RDMxbCFS · Part 1 · §2–8

The Design

Two binocular 2AFC arms, within participant — the structure, the three candidate versions, the stimuli, the novel obscuring mechanism, the best-practice spine, and the working agreement (roles & milestones).

Contract for discussion · 2026-07-23

Note on § numbering: section numbers are global across the single design-contract source document, not per-page. This page carries §2–8; the gap at §6 (Power) is intentional — it lives on the Power page. Numbers are not renumbered per page so cross-references stay stable.

2 · Experimental structure — two arms, within participant

Each participant completes two arms of a forced binary choice task. Presentation is binocular (both eyes, no dichoptic rivalry) — 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. Both arms yield choice + RT on every trial → DDM.

Arm A — RDMArm B — Faces (RaFD)
Binary choiceleft vs. right motiongaze L/R, or angry/happy — see §3
Difficulty ladder~5 motion-coherence levels {3.2, 6.4, 12.8, 25.6, 51.2}%~5 graded binocular flashing-Mondrian mask levels
DDM predictiondrift v ↑ with coherence (μ′ = k·x, k ~ N(21,6))drift v ↓ with obscuring (Δv ≈ −0.38 … −1.12)
AnchorPalmer, Huk & Shadlen 2005PDFWilliams et al. 2023PDF (RaFD, DDM)
Dependent measureschoice + RT → v, a, t₀, z (both arms)
Two arms, one participant, one pipeline ONE PARTICIPANT within-subject, same session ARM A — Random-dot motion ◀ left vs right ▶ (2AFC) 5 coherence levels 3.2–51.2% drift v ↑ with coherence ARM B — Masked RaFD face angry / happy (V2) · gaze L/R (V1) 5 graded Mondrian mask levels drift v ↓ with obscuring SAME DDM PIPELINE EZ (screen) + HDDM (confirm) choice + RT → v , a , t₀ , z (both arms)
Two arms, one participant, one pipeline. Both the random-dot-motion arm and the masked-face arm feed the same EZ+HDDM pipeline, yielding the identical parameter set v, a, t₀, z on every trial.

The scientific tests

🎧 Contextual deep-dive

b-CFS framing: why Part 1 is deliberately not yet CFS

A spoken explainer on why the project name says “bCFS” but Part 1 uses plain binocular graded masking, not interocular suppression — and what breaking-CFS (b-CFS) would add in a later part.

The whole design in one figure One participant · two 2AFC arms · one drift-diffusion readout (v, a, t₀, z) · four tests T1–T4 ● ONE PARTICIPANT both arms, within-subject, same session ARM A — Random-dot motion ◀ left vs right ▶ (2AFC) ARM B — Masked RaFD face angry / happy (V2) · gaze L / R (V1) difficulty ladder — motion coherence (%) 3.2 6.4 12.8 25.6 51.2 harder easier → difficulty ladder — 5 graded mask levels L5 L4 L3 L2 L1 harder easier → coherence → v (slope A) v difficulty PHS05: µ′=k·x, k~N(21,6) T1 obscuring → v (slope B) v difficulty Williams 2023: Δv −0.38…−1.12 T1 DRIFT-DIFFUSION MODEL upper bound → choice A lower bound → choice B a t₀ z v response time (RT) = t₀ + decision T3 slope A ≡ slope B (TOST) choice + RT fit v,a,t₀,z v drift rate evidence quality — how fast good evidence arrives a boundary sep. caution / threshold — speed–accuracy trade-off t₀ non-decision encoding + motor time, outside accumulation z start point prior bias — where begins accumulation THE FOUR TESTS T1 Graded slope Does obscuring lower drift? v changes monotonically across the ladder — each arm. T2 Selectivity Is it drift-specific? v moves while a and t₀ stay put. T3 Cross-arm equivalence (TOST) Is slope A ≡ slope B in the SAME person? Certifies the pipeline. T4 Across people Do motion-drift and face-drift covary across participants (r)?
The whole design in one figure. One participant spans both arms; each arm has a graded difficulty ladder feeding a central drift-diffusion model that outputs the four fitted parameters. The four tests (T1–T4) are annotated, with T3 linking the two arms’ drift slopes. Standalone file: assets/flagship-design.svg.

3 · The three design versions

Stimulus set for all versions: RaFD (Radboud Faces Database) — on disk, 8,040 images, 67 IDs × 8 emotions × 5 camera angles × 3 gaze directions (left / frontal / right). Frontal camera angle used throughout.

V1 · Gaze

Left vs. right gaze direction

Literature anchor: none — no published gaze-discrimination drift estimate exists. Elegant structural parallel to RDM motion-direction.

Highest novelty; pilot-dependent.

V2 · Emotion · flagship

Angry vs. happy

Literature anchor: Williams 2023PDF (masking→v on RaFD) — the closest published anchor the field offers, though its occlusion geometry differs from our graded noise mask (see Power caveats).

Best-anchored available; recommended flagship.

V3 · Factorial

Gaze × emotion (2×2)

Literature anchor: 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.

Example stimuli — the manipulated dimensions

Gaze LEFT
Gaze RIGHT
ANGRY
RaFD angry face, gaze leftRaFD angry face, gaze right
HAPPY
RaFD happy face, gaze leftRaFD happy face, gaze right
GAZE (V1: left vs right) Gaze LEFT Gaze RIGHT EMOTION (V2: angry vs happy) ANGRY HAPPY V3 = the full 2 × 2 factorial (gaze × emotion) Schematic depiction of the two manipulated dimensions — the real stimuli are photographic RaFD faces.
Schematic of the two manipulated dimensions — gaze (columns) and emotion (rows).

