Hypothesis registry (model category labelling)
| id | statement | primary statistic | p raw | p Holm | status |
|---|---|---|---|---|---|
| H1 | Online assortment composition differs across regions beyond what merchant counts imply | Cramér's V (M) = 0.112, store-reshuffle p = 0.0005; (T) V = 0.191, p = 0.429; (L) p = 0.199 | 0.4293 | 0.8586 | not supported (preregistered joint criterion) |
| H2 | Regional diversity is associated with regional scale | Spearman rho(rarefied entropy, log population) = 0.04, 95% CI [-0.65; 0.62], n = 16 | 0.8995 | 0.8995 | inconclusive |
| H3 | Merchant catalogue sizes are highly skewed | Gini = 0.849 [0.811; 0.878]; top-10% share = 0.789 [0.730; 0.836] | supported | ||
| H4 | Related diversification (exploratory) | LPM density coefficient 0.102 (SE 0.031), placebo p = 0.005; 151 entries; 1 region-level entries | exploratory: consistent with relatedness at the store level; region level untestable | ||
| H5-T1 | Matched-product prices are geographically structured | Wald(14) = 164.2, wild-cluster-bootstrap p = 0.0975; 1064 groups, 143 stores, 9 regions with >= 5 stores | 0.0975 | 0.2925 | not supported |
| H5-T2 | Matched-product prices are competitively structured (reseller vs producer) | reseller coefficient -0.116 (SE 0.026), wild-bootstrap p = 0.0041 | 0.0041 | 0.0164 | supported |
| H6 | Local-origin price premium | not estimated | untestable (declared ex ante) | ||
| H7 | Validated digital-assortment complexity indicator | ECI bootstrap rank stability median rho = 0.68 (criterion 0.8); lambda2 null p = 0.00; LOO predictive rho = 0.01 | not validated: ECI unstable at 17 x 20; omitted from QDACI | ||
| QDACI | Composite index | median agreement across weightings rho = 0.29 (rule 0.7); bootstrap rank stability 0.45 | components published; composite withheld |
Notes:
- H1: Preregistered criterion required p < 0.05 under both merchant-equal and trimmed-listing weights; merchant-equal p = 0.0005, trimmed p = 0.429. The merchant-equal dependence is reported as a descriptive, non-preregistered finding; the listing-weighted null is a power-limited result (null SD much larger under L/T).
- H2: CI includes zero and economically meaningful values in both directions; n = 16 regions. No association with business counts or density either (see table).
- H3: Both preregistered thresholds (Gini >= 0.70, top-10% >= 0.50) exceeded with CIs entirely above them; power-law tail favoured over log-normal on the tail.
- H4: Fewer than 10 region-level entries (preregistered untestability rule); store-level association over 5 weeks, no causal claim.
- H5-T1: Region effects identified only through groups spanning regions; posted prices, no shipping/taxes. Wild cluster bootstrap with group-demeaned disturbances (corrected after referee 1); leave-one-region-out Wald: {'Abitibi-Témiscamingue': 163.81, 'Capitale-Nationale': 141.04, 'Centre-du-Québec': 128.76, 'Chaudière-Appalaches': 162.46, 'Côte-Nord': 152.42, 'Estrie': 162.58, 'Gaspésie–Îles-de-la-Madeleine': 162.96, 'Lanaudière': 87.95, 'Laurentides': 161.58, 'Laval': 163.22, 'Mauricie': 163.99, 'Montérégie': 162.41, 'Outaouais': 51.35, 'Saguenay–Lac-Saint-Jean': 163.63}.
- H5-T2: Resellers/collectives post lower prices than producers for the same product.
- H6: No product-level provenance; a store-certification contrast is reported descriptively and is not H6.
- H7: Fitness and plain diversity are more stable but still below the criterion; the region-category matrix is not more nested than the store-reshuffle null.
- QDACI: Components describe observed online catalogues of Quebec-based merchants, not production or output. Complexity omitted because the ECI failed the preregistered stability criterion.