P-D2 Pre-registration: Thresholds
Pre-registered: 2026-08-29 · Bet: P-D2 — does semantic priming follow embedding proximity or the association edge?
Published on this site 2026-10-05; content as frozen on 2026-08-29.
This page reproduces sections 7–10 of the pre-registration: the primary metric and decision rules, the secondary tests, the blind twins, and the statistical plan. The pre-registration was written before any contact with the data. Section numbers are kept from the original document.
Context needed to read the rules
These points are taken from the earlier sections of the same document.
- BMC’s hypothesis (H1). Among prime–target pairs with no association edge in either direction, priming increases with proximity in the embedding space (Definition 14.2 on the Network Memetics page), over and above word-level nuisance variables and over and above graded multi-step association strength. H1b: the effect is rank-gated — present for primes inside the target’s top-$K$ embedding neighbourhood and absent outside it, producing a knee rather than a smooth decay.
- The rival. Graded spreading activation over an associative network (Collins & Loftus 1975 and its descendants), with free-association norms as the edge set and multi-step random-walk strength as the graded quantity. It predicts $\beta_{\text{walk}} \neq 0$ , $\beta_{\cos} \approx 0$ .
- Design. In the Semantic Priming Project (SPP), every target is preceded, in different trials, by two unrelated primes. By construction these have zero forward association to the target, but their embedding proximity to it varies by chance. The test is a within-target paired contrast over these unrelated primes.
- Graded-rival block. Two-step random-walk strength from prime to target over the Small World of Words (SWOW-EN) weighted association graph, plus USF forward and backward association strength as separate terms.
- Nuisance block (in every model). Prime log frequency, prime length, prime orthographic neighbourhood size, target identity (random intercept), subject identity (random intercept), task (lexical decision / naming), SOA (200 / 1200 ms).
- Stage 0. Apparatus gates run before the primary: recovery of the standard relatedness effect (positive control), embedding coverage, a minimum number of usable pairs, and a zero-association rule (forward and backward strength must be zero in both norm sets).
- Prior evidence that leans against H1 (added on publication; not part of the frozen document). In an item-level analysis of 300 associated prime–target pairs, priming grew with forward associative strength but did not vary with LSA similarity (Hutchison, Balota, Cortese & Watson 2008, Quarterly Journal of Experimental Psychology 61(7):1036–1066, doi:10.1080/17470210701438111). LSA is a different similarity measure from the embedding used here, and that sample contained only associated pairs, so the result does not decide P-D2; it is the published finding closest to the rival’s side.
7. Primary metric, and the falsification thresholds in both directions
Primary metric. $\beta_{\cos}$ — the standardized fixed-effect coefficient of prime–target cosine similarity on z-scored RT, in a mixed-effects model over unrelated trials only, with crossed random intercepts for subject and target, containing the nuisance block and the graded-rival block. Sign convention: BMC predicts $\beta_{\cos} < 0$ (more proximity ⇒ faster).
One primary test. Two-sided, $\alpha = 0.05$ . The verdict is read off the primary alone.
| Outcome | Condition |
|---|---|
| BMC-SUPPORTED | $\beta_{\cos} < 0$ , 95% CI excluding 0, and $\lvert\beta_{\cos}\rvert \ge 2\lvert\beta_{\text{walk}}\rvert$ and the blind twin S2 does not reproduce it (below) |
| RIVAL-SUPPORTED | $\beta_{\text{walk}}$ CI excludes 0 and $\lvert\beta_{\text{walk}}\rvert \ge 2\lvert\beta_{\cos}\rvert$ ; or the equivalence test on $\beta_{\cos}$ passes (TOST, bound $\lvert\beta\rvert < 0.02$ ) |
| NON-SEPARATING | Both CIs exclude 0 with a magnitude ratio inside [0.5, 2] — reported as such, not as a BMC win |
| GEOMETRY-NULL | $\beta_{\cos}$ CI excludes 0, but the PPMI blind twin (S2) reproduces ≥ 80% of it ⇒ the sign is carried by corpus co-occurrence density, not by embedding geometry |
| INCONCLUSIVE AT THIS POWER | $\beta_{\cos}$ CI includes 0 and the TOST equivalence bound is not met. Explicitly not a rival win. |
| APPARATUS-ABSENT | A Stage 0 gate fails |
The INCONCLUSIVE row exists deliberately. Reading an underpowered null as a confirmation is an error this programme has already made once and retracted (P-BM28); here it is ruled out by a rule, not by intention.
8. Secondary tests — where the separating weight actually sits
Three secondary tests, Holm-corrected across them. They cannot change the primary verdict; they qualify what a primary pass means.
