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The convention inventory

Part of the numerical-validation suite. Every statistic in the catalog with more than one defensible definition, and where ChakataStat's choice is written down. Built for 0.23.0 item 9 on 2026-08-28; maintained with the catalog.

"Validated against package X" says the number matches X. "Defined as" says what the number is, so a reader can compare it with any other tool's without guessing why they differ. The conventions pages hold the definitions; this page is the index that proves nothing was left implicit.

How to read the Status column

Mark Meaning
✅ recorded the choice was already written down; the link is the section
🆕 recorded now the choice was implicit until this sweep — chosen in the engine and matched by a reference, but never stated; written in classical.md (or the page linked) on 2026-08-28
— single the sweep considered the statistic and found one definition in practice; nothing to choose, said so here
⏳ item 6 the choice was a degenerate-input decision that the adversarial fixture battery (0.23.0 item 6) forced; both such rows were closed on 2026-08-29 and link to degenerate inputs — no row carries this mark now

The three feeds (per the plan): the four prior conventions pages (regression, latent-variable, clinical-and-survey, resampling-and-time-series) and tolerances.md; the between-oracle disagreements item 8 found (validation.md); and the decisions item 6 will force. Plus the classics, checked whether or not a disagreement surfaced them: quantile type, ANOVA df, tie corrections, continuity corrections, CI families, small-sample factors.

Descriptive statistics (descriptives, frequencies, explore, bin_variable)

Statistic ChakataStat's definition Status
Percentiles, median, quartiles Hazen, (k − ½)/n; weighted on cumulative weight ✅ tolerances · quantiles
Skewness, kurtosis bias-adjusted G₁, G₂ (SPSS / SAS / Excel / R type 2) 🆕 skewness and kurtosis
SD, variance, SE of the mean divisor n − 1; s/√n 🆕 standard deviation
Case weights frequency weight ≡ replication, every procedure ✅ tolerances
Missing-data policy listwise per procedure; correlations pairwise by default 🆕 missing-data policy
Binning (bin_variable) equal width, Hazen-quantile, or custom cut points — single (the quantile rule is the row above)
Mean, sum, range, min/max, mode — — single

Tables (crosstabs, custom_tables, multiple_response, loglinear)

Statistic ChakataStat's definition Status
Pearson χ² on 2 × 2 no Yates continuity correction 🆕 Pearson chi-square
Likelihood-ratio χ² 2 Σ O ln(O/E) — single
Fisher's exact test, two-sided sum of tables no more likely than the observed 🆕 Fisher's exact test
McNemar exact binomial for b + c ≤ 25, continuity-corrected χ² otherwise 🆕 McNemar's test
φ, Cramér's V uncorrected √(χ²/N), √(χ²/(N(k−1))) 🆕 Cramér's V and φ
Mantel–Haenszel / Cochran's MH continuity-corrected; Cochran's not 🆕 Mantel–Haenszel
Gamma, τ-b, τ-c, Somers' d, λ, kappa the standard Goodman–Kruskal / Kendall / Cohen forms — single (weighted kappa is not offered)
Column-proportion z tests pooled two-proportion z, unadjusted 🆕 column-proportion z tests
Loglinear model Poisson GLM on the counts (not IPF) 🆕 loglinear models
Multiple-response counting dichotomy / category modes — single (a layout rule, validation.md)

Comparing means (means, one_sample_ttest, independent_ttest, paired_ttest, equivalence_ttest, anova, levene)

Statistic ChakataStat's definition Status
Independent t: pooled vs Welch both rows printed; Welch–Satterthwaite df 🆕 both variances rows
Levene's test mean-centred (not Brown–Forsythe) 🆕 Levene
Cohen's d, Hedges' g, paired d pooled n − 1 SD; J = 1 − 3/(4df − 1); d_z; noncentral-t CI 🆕 Cohen's d and Hedges' g
ANOVA df, SS between k − 1, within N − k, Type I on a one-way design — single
η², ε², ω² SS_b/SS_t; Olejnik–Algina ε² and ω² 🆕 ANOVA effect sizes
Post hoc Bonferroni, Scheffé, Tukey HSD on pooled MS 🆕 post hoc tests
Planned contrasts pooled and Welch–Satterthwaite 🆕 planned contrasts
Welch ANOVA Welch's F* with its df — single
Equivalence tests (TOST) bounds centred on the test value; 1 − 2α CI ✅ clinical-and-survey
n = 1 per group, constant variable, zero-case filter pooled t on n₁ + n₂ − 2 df, Welch blank; constants refused; N = 0 is an answer ✅ degenerate inputs (item 6, 2026-08-29)

Correlation (correlate, partial_correlate, polychoric_correlation, canonical_correlation)

