaning — marked as a leaning, not decided.

D1Discrimination axis / design version — V1 gaze vs V2 emotion vs V3 factorial
D2Obscuring mechanism — graded Mondrian mask vs noise degradation vs dichoptic b-CFS
D3Power anchor — Williams 2023 vs Sawada 2022 vs both, bracketed
D4Claim tier — validation vs +convergent vs strong equivalence vs factorial
D5Equivalence margin (if tier ③) — Δ = 0.5 vs 0.3 vs 0.2

Decision D1 · Design version

QWhich face-discrimination axis is the flagship — and why RaFD, not FACES or synthetic?

V1 — Gaze (L / R) 0/19

FOR — elegant structural mirror of RDM motion-direction (left/right ↔ left/right); the single highest-novelty arm.

COST — no published drift anchor exists (Alister: gaze cueing is a t₀ effect; Palmer: no DDM). Sample size is unknowable until a pilot runs.

V2 — Emotion (angry / happy) anchored

FOR — best-anchored (Williams masking→v on RaFD; emotion 12/19). Powerable today; the safe flagship.

COST — direct angry-vs-happy magnitude (Sawada) is paywalled; less structurally parallel to motion than gaze.

V3 — Factorial (gaze × emotion)

FOR — richest, most publishable single study; the only design that tests an interaction on drift.

COST — largest N (≈80, interaction fragile — 79% power only under optimistic effects); inherits the un-anchored gaze arm.

Why RaFD, not FACES: RaFD ships 3 gaze directions; FACES is frontal-only, which would rule out V1 and V3 entirely. RaFD is justified on its own validation (Langner 2010); it is used by our anchor paper (Williams 2023, Study 1), so it is not novel to the corpus.

Why not synthetic: an in-house synthetic set is used only for pipeline/recovery tests — it lacks the ecological validity and norming a substantive face claim requires.

Leaning, not decided: V2 (emotion) as flagship + a ~10-person V1 (gaze) pilot in parallel to buy the missing drift anchor; keep V3 costed and ready.

Decision D2 · Obscuring mechanism

QHow do we grade the face's discriminability across the difficulty ladder?

Graded binocular Mondrian mask novel · 0/19

FOR — mirrors the coherence ladder in Arm A (Newsome & Paré 1988 for per-subject coherence/noise-dot calibration; Tsuchiya & Koch 2005 10 Hz Mondrian dynamics). Sets up the pre-CFS baseline the parent project builds on.

COST — zero face-DDM precedent for graded severity (only 1 distinct study masks at all — Williams; Hartmann is its preprint — and it is binary). The per-level mask→v slope is assumed linear — must be re-estimated from pilot.

Contrast / phase-noise degradation

FOR — psychophysically standard, continuously parametric, trivially energy-matched; easiest to calibrate.

COST — departs from the Mondrian/CFS lineage that motivates the project; weaker bridge to the eventual b-CFS arm.

Dichoptic b-CFS out of scope

FOR — the project's namesake and ultimate target: true interocular suppression.

COST — out of scope for Part 1 — rivalry/awareness confounds are exactly what the binocular pre-CFS baseline is designed to exclude first.

Leaning, not decided: graded binocular Mondrian mask, explicitly flagged NOVEL (0/19 precedent) and justified from the RDM/CFS graded-noise tradition, not a face-DDM template.

Decision D3 · Power anchor

QWhich effect size anchors the masking→drift power analysis?

Williams 2023 only

FOR — the only numerically retrieved masking→v effect (b = −0.38 … −1.12), pre-registered, RaFD, N=228/264.

COST — masking is binary, not graded; a single-source anchor with no independent magnitude to cross-check.

Sawada 2022 only

FOR — the cleanest direct angry-vs-happy control (energy-matched anti-expressions) — closest to our actual task.

COST — magnitude is paywalled / unavailable; only the direction is known — it cannot seed a number.

Both, bracketed chosen

FOR — brackets the plausible range (conservative Δv = −0.38 → optimistic −1.12); power is reported as an honest band, not a false point estimate.

COST — wider N band; because Sawada gives direction only, the bracket ultimately rests on Williams' magnitudes.

Chosen (not merely leaning): anchor on both, bracketed — Williams supplies the numeric range; Sawada corroborates direction. Note the Sawada magnitude is paywalled/unavailable and remains a flagged gap.

