The declared twofold rule is recomputed from all twelve clinic-year rows.
What could have been known, Vienna 1841 to 1849
Before the Washing
The mortality difference was visible years before chlorine hand cleansing. That does not mean the tables contained the remedy. Lock an alarm before the six annual releases appear, then follow every reversal and inspect the information that never entered the ledger.
Semmelweis reports repeated commissions. The primary text does not date the first one.
The institution eventually tried chlorine washing. A risk ratio cannot name hand carriage.
Set the bell before opening the ledger
Each release is one complete calendar year from Semmelweis's Table I. Both clinics exceed 2,000 births in the first year, so the rule is evaluable immediately. The page's declared rule is twofold. The other thresholds are reader-chosen sensitivity checks.
Commit first. The complete six-year run appears only after the rule is locked.
| cutoff | I births | I deaths | II births | II deaths | cumulative ratio | state |
|---|
What the crossing means. It is a clinic-level alarm, no more. It does not distinguish autopsy exposure from teaching intensity, examination frequency, admission mix, room conditions, or the way deaths after transfer were counted.
The comparison the page can honestly make
At each year label, it sums births and deaths available through that label and applies one unchanged threshold.
The administration repeatedly investigated. Semmelweis instituted chlorine washing in mid-May 1847, after connecting Kolletschka's fatal illness with cadaveric material.
The frozen rule does not beat the institution at noticing that something was wrong. It has an earlier dated output than Semmelweis's intervention, but it supplies no cause and no treatment. A numerical score between these unlike actions would pretend they were the same decision, so this page refuses to print one.
Ninety-eight months, one damaged cell
The publication supplies 98 month-labelled Clinic I records from January 1841 through March 1849. This is not a two-clinic monthly archive. December 1841 is absent because the notes were lost. February 1847 prints 912 births and 6 deaths beside 1.92%, values that cannot all be true.
Source literalComputing...not the printed 1.92%
Labelled correctionComputing...312 fits the rate and surrounding scale
Every one of the 98 printed month records is used, later, excluded for the stated inconsistency, or undated. The absent December 1841 sheet is shown as a gap, not invented as a record. Chart: 98 of 98 record positions drawn.
Watching evidence without rewarding the peek
At the May 1847 month boundary, the corrected prewashing survival rate is frozen as the point-null comparator. The next 22 month releases are then replayed to March 1849. The e-process tests whether survival is higher than that frozen rate. The naive column repeatedly recomputes an ordinary one-sided binomial p-value on the same accumulating births.
| release | post births | post deaths | e-value | naive p |
|---|
What exactly is being tested?
The null is a post-May survival probability no greater than the observed prewashing survival probability, whose mortality complement is computed live. The e-process is the shared kit's equal mixture of 19 point likelihood-ratio martingales. It is checked only at month boundaries because the archive gives no order of births within a month.
This is a conditional comparison with a fixed historical baseline, not a randomized causal estimate. The baseline was estimated from earlier patients, patient outcomes within months are treated as Bernoulli observations, and changes other than hand cleansing were not controlled.
The peek trap under a true null
This separate fair-coin demonstration uses the same 0.05 naive boundary and 20 e-value boundary. It is not Vienna data. Run 2,000 seeded null paths and keep every look through 1,000 observations.
Not run yet.
| looks allowed | naive ever p ≤ 0.05 | e ever ≥ 20 |
|---|
The naive ever-crossing rate keeps rising with more looks and approaches 1 in an indefinitely long Bernoulli run. Ville's inequality bounds the e-process ever-crossing probability by 5% under its null.
What no diligence could recover in 1841
The annual ledger can separate clinics. It cannot separate the things that differ with clinics. Choose a proposed explanation and ask what observation would have been needed.
