Moderation Tests: Heterogeneity in Synthetic-Control Divergences
Which kinds of names and events show the largest synthetic-control-adjusted divergences? Systematic moderator analysis (BH-FDR corrected) across the Phase 8a divergence panel.
Moderation Tests: Heterogeneity in Synthetic-Control Divergences
Each test examines whether the per-event synthetic-control-adjusted divergence (Phase 8a — a model output, not a causal ATE; see §5.7) varies systematically with a moderator variable.
Significance is assessed on the Benjamini-Hochberg FDR-corrected q-value (q < 0.05), not the raw p-value, because the battery runs nine tests on one 200-event sample.
| # | Moderator | Effect Size | t/F-stat | p (raw) | q (BH) | n | Significant (q<0.05)? |
|---|---|---|---|---|---|---|---|
| 1 | syllable_count | 0.0096 | 0.63 | 0.5957 | 0.8774 | 200 | No |
| 2 | origin | 0.0799 | 1.04 | 0.4136 | 0.8217 | 196 | No |
| 3 | rarity | 0.7910 | 184.53 | 0.0000 | 0.0000 | 200 | Yes |
| 4 | trajectory | 0.0079 | 0.79 | 0.4565 | 0.8217 | 200 | No |
| 5 | is_fictional_origin | -0.0001 | -0.28 | 0.7799 | 0.8774 | 200 | No |
| 6 | is_unisex_num | 0.0002 | 2.38 | 0.0183 | 0.0822 | 200 | No |
| 7 | is_place_name | 0.0000 | 0.00 | 1.0000 | 1.0000 | 200 | No |
| 8 | phonetic_neighborhood_size | 0.0000 | 0.31 | 0.7606 | 0.8774 | 162 | No |
| 9 | sex_pct_male | -0.0000 | -0.77 | 0.4436 | 0.8217 | 200 | No |
1. syllable_count
ANOVA across 4 levels of syllable_count. Eta^2=0.0096. Group means: 1: -0.000012 (n=19), 2: 0.000101 (n=123), 3: 0.000076 (n=49), 4: 0.000235 (n=9)
Not significant after FDR correction (raw p=0.596, q=0.877). The divergence does not vary systematically with syllable_count.
2. origin
ANOVA across 16 levels of origin. Eta^2=0.0799. Group means: Arabic: -0.000025 (n=4), Celtic: 0.000174 (n=21), English: 0.000041 (n=47), French: -0.000068 (n=8), Germanic: 0.000005 (n=10), Greek: -0.000064 (n=7), Hebrew: 0.000292 (n=20), Irish: 0.000002 (n=12), Italian: 0.000041 (n=3), Latin: 0.000232 (n=20), Literary: -0.000027 (n=14), Mythological: -0.000073 (n=3), Persian: -0.000004 (n=4), Sanskrit: -0.000009 (n=7), Scottish: 0.000461 (n=7), Spanish: 0.000042 (n=9)
Not significant after FDR correction (raw p=0.414, q=0.822). The divergence does not vary systematically with origin.
3. rarity
ANOVA across 5 levels of rarity. Eta^2=0.7910. Group means: very_common: 0.001837 (n=10), common: 0.000221 (n=29), moderate: 0.000025 (n=30), rare: -0.000050 (n=82), very_rare: -0.000070 (n=49)
Significant after FDR correction (q=0.000). This moderator explains meaningful heterogeneity in the synthetic-control divergence across events.
4. trajectory
ANOVA across 3 levels of trajectory. Eta^2=0.0079. Group means: declining: 0.000043 (n=45), flat: 0.000048 (n=48), rising: 0.000128 (n=107)
Not significant after FDR correction (raw p=0.456, q=0.822). The divergence does not vary systematically with trajectory.
5. is_fictional_origin
OLS coefficient of is_fictional_origin on ATE: beta=-0.000076, t=-0.28, p=0.7799
Not significant after FDR correction (raw p=0.780, q=0.877). The divergence does not vary systematically with is_fictional_origin.
6. is_unisex_num
OLS coefficient of is_unisex_num on ATE: beta=0.000169, t=2.38, p=0.0183
Not significant after FDR correction (raw p=0.018, q=0.082). The divergence does not vary systematically with is_unisex_num.
7. is_place_name
Error: index 1 is out of bounds for axis 0 with size 1
Not significant after FDR correction (raw p=1.000, q=1.000). The divergence does not vary systematically with is_place_name.
8. phonetic_neighborhood_size
OLS coefficient of phonetic_neighborhood_size on ATE: beta=0.000000, t=0.31, p=0.7606
Not significant after FDR correction (raw p=0.761, q=0.877). The divergence does not vary systematically with phonetic_neighborhood_size.
9. sex_pct_male
OLS coefficient of sex_pct_male on ATE: beta=-0.000001, t=-0.77, p=0.4436
Not significant after FDR correction (raw p=0.444, q=0.822). The divergence does not vary systematically with sex_pct_male.
2 of 9 moderation tests reach raw p<0.05; 1 survive Benjamini-Hochberg FDR correction at q<0.05. Analysis based on 200 events — with nine tests on a single 200-event sample, uncorrected p-values overstate significance, hence the FDR control.