Decision D4 · Claim tier

QHow strong a claim does Part 1 make — and at what participant cost?

① Validation N≈12–16

FOR — cheap, fast, essentially guaranteed (99.8% power at N=16); proves the pipeline reproduces masking→drift and it's drift-specific.

COST — modest claim; T2 selectivity leans on a/t₀ that EZ recovers poorly (needs HDDM); says nothing about cross-domain generality.

② +Convergent N≈50–65

FOR — affordable and publishable; motion-drift and face-drift covary across people on the best-anchored arm (V2).

COST — correlation attenuated by recovery noise (needs N≈50 for r=0.5); it is convergence, not equivalence.

③ Strong equivalence N≈50–260

FOR — the flagship scientific claim: same accumulation process within a person → the DDM as a domain-general readout.

COST — expensive and margin-driven (N≈130 at Δ=0.3, 260 at Δ=0.2); at N≈50 it is honestly underpowered.

④ Full factorial N≈80

FOR — richest single study; an interaction on drift; the most publishable one-shot.

COST — most fragile (79% power only under optimistic d=0.5; not reached under the conservative bracket); inherits the un-anchored gaze arm.

Leaning, not decided: the PI is drawn to ④ and ① (the two ends); the analyst recommendation is ② — flagship V2 at N≈50 (validation + convergent), with ③ equivalence pre-registered at Δ=0.3 as an honestly-underpowered secondary, upgrading to ④/N≈130 in a committed follow-up.

Decision D5 · Equivalence margin (only if tier ③)

QIf we pursue strong equivalence (T3 / TOST), how tight a margin do we defend?

Δ = 0.5 — lenient N≈50

FOR — affordable (same N as tier ②); claims the two slopes are “not wildly different.”

COST — a weak claim — a 0.5 SD band is wide; a skeptic can dismiss the equivalence as vacuous.

Δ = 0.3 — moderate N≈130

FOR — a genuinely defensible “practically equivalent” claim (N≈130; 160 for 90% power).

COST — ≈2.6× the cost of Δ=0.5; infeasible as a first in-house study without a follow-up commitment.

Δ = 0.2 — strict N≈260

FOR — a strong, hard-to-dismiss equivalence claim — the tightest band anyone would ask for.

COST — ≈260 participants (>260 for 90%) — infeasible for Part 1 by a wide margin.

The margin is a PI judgment call: it fixes what "equivalent" means before any data are seen, and every 0.1 SD tighter roughly doubles the sample.

Leaning, not decided: pre-register Δ = 0.3 as a secondary outcome now (honestly underpowered at N≈50), and commit the full N≈130 only in a follow-up that makes equivalence the headline.

§6 · How we choose N

Simulated power — how each tier's N was set

The N's in D4/D5 are not rules of thumb: each is read off a Monte-Carlo simulation of this exact pipeline.

How to read the next five figures

Each is the empirical sampling distribution of the actual test statistic, 3,200 iterations per arm, at the recommended N.
The H0 curve = no effect; the H1 curve = the true (bracketed) effect.
The 5% α critical value and the power region (target 80%) are shaded directly on the curves.

Which figure backs which decision

Scenario 1 → tier ① (D4) · V2 / T1
Scenario 2 → tier ② (D4) · V2 / T4
Scenario 3 → tier ③ (D4) + D5 margin · T3 TOST
Scenario 4 → tier ④ (D4) · V3 interaction
Scenario 5 → V1 gaze pilot (D1) · extrapolated

How we choose N · Scenario 1 → Tier ①

Validation — N = 16 (V2, test T1)

Power scenario 1: H0 vs H1 distributions for the validation test T1 at N=16, with 5% alpha and 80% power regions

H0 (no masking effect) vs H1 (conservative Δv = −0.38, Williams Study 1) at N=16, 100 trials/cell, α=0.05 two-sided

Because the masking effect is huge relative to N=16 sampling noise, the two distributions barely overlap — achieved power 99.8%. “Obscuring lowers drift” is essentially guaranteed to be detected.

The honest reading: N=16 is already more than this test needs. The real constraint on tier ① is practical (recruit a small cohort), not statistical.

