# 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.