A district mean is not a state figure

The department revised its own FY2024 District Profile Report for exactly this defect. Every figure on the Statewide Data sheet changed from an unweighted mean of 606 district values to an enrolled-ADM-weighted mean: the “statewide” Black enrollment share went from 10.5% — the average of 606 district shares — to 17.3%, which is Ohio’s. Its “statewide” administrator count went from 21.35, the mean district’s, to a state total. #439 adopted the revision and filed the obvious follow-up: the corpus does not read that sheet. It computes its own statewide statistics from district rows. Which convention do those use?

What the audit covered. Every sum::<f64>() / n in the workspace — 62 sites. Most are internal: variance and correlation terms, k-means centroids, three-year averages over years rather than districts, a regression intercept being un-centered. Four are correct by construction and already say so — census_states::national_share and figures::national_share are ratios of sums, achievement_denominator is the department’s own published definition of the top 2% of buildings, implied_divisor averages six schedule-implied divisors and no districts at all.

Five families of unweighted district mean reach a published figure. For each, the question is not whether the number is right but whether the sentence around it is about districts:

• Quantile means of a per-district statistic. fy2016::step_by_quintile, facilities::share_by_quintile, figures::performance_quintiles, figures::quintile_shortfall, project::supplement_reach::by_poverty_quartile, regime_diff::reappraisal_incidence::quartile_gap. Every one of these is measuring spread across districts on purpose. Weighting them would destroy the finding.
• Group comparisons derived from those. The performance-supplement gradient, the share-of-aid ratio, the frozen-parameter gradient.
• A decile mean with its weighted twin already published. ohio_panel::deepest_decile — dispersion/trough-median-decline beside dispersion/trough-weighted-decline, and trough-deepest-decile-pupil-share saying how many pupils the decile holds. This is the practice the rule below generalizes; it was already here.
• A model comparison already aggregated correctly. foundation::refresh’s average_per_pupil is a ratio of sums; its bound_mean_per_pupil and free_mean_per_pupil are group means used only against each other.
• Quartile levels in dollars per pupil. national_peers::ohio_by_local_wealth and ohio_panel::equalization_by_year. This is the family that bites, because the figures are dollars per pupil and read as statements about Ohio’s pupils.

Every group comparison survives the weighting, and most strengthen. Measured, not assumed, because the non-goal of this audit was a sweep and the sweep had to be shown unnecessary rather than asserted to be:

finding                              unweighted   ADM-weighted
performance-supplement gradient          2.5605        2.5983
share of aid, least-poor / poorest        5.251         7.090
frozen-parameter shortfall gradient       4.084         4.573
frozen-parameter statewide level         $73.56        $73.19
foundation::refresh, bound / free   346.28/322.87  341.64/322.65

Not one changes sign, and the two that carry the strongest claims get stronger. So the levels are where the convention shows, and only where a level is stated as a fact about Ohio.

One published finding is wrong rather than unlabeled. doctrine/equity published, on ohio_panel::equalization_by_year: “The state’s share of the gap it closes does not move: 42.4% at the start, 43.9% at the end, and never outside 40.0% to 48.8% in any of the thirteen years. There is no trend inside that window, and the absence of one is the finding rather than a null result.”

Same panel, same population, same quartile membership, summed over pupils instead of over districts:

statistic                              FY2012   FY2024   slope/yr   R2    band
unweighted district mean (published)    42.4%    43.9%     +0.26   0.17   40.0-48.8
ADM-weighted, district quartiles        46.6%    53.6%     +0.79   0.44   45.2-59.5
ADM-weighted, pupil quartiles           40.4%    50.0%     +1.06   0.60   36.5-52.5

Both aggregate readings rise by seven to ten points across the window. Only the district mean is flat. The published sentence makes the absence of a trend the finding, and that absence belongs to the statistic. This is a different kind of defect from a level that is correct and unlabeled: relabeling it does not repair it, because the claim is about movement over time and the movement is real.