How we choose N · Scenario 2 → Tier ②

Convergent validity — N = 50 (V2, test T4)

Power scenario 2: one-sided H0 vs H1 distributions for the cross-arm correlation T4 at N=50

Cross-arm drift correlation, true r=0.5, N=50, 100 trials/cell; one-sided α=0.05 (H1: r>0)

Recovered r is centered near 0.35–0.40 — attenuated well below the true 0.5 by EZ-recovery noise. That attenuation is exactly why N=50, not the textbook ~28, is required for 80% power.

Achieved power 81.0% — matches the report's headline N=50 recommendation for the recommended default tier.

How we choose N · Scenario 3 → Tier ③ + margin D5

Strong equivalence — N = 130, Δ = 0.3 (test T3, TOST)

Power scenario 3: TOST equivalence geometry at N=130 with a 0.3 SD acceptance interval

TOST cross-arm slope difference: H1 = true equivalence (diff=0); H0 = boundary of non-equivalence (diff=+0.3 SD). Dashed lines = the Δ=0.3 acceptance interval, N=130

Mass of the true-equivalence curve inside the acceptance interval = power (87.6%); the boundary-null curve inside it = Type-I error (≈5%).

The single most expensive claim in the design. N=130 buys only the moderate Δ=0.3 margin (D5); a tighter, more defensible Δ=0.2 needs roughly double.

How we choose N · Scenario 4 → Tier ④

Full factorial — N = 80 (V3, gaze × emotion interaction)

Power scenario 4: H0 vs H1 distributions for the gaze-by-emotion interaction at N=80 under an optimistic effect

Gaze×emotion interaction contrast on v, N=80, 100 trials/cell, α=0.05 two-sided; effect = extrapolated d=0.5 (optimistic bracket, paired with Δv=−1.12)

Achieved power 79.1% — right at the 80% line, but only under the optimistic effect. No published anchor exists for this interaction.

The design's most fragile confirmatory claim: under the conservative bracket it is not reached at all without N well beyond 80.

How we choose N · Scenario 5 → V1 gaze (D1)

Gaze arm — N = 10 pilot (V1, EXTRAPOLATED)

Power scenario 5: gaze-arm T1 at N=10 with an inset sensitivity band sweeping baseline drift

Masking→drift (T1) applied to the gaze arm, N=10, 60 trials/cell. Main panel: baseline v=2.0 (85.9% power). Inset: sensitivity band sweeping the un-anchored baseline v ∈ {1.0,1.5,2.0,2.5}

The Williams Δv=−0.38 slope is borrowed onto a gaze task with no published drift anchor (Alister: gaze cueing loads on t₀, not v). So the power claim is a range (71–94%), not a point.

The band straddles the 80% line — which is the argument for running the ~10-subject pilot (D1) before committing a full V1 sample.

§7–8 · Plan

Best-practice spine + roles & milestones

Pre-registration (hypotheses, N, exclusions, margin)
Adaptive per-subject calibration (QUEST/Ψ) — novel for face-DDM
Graded difficulty in both arms, matched levels
EZ (screen) + HDDM (confirm); report recovery
Low-level confound controls; counterbalancing
Distributional RT analysis — never mean-RT
Open task, analysis, and data

M0
Contract approved
today

M1
RaFD subsets + masks built
+2 wk

M2
Two-arm PsychoPy task running
+4 wk

M3
V1+V2 pilot (~10)
+6 wk

M4
Pre-registration
+8 wk

M5
Main collection (N≈50)
+8–16 wk

M6
DDM analysis + writeup
+16–20 wk

§9 · Where the science is

Research gaps — the decision to be made today

No drift-rate estimate exists for gaze-direction discrimination — V1 answers this.
Graded masking of faces + full DDM has never been run — T3 answers this.
Within-person equivalence of a "high-level" and "low-level" decision is untested — a domain-general accumulation claim.
Reliability/individual-differences of face-DDM parameters is essentially unstudied (T4) — a tool for clinical/developmental work.
Sawada 2022 magnitude gap — a concrete literature-completion task.

The decision for the room: which claim tier (§6) and which design version (§3) do we commit to for Part 1?

Listen

Two audio deep-dives

Spoken walkthroughs — a general overview and a focused dive on the design decisions and DDM parameters.