S1 — the rank knee (H1b), the only genuinely novel prediction. BMC’s diffusion sums only over the top-$K$ non-edge neighbours (Definition 14.2 and the equation that follows it). Fit a segmented model of the priming effect on the prime’s cosine rank among the target’s nearest neighbours. BMC requires a breakpoint $\hat K$ with the slope beyond it not distinguishable from zero (TOST). $\hat K$ is estimated on a random half of the targets and predicted on the held-out half; this is what stops $K$ from being a free parameter. Feasibility gate: at least 200 unrelated pairs inside the target’s top-100 embedding neighbourhood. Below that, S1 is recorded as untested, not as failed.
A structural consequence, recorded before the run. If $K$ is small (of order 10), almost no SPP unrelated prime is inside the target’s neighbourhood, and BMC’s own equation predicts a null on the primary. Either $K$ is large, in which case the top-$K$ restriction in the diffusion equation is vacuous and should be removed from the theory, or it is small, in which case the primary is the wrong place to look and S1 is the whole test. Both branches cost the theory something, which is why this is stated here rather than discovered afterwards.
S2 — the blind twin: PPMI substitution. Replace cosine with pointwise mutual information (PPMI) between prime and target, computed on the same corpus. PPMI is a graph-valued, geometry-free quantity of the same density. If PPMI reproduces $\beta_{\cos}$ , the embedding geometry contributes nothing and only corpus density does — and BMC loses to its own sentence, “the memeplex is literally a network”. Threshold in §7.
S3 — automaticity and robustness. BMC’s diffusion is a passive mechanism, so it must be present at the 200 ms SOA. An effect confined to the 1200 ms SOA indicates strategic expectancy and does not support the diffusion account; this is pre-registered as a disconfirming pattern. Also checked: the two alternative embeddings, SPP’s own LSA column, and lexical decision vs naming.
9. Blind twins — the full list, and what each would explain more cheaply
| # | Family | The cheaper account | How it is neutralised |
|---|---|---|---|
| 1 | (b) measurement | Prime word frequency and length. Frequent, short primes are processed faster and are also denser in embedding space. | In the nuisance block; and the paired design holds the target fixed |
| 2 | (b) measurement | Undersampled zeros. A pair with zero norm strength may simply be undersampled. | Stage 0 zero-association rule: zero required in both norm sets |
| 3 | (b) measurement | Item-level unreliability (Heyman et al. 2018) manufacturing a null. | The design avoids item-level effect estimates entirely; Stage 0 requires a known effect to be recovered first |
| 4 | (b) measurement | Regression to the mean: targets with extreme baseline latency show inflated apparent priming. | Target held fixed within pair; baseline latency absorbed by the random intercept |
| 5 | (c) published theory | Graded spreading activation over indirect paths. | The rival block, entered in the primary model; a magnitude ratio is required, not just a sign |
| 6 | (c) published theory | Distributional similarity predicts priming — already published (Günther et al. 2016). A bare positive result is a retrodiction. | Only S1 (the knee) and the S2 margin count as novel content; scored separately |
| 7 | (d) BMC minus the mechanism | BMC with the diffusion engine deleted: a graph whose edge weights are learned by Hebbian co-activation from corpus co-occurrence would look like proximity. | S2 (PPMI) is exactly this ablation |
| 8 | (a) resource | Not applicable: the design has no capacity manipulation. Recorded as N/A rather than omitted. | — |
10. Statistical plan, expected effect size, and power
Expected effect size. From the only directly comparable published estimate, Günther et al. (2016): standardized $\beta \approx 0.03$ –$0.04$ for distributional similarity on priming. This is the number the design must be able to see.
Power. The effective sample size is the number of distinct prime–target pairs, $n_{pairs}$ . At $n_{pairs} = 1{,}200$ , a single task × SOA cell gives 0.80 power for $\lvert\beta\rvert \gtrsim 0.08$ . Averaging the four task × SOA cells into one pair-level estimate raises reliability and brings the 0.80-power threshold to roughly $\lvert\beta\rvert \approx 0.045$ .
Stated plainly: that is still above the literature’s estimate of 0.03–0.04. The design sits at the edge of its own sensitivity. This is why INCONCLUSIVE AT THIS POWER is a pre-registered outcome with its own row, and why a null may not be reported as a rival win unless the TOST equivalence bound $\lvert\beta\rvert < 0.02$ is met. Power figures are recomputed from the realised $n_{pairs}$ and variance components after Stage 0 and before the primary is fitted; the recomputation is appended to the pre-registration as an amendment, and it may not change any threshold.
Multiple comparisons. One primary, uncorrected. Three secondaries, Holm-corrected. Robustness checks within S3 are descriptive and carry no verdict weight. No metric may be redefined after the primary is seen — the programme has recorded a goalpost shift of exactly that kind before (2026-08-09).
Deviations. Any departure from this document is written as a numbered amendment, recorded before it is executed, with the reason stated. Unamended departures void the pre-registration.
Back to the six bets.