Not recorded: examiner-level autopsy contact and hand contact for each patient. A clinic label cannot isolate cadaveric transfer from other clinic-correlated differences.
| quantity | in annual table? | why it matters |
|---|---|---|
| births and maternal deaths | yes | estimates the clinic association |
| individual examiner contacts | no | needed to connect exposure to outcome |
| autopsy exposure | no | needed to distinguish hand carriage |
| onset and transfer outcome | no | needed to repair outcome accounting |
| organisms | no | not observable with this aggregate record |
| mortality under chlorine washing | not in 1841 | the intervention had not yet occurred |
The honest counterfactual. The observed record can score an alarm against what later happened. It cannot tell us how many deaths would have occurred if chlorine washing had begun in 1841, because that branch was never observed.
The check
Published anchor, recomputed here
Semmelweis prints Clinic I totals of 20,042 births, 1,989 deaths, and 9.92% for 1841 to 1846.
Computing Clinic I...
Clinic II is printed as 17,791 births, 691 deaths, and 3.38%. The counts disagree with that percentage.
Computing Clinic II...
Recomputing all fourteen printed percentages
The obvious next question is whether that one cell is unusual or whether the whole table is loose, and the honest way to answer it is to recompute every printed percentage from the counts printed beside it. The table does not use one convention: some cells are rounded to the last printed digit and some are truncated, and three match neither. So the interesting quantity is not whether a cell reproduces exactly, it is by how much each one misses.
| cell | counts give | printed | miss | rounds? | truncates? |
|---|---|---|---|---|---|
| Recomputing... | |||||
Summarising...
Eleven of the fourteen cells land on the printed digit under one convention or the other, and the annual cells that miss, miss by about a tenth of a point, the size of a single mis-set digit in the last place. Clinic II's Summa misses by half a point, several times any other cell in the table. Its shape is a mis-set digit too, but one place further left: 3.88 set as 3.38.
It happens to matter. On the same printed page, immediately above the table, Semmelweis writes that mortality in the first division was, over six years, durchschnittlich dreimal so gross as in the second. There are three defensible ways to read that against his own numbers, and the page computes all three rather than choosing one:
| reading | value |
|---|---|
| ratio of the summed risks, Clinic I over Clinic II | ... |
| mean of the six annual risk ratios | ... |
| ratio implied by the printed 9.92 over 3.38 | ... |
What this is not. It is not evidence that Semmelweis massaged anything. Read as the mean of his six annual ratios, which is the natural reading of durchschnittlich, his sentence is a fair rounding of his own data. The finding is about one printed number, not about a man's integrity, and he was right about the thing that mattered. What the arithmetic does show is that the only figure in the table which cannot be recovered from its own inputs is also the one that sits closest to the claim printed above it, and a reader checking the table in 1861 could have found that with nothing but the counts on the page.
Firewall and negative control
The source timestamps are its printed year and month labels, treated at only that precision. No day or clock time is assigned. Year comparisons occur only after a complete labelled year.
Running planted-row audit...
The plant is inserted into the same annual data array and passed through the same cutoff function used by the instrument.
Free choices
- Twofold cumulative risk ratio after at least 2,000 births per clinic.
- Inclusive year and month labels, with no invented finer time.
- The optional 312 correction for February 1847.
- May 1847 as the last prewashing month because the intervention began sometime in its second half.
- Equal mixture over 19 higher survival alternatives, alpha 0.05.
- Fair-coin null audit: seed 184705, 2,000 paths, 1,000 looks.
Uncertainty and refusal
- The exact day chlorine washing began is unknown.
- December 1841 monthly notes were lost.
- February 1847's printed births conflict with its printed rate.
- The annual and monthly archives have different resolution.
- Deaths after transfer were not counted symmetrically.
- The aggregate record cannot identify a clean causal effect.
Literal-source mode refuses downstream cumulative monthly rates after the inconsistent cell.
Independent check: node research/semmelweis-before-the-washing/verify.mjs. All displayed results are computed in the browser from the shipped rows. No numerical result is precomputed.