General deep-dive

The whole design contract — two-arm structure, the three versions, the golden-standard literature comparison, the power analysis, and the open questions.

Design decisions & parameters

A focused dive on the design choices and the four DDM parameters (v, a, t₀, z) — why each option was taken and what it buys.

Annex

Supporting material — full tables, checklists, figures, and references

A1Full 19-paper comparison table
A1·Which design each paper uses — linked (bib + PDF)
A2The 8-criterion checklist
A3Per-test / per-version N tables
A4Equivalence-margin table (T3, full)
A5Parameter recovery — recovery_scatter.png
A6Effect-size provenance table
A7Full milestone timeline + roles
A8RaFD dataset structure
A9Glossary of DDM terms
A10References — key anchors & corpus

Annex A1

Full 19-paper comparison table

Verdicts against the 8-criterion checklist. Every paper's reference + full text is linked in the companion design table on the next slide.

Paper	DOI	Verdict	One-line reason
Sawada, Sato, Nakashima & Kumada 2022	10.1016/j.cognition.2022.105235	PARTIAL	Face-in-crowd detection, not single-face 2AFC; no graded masking; best precedent for anger/happy→v direction.
Brennan & Baskin-Sommers 2020	10.1177/0956797620904157	PARTIAL	Emotion-identification (likely >2 alternatives); no masking; individual-difference design.
Brennan & Baskin-Sommers 2021	10.1037/per0000473	PARTIAL	3-way blend/context grading, not occlusion; >2 response options.
White, Ratcliff, Vasey & McKoon 2010	10.1037/a0019474	FAIL	Threat words, not faces — fails stimulus criterion outright.
Williams, Haque, Mai & Venkatraman 2023	10.1038/s41598-023-35381-4	PARTIAL	Best masking precedent; but 6-way choice and binary (not graded) masking. Strongest structural match overall.
Hartmann et al. 2021 (preprint)	10.31234/osf.io/a8yxf	PARTIAL (low conf.)	Duplicate of Williams 2023 design; no independent verifiable data.
Ozturk et al. 2024	10.1016/j.bpsgos.2023.07.005	PARTIAL	Graded manipulation is cue uncertainty, not masking of the face itself.
Nagrodzki et al. 2025	10.1037/emo0001499	FAIL	Face is a task-irrelevant incidental prime, not the judged stimulus.
Klein & Todd 2024	10.3758/s13423-024-02526-z	FAIL	2AFC axis is weapon-vs-tool identification; face is priming context.
Nan et al. 2024	10.1016/j.psyneuen.2023.106948	PARTIAL (strong)	Morph-continuum grading, not occlusion/masking; pharmacological RCT design.
Schreiber, Hall, Parr & Hallquist 2025	10.1017/S0033291725000595	PARTIAL	Difficulty via congruent/conflicting emotion words, not masking.
Haller et al. 2024	10.1093/scan/nsae034	PARTIAL (strong)	Morph-continuum labeling, closest emotion-axis analog; small N=44 (fMRI).
Schrader, Habel, Jo, Walter & Wagels 2023	10.1016/j.concog.2023.103493	PARTIAL (strong)	Graded exposure duration — genuine masking-like manipulation; but 3-way choice.
Yang, Brunet-Gouet, Burca, Kalunga & Amorim 2020	10.3389/fnhum.2020.00340	PARTIAL	Upright/inverted × photo/sketch degradation; binary factorial, not graded continuum.
Evans et al. 2025	10.1080/02699931.2025.2533382	FAIL (axis)	Approach-vs-avoid choice, not emotion/gaze identification.
Maka, Chrustowicz & Okruszek 2023	10.1111/psyp.14406	FAIL (axis)	Dot-probe task — response is about probe location, not the face.
Tipples 2023	10.1037/emo0001098	PARTIAL	Methods-critique paper, not a new effect-size report; no masking.
Alister, McKay, Sewell & Evans 2023	10.1177/17470218231181238	PARTIAL	Best-powered gaze precedent (N=171, 139,001 trials); but cueing task, not direct gaze judgment.
Palmer, Caruana & Clifford 2018	10.1098/rsos.180885	PARTIAL	Closest gaze-axis task structure; but no DDM fit at all — threshold-only.