Radboud Faces Database (RaFD), Langner et al. 2010PDF — academic use, kept local. Frontal camera (Rafd090). These are the real manipulated dimensions the task discriminates.

A separate in-house synthetic face set (assets/faces/ex_*.png) exists only as an illustrative pipeline-test set — the study stimuli are RaFD.

4 · Stimuli, apparatus, task — and where each choice comes from

Arm A — Random-dot motion Fixation ~0.5 s Motion stimulus until response coherence 3.2–51.2% Response LEFT RIGHT choice + RT recorded Arm B — Masked RaFD face Fixation ~0.5 s Face + Mondrian mask until response 5 graded mask levels Response ANGRY / HAPPY or gaze L / R choice + RT recorded time Both arms yield choice + RT on every trial → drift-diffusion model (v, a, t₀, z)
Trial timeline. Fixation → stimulus (motion coherence or a graded face mask) → response, one row per arm. Both arms share the same three-stage structure and record choice + RT.
🎧 Contextual deep-dive

The RaFD face stimulus set

A spoken walkthrough of the Radboud Faces Database — its validation, the frontal/gaze/emotion subsetting this design needs, and why using it is justified on its own norming merits — RaFD is used by our anchor paper (Williams 2023), so it is not novel to the corpus (see Comparison §3.5(a)).

The obscuring mechanism — a novel contribution

The single largest methodological gap the golden-standard comparison surfaces (see Comparison) is that no paper in the 19-paper corpus grades face-masking severity continuously — occlusion/masking has only 1 distinct precedent (Williams 2023; Hartmann 2021 is its preprint, not an independent study), and it is binary (masked vs. unmasked). A continuously graded occlusion/masking manipulation (percentage of face area obscured, or a stepped noise-mask series) has zero precedent in the reviewed literature. This design's graded binocular flashing-Mondrian mask — mirroring the coherence ladder in the RDM arm — must be justified from the RDM/b-CFS graded-noise literature (with Newsome & Paré 1988 cited specifically for per-subject coherence/noise-dot calibration) rather than from a face-specific precedent, since none exists.

Parallel graded difficulty — coherence ↔ mask Arm A: motion coherence Arm B: face-mask level 51.2% 25.6% 12.8% 6.4% 3.2% easiest hardest drift v ↑ with coherence (µ′ = k·x, k ~ N(21,6)) Palmer, Huk & Shadlen 2005 level 1 least obscured level 2 level 3 level 4 level 5 most obscured drift v ↓ with obscuring (Δv ≈ −0.38 … −1.12) Williams et al. 2023 EASIER ↑ HARDER ↓ matched in number of levels titrated per-subject (QUEST / Ψ)
Matched graded difficulty. The motion-coherence ladder (Arm A) and the graded flashing-Mondrian mask ladder (Arm B), matched in number of levels and titrated per subject — coherence ↔ mask.
🎧 Contextual deep-dive

RDM & DDM best practices behind this design

A spoken walkthrough of the RDM/psychophysics tradition this design borrows from: coherence-based graded difficulty, adaptive per-subject calibration, and the EZ+HDDM estimator pairing.

5 · Analysis pipeline (open-source)

The drift-diffusion model — accumulation to a bound a noisy evidence signal races from a start point to one of two boundaries upper boundary → choice A lower boundary → choice B a t₀ z v response time (RT) = t₀ + decision time v drift rate evidence quality / how fast good evidence arrives a boundary separation caution — the speed vs accuracy trade-off t₀ non-decision time encoding + motor time, outside accumulation z start point prior bias — where accumulation begins
The drift-diffusion model. A noisy evidence path starts at z, drifts at rate v across the gap a between two boundaries after a non-decision time t₀, producing a choice and a response time.

7 · Best-practice spine (golden standards)

  1. Pre-registration of hypotheses, N, exclusion rules, and the equivalence margin (before data).
  2. Adaptive per-subject calibration (QUEST/Ψ) to equate difficulty across arms — novel for face-DDM.
  3. Graded difficulty in both arms (coherence ↔ mask), matched in number of levels.
  4. EZ (screen) + HDDM (confirm); report parameter recovery.
  5. Low-level confound controls on RaFD stimuli; counterbalancing of arm order, response mapping.
  6. Distributional RT analysis — never mean-RT (Tipples 2023PDF: conclusions flip with outlier/model choice).
  7. Open task, analysis, and data; local-first tooling.

8 · Roles, milestones, deliverables

Roles

PI

Theory, design sign-off, pre-registration, equivalence-margin decision, writeup lead.

Lab techs

RaFD subsetting (frontal; gaze L/R; angry/happy); graded Mondrian mask generation; PsychoPy task build (extend abcsds/RDM); apparatus & binocular presentation; data collection.

Analysts

EZ + HDDM pipeline; parameter-recovery checks; QUEST/Ψ calibration code; power re-estimation from pilot variance; TOST equivalence; figures.

Milestones (relative to 2026-07-23)

#MilestoneOwnerTarget
M0This contract approvedalltoday
M1RaFD subsets + graded Mondrian masks builttechs+2 wk
M2PsychoPy two-arm task (RDM + face) runningtechs + analysts+4 wk
M3V1 gaze + V2 emotion pilot (~10) → real drift anchors, mask-level slopesall+6 wk
M4Pre-registration (final N, margin, exclusions) from pilot variancePI + analysts+8 wk
M5Main data collection (flagship V2, N≈50)techs+8–16 wk
M6DDM analysis, equivalence, writeupanalysts + PI+16–20 wk

Deliverables of this KB effort: the contract; this interactive KB website; the illustrated slide deck (main acts + annex); the golden-standard comparison; the grounded power analysis.