Statistic ChakataStat's definition Status
Pearson r, p t on n − 2 df — single
Spearman ρ mid-ranks; t approximation (not exact / AS 89) 🆕 Spearman
Kendall τ τ-b; normal approximation, no-tie variance 🆕 Kendall
Partial correlation inverse-matrix first-order; n − 2 − k df 🆕 partial correlation
CI on r none printed (Bayesian credible interval instead) 🆕 no CI on r
Missing data pairwise default, listwise option 🆕 missing-data policy
Polychoric correlation two-step ML on thresholds ✅ latent-variable
Canonical correlation Bartlett's sequential χ² — single

Regression and modelling (linear_regression … mediation)

Statistic ChakataStat's definition Status
Linear least squares by QR; singularity verdict scale-invariant ✅ regression · scale invariance
Regression through the origin uncentred R², adjusted R², F ✅ regression
Standardized β B·sd(x)/sd(y), n − 1 SDs — single (pin reg_linear/age_beta)
Adjusted R², Durbin–Watson, tolerance / VIF the textbook forms — single
Stepwise selection p-enter .05, p-remove .10 🆕 stepwise
CI on GLM coefficients, Exp(B) Wald, z (t under a design); not profile likelihood 🆕 Wald, z
GLM fitting IRLS through the QR; Cholesky for information matrices ✅ regression · SPD route
Gamma dispersion and likelihood Pearson φ̂; likelihood at the Pearson scale ✅ regression (item 8)
Negative binomial NB2, α by ML ✅ tolerances
Zero-inflated / hurdle joint likelihood; Hessian with α fixed ✅ validation.md
GLM quantile residuals randomized, seeded; per-family brackets ✅ regression
Hosmer–Lemeshow 10 deciles of risk by rank; g − 2 df ✅ validation.md
Multinomial reference category the lowest category 🆕 multinomial and ordinal
Ordinal parameterization logit P(Y ≤ c) = θ_c − β·x 🆕 same
Type III SS sum-to-zero contrasts ✅ tolerances
Repeated measures: sphericity Mauchly; Greenhouse–Geisser and Huynh–Feldt ε — single (the standard definitions)
MANOVA statistics and partial η² Pillai / Wilks / Hotelling–Lawley / Roy; SPSS partial η² ✅ validation.md
Robust regression Huber 1.345, Tukey 4.685, MAD/0.6745, sandwich 🆕 robust regression
Quantile regression IRLS on the check loss; Koenker iid SE ✅ validation.md
GEE working correlations; sandwich covariance ✅ validation.md
Mixed model: ML vs REML REML default (changed 2026-08-28), ML option 🆕 mixed models
GLMM integration Gauss–Hermite quadrature 🆕 same
Nonlinear regression Levenberg–Marquardt; Gauss–Newton covariance 🆕 nonlinear regression
IV / 2SLS σ̂² on structural residuals; first-stage F — single (pins iv/*)
Regularized regression standardized; 10-fold CV; min and 1-SE λ 🆕 regularized regression
Panel: variance components, cluster factor, R²s, Hausman Swamy–Arora with harmonic T̄; Stata cluster factor; linearmodels R²s ✅ tolerances · unbalanced panel (item 8)
Mediation, moderated mediation, JN regions, serial PROCESS shapes; Aiken–West probes; bootstrap CIs ✅ regression · tolerances
p-value far tail, normal quantile, erfc dedicated erfc; Φ⁻¹ at 1e-15 ✅ regression
Complete / quasi-complete separation, exact collinearity verdict text, weights ≤ 0 separation refused at R's threshold, naming Firth; collinear (singular matrix); non-positive weights exclude the case ✅ degenerate inputs (item 6, 2026-08-29)

Nonparametric tests (mann_whitney … normality)

Statistic ChakataStat's definition Status
Mann–Whitney smaller U; tie-corrected z; no continuity; exact when untied and small ✅ tolerances · validation.md
Rank-biserial r Kerby; positive when the first group ranks higher ✅ validation.md
Wilcoxon signed-rank zeros dropped; tie-corrected; no continuity 🆕 Wilcoxon
Sign test, runs test continuity-corrected normal; runs cut at the median 🆕 sign and runs
Binomial test tails two-tailed at ½, one-tailed otherwise (SPSS) 🆕 binomial test
Kruskal–Wallis tie-corrected H; ε² = H/(N − 1); exact upper tail ✅ validation.md
Friedman, Kendall's W W = χ²/(N(k − 1)) ✅ validation.md
Dunn's test tie-corrected z; Bonferroni / Holm / none ✅ validation.md · post hoc tests
Cochran's Q, Jonckheere–Terpstra standard forms; exact null variance ✅ validation.md
Normality Shapiro–Wilk (Royston); KS with Lilliefors p 🆕 normality tests
Exact-test caps and tie fallback exact only when untied and enumerable ✅ validation.md
Permutation tests two-sided / observed-inclusive counting; seeded MC ✅ resampling-and-time-series