Annex A1 · continued

Which design does each paper use — linked

Stimulus set · axis · degradation · DDM software · titration · N. Each row links to its bibliography entry (bib) and full text (pdf local, or doi where no PDF is held).

Paper	Stimulus set	Axis	Degradation	DDM software	Titration	N
Sawada et al. 2022bib doi	not stated (face-in-crowd)	Emotion (angry/happy vs anti-expr.)	anti-expression control (not graded mask)	custom (Ratcliff-style)	none	n/r
Brennan & Baskin-Sommers 2020bib doi	not stated	Emotion (anger)	none (individual-difference)	not stated (DDM)	none	90
Brennan & Baskin-Sommers 2021bib doi	not stated	Emotion (anger/happy/fear blends)	blend + threat context (not mask)	not stated	fixed blend levels	92
White, Ratcliff, Vasey & McKoon 2010bib pdf	threat words (not faces)	lexical decision	none	Ratcliff full-DDM	none	n/r
Williams, Haque, Mai & Venkatraman 2023bib pdf	RaFD (S1) / RADIATE (S2)	Emotion (6-way, incl. anger)	mask occlusion (binary)	DDM (not named)	none (binary)	228 / 264
Hartmann et al. 2021 (preprint)bib pdf	as Williams	Emotion (6-way)	mask occlusion (binary)	not stated	none	as Williams
Ozturk et al. 2024bib doi	not stated	Threat vs neutral	pre-stimulus cue uncertainty (not face mask)	HDDM + SDT	none	55
Nagrodzki et al. 2025bib doi	not stated	Angry/neutral (task-irrelevant)	none (incidental prime)	DDM	none	134
Klein & Todd 2024bib pdf	Black/White faces (prime)	weapon ID (face incidental)	expression salience factor	diffusion decision model	none	546
Nan et al. 2024bib pdf	not stated	Emotion (anger/fear morphs)	morph continuum (not occlusion)	DDM + SDT	fixed morph levels	120
Schreiber, Hall, Parr & Hallquist 2025bib pdf	not stated	Emotion decoding	emotion-word conflict (not mask)	HDDM	none	86
Haller et al. 2024bib doi	not stated	Emotion (happy-angry morph)	morph continuum	DDM (sens./bias)	fixed continuum steps	44
Schrader, Habel, Jo, Walter & Wagels 2023bib doi	not stated	Emotion (sad/neutral/happy, 3-way)	graded exposure duration (8.3/16.7/25 ms)	HDDM	3 fixed durations	40
Yang et al. 2020bib pdf	photo / sketch versions	Emotion recognition	inversion + sketch (not occlusion)	DDM + ERP	none (binary factorial)	n/r
Evans et al. 2025bib doi	happiness/anger morphs	approach/avoid (face incidental)	morph continuum	DDM	fixed morph levels	n/r
Maka, Chrustowicz & Okruszek 2023bib doi	not stated	dot-probe (face incidental)	none	DDM + N2pc	none	52
Tipples 2023bib pdf	not stated	Emotion (angry vs happy, 2AFC)	none (methods critique)	recommends DDM / ex-Gaussian	none	n/r
Alister, McKay, Sewell & Evans 2023bib doi	real face photos (gaze-cueing)	Gaze (cue; response = target)	none (congruent/incongruent)	diffusion / LBA, hierarchical Bayes	none	171
Palmer, Caruana & Clifford 2018bib doi	own gaze photos (not RaFD)	Gaze (left/right, direct 2AFC)	head × eye angle (graded angle, not occlusion)	none (threshold-only)	per-participant threshold	22 SZ / 27 HC

“not stated” = the value is absent from the KB card and needs primary-source retrieval; “n/r” = no numeric N reported. Values quoted verbatim from data/analysis/ddm-face-comparison.md §3.

Annex A2

The 8-criterion checklist

#	Criterion	Operational test
C1	Forced binary choice (2AFC)	Exactly two response options — not go/no-go, not >2-way categorization, not a rating scale.
C2	Face stimuli	Discriminated stimulus is a face image — not words, dot arrays, or objects.
C3	Axis = gaze OR emotion of the face itself	Judgment is about the face's own gaze/emotion — not a downstream cued target or orthogonal task.
C4	Graded difficulty via masking/obscuring	Discriminability parametrically manipulated by occlusion/noise/masking — not fixed-intensity prototypes only.
C5	Full DDM fit reported	Drift rate v recovered via a diffusion/sequential-sampling model — not threshold-only or SDT d′ alone.
C6	Within-participant repeated measures	Same subjects run across multiple difficulty/condition levels.
C7	RaFD or comparably validated stimulus set	RaFD, KDEF, NimStim, or FACES with reported norms — not unvalidated in-house photos.
C8	Adequate trial counts for per-cell recovery	N and trials/condition sufficient in principle for stable v estimation (≥100/cell EZ, ≥20–40/cell HDDM).

