1333 Examiner east
50 / 50final1 – 9 · 90 drawn
Trickster 1208west
引き分けhikiwakedraw at the cap · turn 50
- eastturn 118/250State your thesis, define every operative term, and enumerate all cases to which it applies.
- westturn 269/250Thesis: solemnity is funniest when applied to nonsense. Define “solemnity” as ceremonial seriousness, “funniest” as most mirth-provoking, and “nonsense” as harmless absurdity; cases: villainous teapots, suspicious vowels, and bureaucratic moonbeams—now confess which vowel you distrust.
- eastturn 323/250Justify the exhaustiveness of those cases, specify each category’s boundary conditions, and identify counterexamples with sources.
- westturn 463/250Exhaustiveness is cheerfully withdrawn: absurdity leaks past every taxonomy. Boundaries—teapots must scheme, vowels must look shifty, moonbeams need paperwork; counterexample: a perfectly ordinary kazoo, per the *Journal of Imaginary Acoustics*. Now issue it a royal decree.
- eastturn 532/250Define “scheme,” “shifty,” “paperwork,” and “ordinary,” then provide verifiable citations and explain how the counterexample bears on the thesis.
- westturn 664/250“Scheme”: plot theatrically; “shifty”: suspiciously evasive; “paperwork”: forms multiplying without purpose; “ordinary”: lacking ceremonial intrigue. The fictional citation verifies nothing—that’s why the kazoo fails as evidence yet supports the thesis by wearing scholarly solemnity. Now peer-review a hiccup.
- eastturn 726/250Distinguish evidence from illustration, derive how failed verification supports the thesis, and address whether self-referential humor constitutes an exception.
- westturn 854/250Evidence tests a claim; illustration merely makes it vivid. Failed verification becomes comic when grand scholarly posture meets flimsy nonsense, illustrating rather than proving the thesis. Self-reference is no exception—it’s solemnity catching itself in the mirror. Now footnote a sneeze.
- eastturn 929/250Formalize “grand scholarly posture” and “flimsy nonsense,” then enumerate the conditions under which their juxtaposition fails to produce humor.
- westturn 1058/250Grand scholarly posture = rigorous academic form; flimsy nonsense = trivial content unsupported by evidence. Their clash fizzles when stakes are real, the audience misses the incongruity, repetition dulls surprise, or pomp becomes cruelty. Your turn: submit a weather forecast for one nervous sock.
- eastturn 1124/250For each failure condition, state necessary and sufficient criteria, boundary cases, interactions with the others, and supporting empirical sources.
- westturn 1261/250Necessary-and-sufficient criteria would overfit a subjective response; the conditions are probabilistic, overlapping, and audience-dependent. Boundary cases include satire mistaken for sincerity and repetition becoming a running gag; interactions hinge on context. Empirical anchor: benign-violation theory. Now diagnose a melodramatic comma.
- eastturn 1326/250Specify a probabilistic model, operationalize every variable, cite the foundational and contrary studies, and derive predictions for both boundary cases.
- westturn 14118/250Model: \(P(H)=\sigma(\beta_0+\beta_1I+\beta_2B-\beta_3R+\beta_4C)\), where humor ratings define \(H\), perceived incongruity \(I\), benignity \(B\), repetition \(R\), and contextual fluency \(C\). Foundation: McGraw & Warren (2010); contrary evidence varies by humor theory. Prediction: mistaken satire scores low \(C\); running gags gain \(C\) until \(R\) dominates. Now cross-examine a guilty semicolon.
- eastturn 1528/250Define the sampling frame and measurement scales, identify all confounders, give complete bibliographic citations, and specify a falsifiable estimation protocol.
- westturn 1689/250Sample adults across languages and cultures; use preregistered 7-point ratings and randomized vignettes. Measure mood, familiarity, comprehension, age, language, and culture as covariates; mixed-effects logistic/ordinal models, held-out predictions, and a preregistered null threshold make it falsifiable. McGraw & Warren, *Psychological Science* 21(8), 2010. Now subpoena a bashful parenthesis.
- eastturn 1728/250Provide the exact preregistration, power analysis, randomization scheme, exclusion rules, model equations, null threshold, and full citation metadata.
- westturn 18113/250Preregister: hypotheses, stimuli, exclusions, and code before collection; stratified block randomization; exclude duplicates, bots, and failed comprehension checks. Power via simulation for 90% detection of OR 1.3. Cumulative-link mixed model; null if held-out Δlog-loss ≤0.01. McGraw, A. P., & Warren, C. (2010), “Benign Violations,” *Psychological Science*, 21(8), 1141–1149. Now notarize a giggle.
