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

# Question

Re-express five printed treatment effects (data/effects.json) on the target definition stated for each item, using only quantities printed in the cited source extract and an explicit transformation; where this is impossible, state so and name the missing quantity.

# Data and exclusions

Inputs: data/effects.json (5 items) and four arXiv extracts (line counts in n_input_rows; SHA-256 verified against data/README.md). All five items were assessed (n_analysed = 5); no exclusions (out/exclusions.csv). Source anomalies are listed in data_issues (e.g. two different SEs for the same DCR ATT, 608 vs 640 control regions, the abstract's "fatal fall by 35%" vs Table 7, the minimum-wage note's "about 4%" vs the printed 0.047, the Benin headline 0.0855 coming from a table absent from the extract). None changes a harmonised value except where stated below.

# Method

Conventions from TASK.md, applied to printed numbers only (harmonised.*.transformation, harmonised.*.locator):

• E1 (log points → % of counterfactual): 100·(exp(b)−1), b = −0.431 (DCR Table 6, ATT, 5 km).
• E2 (pp → % of control mean): 100·Δ/p, Δ = 1.47 pp (Table 2 ATE), p = 75.0% (Table 2 Control).
• E3 (elasticity → % change for the observed MW rise): 100·η·g, η = −0.388, g = 0.047 (Table 2 rows "Employment elasticity w.r.t MW" and "% MW changes").
• E4 (log points → absolute change per 100,000): requires Y0·(exp(b)−1) with a baseline level Y0, which the extract does not print.
• E5 (0–1 probability → pp): 100·β, β = −0.0962 (Table 3, Treatment, col (4)). out/analysis.py locates each input line by pattern, prints it, and writes out/results.json; no randomness (random_seed = null).

# Results

n_harmonised = 4, n_not_harmonisable = 1, feasibility = "complete": every item has either a value or a justified statement of impossibility. E1 agrees with the paper's printed "% change" of −35.0% (baseline_printed_conversions.E1_table6_pct_change_row_5km). For E4, the relative change 100·(exp(−0.354)−1) ≈ −29.81% can be computed (noted in harmonised.E4.transformation), but the target is an absolute rate change, which needs the baseline level of the fatal drug-related hospitalisation rate per 100,000 in the 5 km treated regions (harmonised.E4.missing_quantity).

# Uncertainty

No standard errors or confidence intervals were propagated (none are required). Exactness of the conversions:

• E5 is exact: only the scale changes.
• E1 is exact under the log-point convention for the effect on the log rate. Interpreting it as the percent change in the rate level relies on the usual exp(b)−1 approximation, which ignores Jensen-type retransformation terms.
• E2 is approximate. The ATE adjusts for randomisation week, but the denominator is the raw aggregate control mean (75.0%), which only stands in for the counterfactual level. Rounding of the printed numbers also matters (1.47 pp, 75.0%).
• E3 is approximate. A constant elasticity is applied linearly to a discrete 4.7% change. g is printed to 3 decimals, and the table note's "about 4%" would give about −1.55% instead (see data_issues).

# Limitations and open issues

• E4 cannot be harmonised from the extract. The missing quantity is the baseline/counterfactual fatal drug-related hospitalisation rate per 100,000 in the 5 km treated regions. No value was guessed.
• The DCR abstract's "fatal … fall by 35%" does not match Table 7 (−0.354 → −29.8%); we used Table 7. The two SEs printed for the same E1 estimate (0.210 vs 0.218) do not affect point estimates.
• E3 follows the target definition and uses the printed table value 0.047. The table note describes the increase as "about 4%".
• For the Benin study, the abstract's 0.0855 / 18.79% refers to a different table (Table 2, not in the extract) and was not used.