All eight required for a strict PASS; satisfying task-family intent but failing structural items = PARTIAL; failing the core task family = FAIL.

Annex A3

Per-test / per-version minimum-N tables

T1 / T2 — validation core

Test	V1	V2	V3
T1 (masking lowers v)	≤8	≤8	≤8
T2 (drift-specific)	8–10	8–10	8–10

T4 — convergent validity

True r	min N 80%	min N 90%
r = 0.5	50	65
r = 0.3	>100	>100

V3 factorial — main effects & interaction (optimistic bracket)

Contrast	min N 80%	min N 90%
Gaze main effect	50	65
Emotion main effect	50	65
Gaze × emotion interaction	80	>80

Conservative bracket: V3 main effects/interaction not reached within the simulated grid — factorial version viable only under optimistic effects or N ≥ ~80.

Annex A4

T3 equivalence — full margin table

Target power	Margin Δ (SD)	Min N
80%	0.2 (strict)	260
80%	0.3 (moderate)	130
80%	0.5 (lenient)	50
90%	0.2 (strict)	>260 (not reached)
90%	0.3 (moderate)	160
90%	0.5 (lenient)	65

This is the binding constraint and the PI's decision. Trials/cell (60/100/150) barely move these N's — the cost is entirely in participants. Williams' masking is binary; our graded severity is an interpolated assumption, to be re-estimated from pilot data.

Annex A5

Parameter recovery — recovery_scatter.png

Simulated parameter recovery scatter plots for v, a, t0

True vs. recovered v, a, t₀ under EZ-diffusion, n=2000 synthetic subjects

r_v: 0.9873 — excellent
r_a: 0.5894 — weak
r_t₀: 0.5317 — weak
RT-variance inflation: ≈ 3.95×
Drift rescaling: SCALE_K = 0.32552 (PHS05 k=21.0 → top-coherence v=3.5)

n=2000 synthetic subjects, seed 20260723. Drift is recovered cleanly; boundary and non-decision time are not — motivates HDDM confirmatory fitting for the selectivity claim.

Annex A6

Effect-size provenance table

Source	Design	Value	Status
Williams et al. 2023, Study 1	RaFD, N=228, DDM (software not named), 648 trials/pp	masking→v: b=−0.38 [−0.41,−0.34]	Retrieved (PMC full text)
Williams et al. 2023, Study 2	RADIATE, N=264, DDM (software not named), 324 trials/pp	masking→v: b=−0.65 [−0.71,−0.59]; happiness/sadness up to b=−1.12	Retrieved (PMC full text)
Williams et al. 2023 (boundary a)	same	a ≈ 1.67–1.80 across mask/emotion conditions	Retrieved; no t₀/z reported anywhere
Sawada et al. 2022	face-in-crowd detection	direction only: v↑, t₀↓, a↑ for normal vs. anti-expression	GAP — paywalled, no OA/preprint found
Palmer, Huk & Shadlen 2005 (PHS05)	6 observers, coherence 3.2–51.2%	µ′=k·x; mean k=20±3 (Exp.1), k=21±1/22±1 (Exp.3); A′≈0.6–0.86; t_R≈300–420ms; threshold ratio≈3.0–3.8	Retrieved (author PDF, PyMuPDF extraction)
Alister, McKay, Sewell & Evans 2023	3 gaze-cueing datasets, N=171, 139,001 trials	v has lowest model-inclusion probability (3–13%) of the 3 DDM parameters; no numeric v/z shift reported	GAP — v/z magnitudes not numerically reported
Palmer, Caruana, Clifford & Seymour 2018	gaze 2AFC, N=22 SZ / 27 HC	cone-model half-difference: SZ 9.94° (sd 9.58°); HC 10.68° (sd 6.81°)	Retrieved; no DDM fit exists in this paper