Survival (kaplan_meier, cox_regression, parametric_survival, competing_risks)

Statistic ChakataStat's definition Status
KM variance, median Greenwood SE printed, no band; median = first t with S ≤ ½ 🆕 Kaplan–Meier
Log-rank Mantel–Cox, hypergeometric variance — single (Peto / Gehan not offered)
Cox ties Efron default (changed 2026-08-28), Breslow option 🆕 Cox regression
Hazard-ratio CI, baseline hazard Wald; Breslow 🆕 same
Proportional-hazards test form 1994 simplified statistic (lifelines) ✅ clinical-and-survey (item 8)
AFT models, competing risks ML on log-time; Fine–Gray / CIF ✅ validation.md

Meta-analysis and resampling (meta_analysis, bootstrap_ci)

Statistic ChakataStat's definition Status
τ² (DL truncated at 0; REML), I², Egger, Wald CIs, no Knapp–Hartung — ✅ tolerances
Bootstrap CI (percentile / BCa), seed, PRNG SplitMix64, seed 1 ✅ validation.md

Time series (autocorrelation … exponential_smoothing)

Statistic ChakataStat's definition Status
ACF divisor, Bartlett SE, Box–Ljung df n; cumulative; k 🆕 autocorrelation
PACF method Durbin–Levinson 🆕 same
ARIMA estimation CSS default, ML option; constant by default ✅ tolerances · ARIMA
ADF / KPSS lags and p Schwert rule; MacKinnon 1994 🆕 stationarity tests
Exponential smoothing init; decomposition l₀ = y₁; classical centred MA 🆕 exponential smoothing
VAR / Granger vars scalings; pairwise Granger ✅ resampling-and-time-series
LOESS tricube local-linear; degenerate windows ✅ resampling-and-time-series

Scale reduction and classification (reliability … multidimensional_scaling)

Statistic ChakataStat's definition Status
Cronbach's α (raw and standardized) both printed 🆕 reliability
ICC forms Shrout–Fleiss six ✅ validation.md
Bland–Altman direction, 1999 exact LoA SE ✅ clinical-and-survey
Factor extraction / retention / rotation PCA; Kaiser > 1; Varimax (Kaiser-normalized), Promax κ = 4 🆕 factor analysis
CFA (scale, χ² divisor, information, baseline, RMSEA CI) marker; N; expected; independence; 90 % ✅ tolerances · latent-variable
IRT, LCA recorded per reference ✅ latent-variable
k-means seeding, distance, standardization maximin; squared Euclidean; none 🆕 clustering
Hierarchical linkage default; Ward's distance average; squared Euclidean 🆕 same
Discriminant priors; stepwise F proportional; F = 3.84 🆕 discriminant · stepwise
Decision tree Gini default; CHAID — single (documented options)
ROC larger = positive; ties half credit; Hanley–McNeil; Youden ✅ validation.md
Propensity score logit-scale distance; greedy 1:k; unadjusted pooled SD ✅ tolerances
MDS, correspondence, canonical classical / Torgerson; standard ✅ validation.md

Complex samples, Bayesian, power, imputation, charts

Statistic ChakataStat's definition Status
Survey designs (five estimation conventions; regression under a design) — ✅ clinical-and-survey
Bayesian t / correlation / ANOVA / regression priors JZS r = 0.707; stretched-beta κ = 1; Zellner–Siow ✅ validation.md
Power: tails and noncentral distributions two-tailed default 🆕 power analysis
Multiple imputation chained equations, 10 cycles, Rubin + Barnard–Rubin ✅ validation.md
Box plot fences, histogram bins, Q–Q positions Tukey 1.5 IQR; 10 equal bins; Blom 🆕 charts
Violin density Silverman factor; 96-point grid; frequency weights ✅ tolerances
Chart provenance, dataset fingerprint — ✅ recorded app-side in docs/development/conventions.md (outside the guide)

The count

Of the rows above: 46 recorded before this sweep, 48 recorded on 2026-08-28 (all in classical.md unless linked elsewhere), 15 single-definition (said so), and 2 recorded on 2026-08-29 by the adversarial fixture battery (0.23.0 item 6, the degenerate inputs section) — the two rows this inventory could not close by itself, because their definition was the battery's decision. No row is waiting.

Adding to this page

A new analysis adds its rows here in the same commit (the add-an-analysis walkthrough's checklist: record the conventions before the pin). A row is never "TBD": it is recorded, single, or pending a named item.