# 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) = 0.111, store-reshuffle p = 0.0005; (T) V = 0.191, p = 0.445; (L) p = 0.212 | 0.4453 | 0.8906 | **partially supported** |
| H2 | Regional diversity is associated with regional scale | Spearman rho(rarefied entropy, log population) = 0.00, 95% CI [-0.63; 0.60], n = 16 | 1.0000 | 1.0000 | **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 0.065 (SE 0.019), placebo p = 0.010; 104 entries; 3 region-level entries |  |  | **exploratory: consistent with relatedness at the store level; region level untestable** |
| H5-T1 | Matched-product prices are geographically structured | Wald(14) = 164.4, wild-cluster-bootstrap p = 0.0045; 1064 groups, 143 stores, 9 regions with >= 5 stores | 0.0045 | 0.0135 | **supported** |
| H5-T2 | Matched-product prices are competitively structured (reseller vs producer) | reseller coefficient -0.116 (SE 0.026), wild-bootstrap p = 0.0012 | 0.0012 | 0.0048 | **supported** |
| H6 | Local-origin price premium | not estimated |  |  | **untestable (declared ex ante)** |
| H7 | Validated digital-assortment complexity indicator | ECI bootstrap rank stability median rho = 0.67 (criterion 0.8); lambda2 null p = 0.00; LOO predictive rho = 0.00 |  |  | **not validated: ECI unstable at 17 x 20; omitted from QDACI** |
| QDACI | Composite index | median agreement across weightings rho = 0.25 (rule 0.7); bootstrap rank stability 0.47 |  |  | **components published; composite withheld** |

Notes:
- H1: Preregistered criterion required p < 0.05 under both merchant-equal and trimmed-listing weights; met for merchant-equal only. Specialization is a property of the merchant population, not of listing volumes.
- 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.
- 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.