Annex A7

Full milestone timeline + roles

#	Milestone	Owner	Target
M0	This contract approved	all	today
M1	RaFD subsets + graded Mondrian masks built	techs	+2 wk
M2	PsychoPy two-arm task (RDM + face) running	techs + analysts	+4 wk
M3	V1 gaze + V2 emotion pilot (~10) → real drift anchors, mask-level slopes	all	+6 wk
M4	Pre-registration (final N, margin, exclusions) from pilot variance	PI + analysts	+8 wk
M5	Main data collection (flagship V2, N≈50)	techs	+8–16 wk
M6	DDM analysis, equivalence, writeup	analysts + PI	+16–20 wk

Roles

PI: theory, design sign-off, pre-registration, equivalence-margin decision, writeup lead
Lab techs: RaFD subsetting, graded Mondrian mask generation, PsychoPy task build, apparatus, data collection
Analysts: EZ+HDDM pipeline, parameter-recovery checks, QUEST/Ψ code, power re-estimation, TOST, figures

Deliverables

This contract
Interactive KB webpage (report/)
This illustrated deck — main acts + annex (presentation/)
Golden-standard comparison
Grounded power analysis

Annex A8

RaFD dataset structure

Radboud Faces Database (Langner et al. 2010)

67 IDs × 8 expressions × 5 camera angles × 3 gaze = 8040 images

Models: 67 (adults + children)
Expressions (8): anger, disgust, fear, happiness, sadness, surprise, contempt, neutral
Camera angles (5): full range; frontal angle used for this study
Gaze directions (3): left / frontal / right
Access: free for academic use; on disk locally
Used for: V1 (gaze L/R), V2 (angry/happy), V3 (2×2 factorial)

Annex A9

Glossary of DDM terms

Term	Meaning
2AFC	Two-alternative forced choice — exactly two response options per trial
v (drift rate)	Average rate of evidence accumulation; the signal-quality parameter
a (boundary separation)	Distance between the two decision thresholds; speed–accuracy tradeoff
t₀ / Ter (non-decision time)	Encoding + motor time outside the accumulation process
z (starting point / bias)	Where accumulation begins relative to the two boundaries
µ′ = k·x	Proportional-rate diffusion model: drift scales linearly with stimulus strength x, sensitivity k
EZ-diffusion	Fast, closed-form per-subject DDM estimator (Wagenmakers 2007)
HDDM	Hierarchical Bayesian DDM fitting package (Wiecki, Sofer & Frank 2013)
TOST	Two one-sided tests — the standard statistical procedure for testing equivalence
QUEST / Ψ	Adaptive psychophysical staircase procedures for per-subject difficulty calibration
Parameter recovery	Simulation check: can the fitting procedure recover known true parameter values?

Annex A10

References — key anchors & corpus

Key anchors

Palmer, Huk & Shadlen 2005 — J. Vision, DOI 10.1167/5.5.1
Williams et al. 2023 — Sci. Reports, DOI 10.1038/s41598-023-35381-4
Ratcliff & McKoon 2008 — DDM foundations
Wiecki, Sofer & Frank 2013 — HDDM
Wagenmakers et al. 2007 — EZ-diffusion
Langner et al. 2010 — RaFD validation, DOI 10.1080/02699930903485076
Tsuchiya & Koch 2005 — Mondrian CFS dynamics
Stein, Hebart & Sterzer 2011 — b-CFS background
Tipples 2023 — Emotion, DOI 10.1037/emo0001098

Full bibliography: data/biblio/references.yaml (140 entries).

Corpus & provenance sources

19-paper golden-standard comparison: data/analysis/ddm-face-comparison.md
Retrieved effect sizes: data/analysis/effect-sizes-retrieved.md
Power analysis: data/power/power_report.md, power_analysis.py
Contract source: design/2026-07-23-rdmxbcfs-part1-design.md
Alister, McKay, Sewell & Evans 2023 — QJEP, DOI 10.1177/17470218231181238
Palmer, Caruana, Clifford & Seymour 2018 — R Soc Open Sci, DOI 10.1098/rsos.180885
Sawada, Sato, Nakashima & Kumada 2022 — Cognition, DOI 10.1016/j.cognition.2022.105235