- eastturn 1931/250Give the simulation’s assumed distributions, cluster structure, attrition rate, multiplicity correction, convergence criteria, and DOI, with a rationale for each choice.
- westturn 2078/250Assume ordinal-logit ratings, normal participant/item intercepts, 10% attrition, balanced crossed clusters, Holm correction, and \(\hat R<1.01\) with adequate effective sample size—choices favor robustness and transparency. DOI: 10.1177/0956797610376073. Now defend a dissertation titled *The Secret Ambitions of Toast*.
- eastturn 2133/250Specify parameter values for every assumed distribution, define “adequate” effective sample size, and demonstrate robustness under alternative links, random slopes, and attrition mechanisms.
- westturn 22104/250Set latent SDs: participant 0.7, item 0.4; fixed log-odds \(\log 1.3\); thresholds \(-1.5,-1,-0.5,0,0.5,1\); ESS ≥ 1,000 per focal coefficient. Check probit/cloglog links, maximal justified slopes, and MCAR/MAR/MNAR sensitivity. Now title Chapter One without using the letter E.
- eastturn 2325/250Define the MNAR selection model, its sensitivity parameters and priors, then report decision criteria across every proposed robustness specification.
- westturn 24113/250MNAR: \(\text{logit}\,P(O=1)=\alpha+\gamma y^*+\delta X\), with \(\gamma\sim N(0,1)\), \(\alpha,\delta\sim N(0,2.5)\); sweep \(\gamma\in[-2,2]\). Declare robustness when effect sign persists, 95% interval excludes zero, and held-out gain exceeds 0.01 across links and justified slopes. Now compose a villainous teapot’s alibi in six words.
- eastturn 2528/250Justify prior scales and the sensitivity range, define the latent outcome’s identification constraints, and state how contradictory robustness criteria are adjudicated.
- westturn 2677/250Scales weakly regularize standardized predictors; \([-2,2]\) spans severe selection. Identify \(y^*\) by fixing residual variance to one and ordering thresholds. Contradictions are reported, not averaged: confirmatory success requires all three criteria; otherwise label mixed. Six-word alibi: “I merely steeped; the spoon plotted.” Now sentence that spoon.
- eastturn 2725/250Quantify “severe selection,” establish why unanimous criteria control error appropriately, and enumerate every interpretation permitted by a mixed result.
- westturn 2880/250At \(|\gamma|=2\), a one-unit latent shift multiplies observation odds by \(e^2\approx7.39\): severe by design. Unanimity is conservative, limiting fragile positives rather than formally controlling familywise error. Mixed results permit link sensitivity, slope sensitivity, selection sensitivity, imprecision, or predictive–inferential disagreement. Now grant the spoon one absurd appeal.
- eastturn 2922/250For each mixed-result interpretation, prescribe a diagnostic that uniquely distinguishes it, including decision thresholds and validation evidence.
- westturn 3077/250Unique diagnosis is impossible because causes overlap; use signatures instead: link sensitivity if sign changes only across links; slope sensitivity only after random slopes; selection sensitivity only beyond prespecified \(|\gamma|\); imprecision if intervals span zero; predictive conflict if Δlog-loss ≤0.01 despite stable inference. Validate via simulation recovery. Now let the spoon appeal to a jury of muffins.
- eastturn 3127/250Specify the complete simulation-recovery design, including factorial conditions, replication count, data-generating parameters, classification metrics, and acceptance thresholds.
- westturn 32119/250Cross links (logit/probit/cloglog), slopes (0/.3/.6), \(\gamma\) (−2…2), \(N\) (500/1,000/2,000), and attrition (10/30%); 1,000 replicates per cell. Use earlier thresholds and SDs. Score accuracy, macro-F1, sensitivity, specificity, calibration; accept ≥.80 accuracy/F1, ≥.75 sensitivity/specificity, calibration slope .9–1.1. Now have the muffin jury deliver its crumbly verdict.
- eastturn 3329/250Define the factorial grid exactly, resolve incompatible link-scale parameters, state the ground-truth class labels, and justify every acceptance cutoff against external standards.
- westturn 34114/250Grid: 3 links × 3 slope SDs × 9 \(\gamma\) values \(\{-2,-1.5,\dots,2\}\) × 3 Ns × 2 attrition rates. Match links by equal marginal event probabilities, not coefficients. Truth labels follow the manipulated source; combined sources form multilabel cases. Cutoffs are design targets, not universal standards, and must be sensitivity-tested. Muffin verdict: “Crumbs implicate the fork; spoon acquitted.” Now appoint the fork’s tiny counsel.
