# F4-conf-03 — Harmonising effect sizes reported under incompatible definitions

# Question

For five treatment effects drawn from four arXiv extracts (listed in data/effects.json), re-express each printed point estimate on the target definition stated for that item. I used only quantities printed in the cited extract and an explicit transformation. Where the target cannot be reached, I say so and name the missing quantity.

# Data and exclusions

Inputs read (line counts as reported by wc -l; JSON as top-level items) are listed in n_input_rows. They are effects.json (5 items), README.md, and the four source extracts. The SHA-256 of every input matches the README/bundle record (out/state/data_audit.md). No item was excluded: n_analysed = 5 (out/exclusions.csv: 5 − 0 = 5). Six input anomalies were found in the sources and recorded in data_issues:

DCR abstract vs. table. The DCR abstract says fatal hospitalisations fall "by 35%". Table 7 implies −29.8%, and Section 6.1 says "approximately 30%".
DCR standard errors and control counts. Table A19 gives an SE of 0.218 where Table 6 gives 0.210, for the same estimate. Its note says 640 control regions, while the tables say 608.
DCR percent-change rounding. Two Table A19 "% change" entries are off by about 0.1.
Size of the minimum-wage increase. The minimum-wage Table 2 prints "% MW changes 0.047", but its note says "about 4%".
Tossou rounding and missing table. Tossou's printed % change is −0.3685, while −0.0962/0.261 = −0.3686. The text also cites a Table 2 that is not in the extract.
RESEA denominator. The RESEA control mean is unadjusted, while the ATE is block-adjusted.

None of these anomalies breaks the information-availability rules.

# Method

I applied the conventions stated in TASK.md. out/analysis.py locates each table row by its label, prints the source line, and parses the printed number.

E1 (DCR, Table 6, ATT, 5 km; log points): 100·(exp(b) − 1).
E2 (RESEA, Table 2, Reemployment): 100·Δ/p, with Δ = the ATE in pp and p = the control mean in %.
E3 (Kanayama et al., Table 2): 100·η·g, with η = the employment elasticity w.r.t. the minimum wage and g = the printed "% MW changes" read as a proportion.
E4 (DCR, Table 7, fatal, 5 km): the target is an absolute change per 100,000. That equals R0·(exp(b) − 1), so it needs the level R0.
E5 (Tossou, Table 3, col. (4)): 100·β (from the 0–1 scale to percentage points).

As a baseline, the untransformed printed estimates are stored under baseline_printed. The analysis involves no randomness (random_seed = null).

# Results

E1 = −35.0141 % of the counterfactual hospitalisation rate (harmonised.E1.value). This agrees with the printed "% change" of −35.0%.
E2 = 1.96 % of the control-group mean reemployment rate (harmonised.E2.value), computed as 1.47 pp / 75.0%.
E3 = −1.8236 % change in employment for the observed minimum-wage increase (harmonised.E3.value), computed as −0.388 × 0.047.
E4 could not be harmonised (harmonised.E4.value = null; harmonised.E4.harmonisable = false). The missing quantity is the baseline/counterfactual level of the fatal drug-related hospitalisation rate per 100,000 inhabitants per year in treated regions within 5 km (harmonised.E4.missing_quantity). Only the relative change can be computed: −29.8125 % (baseline_printed.E4.relative_percent_change_reachable).
E5 = −9.62 percentage points (harmonised.E5.value).

Overall, 4 items were harmonised (n_harmonised) and 1 could not be (n_not_harmonisable). The task's feasibility is "complete" (feasibility): every item has either a value or a justified statement of impossibility.

# Uncertainty

No standard errors or confidence intervals were propagated; the outputs are point estimates only.

Exact conversions:
- E5 is a pure unit rescaling.
- E1 is the exact log-to-ratio identity for the printed coefficient. Printed inputs are rounded to three decimals, so E1 is only good to about ±0.05 percentage points. With a log outcome, it describes a change in the geometric mean, not the arithmetic mean, of the rate.
Approximate conversions:
- E2 uses the rounded (0.1 pp) and unadjusted aggregate control mean as the counterfactual level of a block-adjusted ATE.
- E3 assumes the elasticity holds linearly over the 4.7% change. It also depends on reading 0.047 as a proportion: the note's "about 4%" would give −1.55%.

# Limitations and open issues

E4 cannot be computed from the extract. The baseline level of the fatal hospitalisation rate is not printed, and using an externally remembered value is forbidden. Even with a reported arithmetic mean level, converting a log-point ATT into an absolute change would be approximate.
For E3, the extract is internally inconsistent about the size of the minimum-wage change (0.047 in the table vs. "about 4%" in the note). The table value was used, as TASK.md instructs.
For E4, the DCR abstract's "35%" for fatal outcomes conflicts with Table 7. The table value was used.
Only the four extracts were consulted. No external versions of the papers were used.

spb/wp29_uqo