STEP: 1519 / 公開日: 2026-08-28 / Test: 22/22 PASS / Lean 4: 7 theorem zero sorry / Type: STEP 1487 データサイエンス arc candidate #2 実装 (47 defer 全体 10 番目)
❶ A/B test verdict: 2 群 conversion 比率 (success/trials) → z-test approx + Cohen's h effect size → verdict。 6 case 決定表。
❷ ★ STEP 1379 Cohen's d BOTH 経路 の A/B test 版: 統計的有意 でも effect size 小 → BOTH (「有意 だが 実用意味なし」 の A/B test 版 discipline)。
❸ 13 姉妹 verdict tool 目。
| # | Condition | Verdict | Reason |
|---|---|---|---|
| 1 | invalid (successes > trials) | NEITHER | invalid_input |
| 2 | trials < 30 (default minSample) | NEITHER | insufficient_sample |
| 3 | p < α AND \|h\| ≥ minEffect | TRUE | significant_meaningful |
| 4 | p < α AND \|h\| < minEffect | BOTH ★ | significant_but_small_effect |
| 5 | p ≥ α AND diff = 0 | ZERO | identical_rates |
| 6 | p ≥ α (no signal) | NEITHER | no_significant_difference |
// Large effect + significant → TRUE
abTestVerdict({ aSuccesses: 10, aTrials: 100, bSuccesses: 50, bTrials: 100 });
// { verdict: 'TRUE', pValue: ~0.0001, cohensH: ~0.87, reason: 'significant_meaningful' }
// Small effect + large sample = significant BUT small → BOTH ★
abTestVerdict({ aSuccesses: 500, aTrials: 10000, bSuccesses: 600, bTrials: 10000 });
// { verdict: 'BOTH', reason: 'significant_but_small_effect' }
// = 10000 sample で 1% 差、 統計的有意 だが 実用 impact 小
// Identical rates → ZERO
abTestVerdict({ aSuccesses: 30, aTrials: 100, bSuccesses: 30, bTrials: 100 });
// { verdict: 'ZERO', reason: 'identical_rates' }
rate_zero_trials / rate_zero_success / rate_full : 比率 identity ab_identical_gives_zero : identical → ZERO ab_significant_meaningful_gives_true : sig + meaningful → TRUE ab_significant_small_gives_both : sig + small effect → BOTH ★ ab_nonsignificant_gives_neither : nonsig → NEITHER
❶ Normal approx (z-test)、 Fisher's exact test 未 embed。 小 sample (min 30) は insufficient 判定。
❷ Cohen's h = 2 arcsin(√p₂) − 2 arcsin(√p₁)、 minEffect 0.2 = small (Cohen convention)。
❸ Multiple comparisons correction 未 (BH FDR は STEP 1371 別 tool で 適用可)。
❹ 「世界初」 なし = Cohen 1988 既知 D-FUMT₈ mapping、 novelty = STEP 1379 BOTH 経路 の A/B test 版。
❺ 累計 defer 39 → 38。