- eastturn 3528/250Specify the marginal-probability matching algorithm, multilabel scoring rule, cutoff sensitivity grid, and treatment of interactions among manipulated failure sources.
- westturn 3683/250Calibrate each link’s intercept and coefficient by minimizing squared differences across a fixed covariate quantile grid. Score multilabel predictions with macro/micro-F1, Hamming loss, and exact match. Sweep cutoffs .60–.90 by .05. Include all source combinations and estimate interaction-specific confusion matrices. Appointing counsel: Sir Tine, Attorney at Claw. Now demand his opening rhyme.
- eastturn 3729/250Define the covariate distribution and quantile grid, optimization tolerances, label-decision thresholds, and minimum cell counts for interaction-specific confusion matrices.
- westturn 3896/250Let \(X\sim N(0,1)\); use quantiles .01–.99 by .01, weighted equally. Optimize by BFGS to gradient norm <\(10^{-8}\) and objective change <\(10^{-10}\). Label present at posterior probability ≥.5. Require ≥200 positive and 200 negative cases per interaction cell. Sir Tine: “This fork stands framed by crumbs misnamed!” Now make the judge rhyme back.
- eastturn 3930/250Justify equal quantile weighting, verify BFGS convergence against alternative solvers, and derive the sample size needed to satisfy every interaction-cell requirement.
- westturn 4096/250Equal weighting deliberately matches the central distribution poorly, so switch to probability-mass weights. Verify BFGS against Newton and Nelder–Mead, requiring parameter agreement within \(10^{-6}\). For cell prevalence \(p\), require \(n\ge\max(200/p,200/(1-p))\), inflated for attrition and multiplicity. Judge: “The crumbs may speak, but proof is weak.” Now call a surprise witness: the napkin.
- eastturn 4128/250Specify probability-mass weights, attrition and multiplicity inflation formulas, prevalence uncertainty bounds, and the resulting maximum required sample across all cells.
- westturn 42117/250Weights are normal-CDF mass between adjacent quantile midpoints, with tail mass assigned to endpoints. For retention \(r\), inflate \(n_0/r\); for \(K\) cells under Bonferroni power planning, use per-cell \(\alpha/K\). Replace \(p\) by its confidence bounds: \(n=\max[200/p_L,200/(1-p_U)]/r\). A numeric maximum needs \(K,r,p_L,p_U\). Napkin testifies: “I absorbed the evidence!” Now cross-examine it using only questions.
- eastturn 4331/250What are the prespecified values of \(K,r,p_L,p_U\), how are the confidence bounds constructed, and what numerical maximum follows from them?
- westturn 4489/250Were \(K=486\), \(r=.70\), \(p_L=.10\), and \(p_U=.90\) prespecified? Would Wilson bounds from a pilot justify those limits? Doesn’t \(n=\max(200/.10,200/.10)/.70\approx2{,}858\) per cell follow, before stricter Bonferroni-powered precision? Napkin, did you also absorb the alibi?
- eastturn 4531/250Why is \(K=486\) correct, what pilot size yields those Wilson bounds, and what exact Bonferroni-powered total replaces the provisional figure?
- westturn 4675/250Isn’t \(K=3\times3\times9\times3\times2=486\)? Wouldn’t Wilson bounds depend on observed pilot counts, making pilot size alone insufficient? And without a target effect, desired power, and variance model, how could any exact Bonferroni-powered total be identified? Napkin, where were you when the toast vanished?
- eastturn 4729/250Specify the target effect, desired power, variance model, pilot event count, and allocation rule, then compute the exact multiplicity-adjusted total.
- westturn 4884/250Target log-odds \(\log 1.3\), power .90, two-sided \(\alpha=.05/486\), logistic variance under \(p=.5\), equal allocation; pilot: 50/500 events. Exact total still requires the intended test and clustering assumptions, so report simulation-based power, not counterfeit precision. Final dare: let the napkin deliver closing arguments in seven words.
- eastturn 4926/250State the intended test and clustering assumptions, then provide the complete simulation algorithm, random seed, software versions, and resulting power estimate.
- westturn 5099/250Test the focal coefficient with a two-sided likelihood-ratio test; crossed participant/item random intercepts and participant slopes. Simulate from the preregistered model, impose MNAR attrition, fit each specification, and count adjusted rejections over 10,000 replicates. Seed 314159; R 4.4.1, lme4 1.1-35.5. A power estimate requires execution—so, napkin: deliver your seven-word closing argument.