The FY2022 single year is the ordinary, milder case. The gap of $9,590 is $8,928 on ADM, state equalization closes $4,922 rather than $4,448, and the headline 46% is 55.1%. The residual falls from $4,229 to $3,214 — a quarter smaller. Every one of those numbers is a correct unweighted mean; each is stated as a fact about Ohio.

A dispersion statistic and an aggregate are different objects, and the corpus does not re-decide per figure.

• A mean over districts answers what does the average district do. It is the right statistic for spread, for gradients, for group comparisons, and for anything whose subject is districts. Most of crates/dispersion is this on purpose.
• An aggregate — a ratio of sums, equivalently an enrollment-weighted mean — answers what does the average pupil’s district do. It is the right statistic for any sentence whose subject is Ohio, its pupils, or its money.
• Where both are wanted, they are two figures. Not one figure with a caveat, and not a recomputation of the first into the second. dispersion/trough-median-decline and dispersion/trough-weighted-decline were already this shape before the audit found the rule.

Applied here:

• Equalization gains weighted_gap, weighted_state_closes, weighted_federal_closes and weighted_state_share, computed over the same quartile membership so that aggregation is the only thing that differs between the pair. Eight new figures publish them, mirroring the four the unweighted reading already had.
• doctrine/equity states both series and withdraws “the rate holds” as a finding about Ohio, keeping it as a property of the district mean. The FY2022 quartile table says in its heading that its columns are district means and carries the weighted line beneath it.
• dispersion::weighted_mean and ohio_panel::Equalization carry the rule in their own docs, so a reader reaching either from code finds it without the corpus.
• Nothing else is recomputed. The other four families are dispersion statistics doing their job.

The corrected finding is stronger than the one it replaces, which is why it had to be checked. “The rate holds and the gap grows” is a bleak, tidy result. What is actually there is that Ohio’s equalization of the local gap has been rising on every reading that weights by pupils — from 47% to 54% on one cut, 40% to 50% on the other — while the gap grows faster still, so the residual grows anyway. The gloomy half survives; the stable half does not.

A third convention exists and is named rather than adopted. Cutting quartiles so each holds a quarter of Ohio’s pupils is a different object again from weighting district-cut quartiles. It is computed in the_rate_that_holds_only_on_the_unweighted_reading and published nowhere: its job is to show the trend is not an artifact of holding the district cut fixed. Two published objects is the rule; three would be the caveat this decision exists to refuse.

The published unweighted figures do not move. dispersion/equalization-band-narrowest is still 0.4002, dispersion/local-revenue-gap-per-pupil still $9,590. A reader who cited them cited a true thing about districts, and the citation survives. Only the sentence that made one of them a sentence about Ohio is withdrawn.

The department’s correction is now readable as a warning rather than a curiosity. Its 10.5%-against-17.3% is the same arithmetic as our 46%-against-55%: a publisher averaging six hundred district values and calling the result a statewide figure. The corpus was doing it in one place, and that place was its central equity claim.

The federal channel’s numbers move least and matter least. $913 becomes $792 and 9.5% becomes 8.9% — inside the noise of a year the corpus already labels as the ESSER peak.

The audit’s non-goal held. Sixty-two sites, five families, one repair. A sweep that ADM-weighted every statistic would have moved the performance-supplement gradient from 2.5605 to 2.5983 and told a reader nothing, while destroying the quintile findings that exist to measure spread.

Recompute the equalization series on ADM and retire the unweighted one. Rejected, and it was the tempting option because the weighted reading is the one the disputed sentence wanted. But ohio_panel is a dispersion module: the distance between what the rich and poor quarters of Ohio’s districts receive is a real quantity that national_peers::ohio_by_local_wealth pins and doctrine/equity uses for its correlations. Retiring it to fix a sentence would break the figures the sentence sits among.

Label the figures and change no number. Rejected on the evidence. It is the right treatment for the FY2022 level — $9,590 is a correct district mean and a label fixes it — and it does not reach a claim about a trend. “There is no trend” cannot be repaired by noting which mean it is the absence of a trend in; the reader’s question is whether Ohio’s equalization is improving, and on the statistic that answers that question it is.

Weight by district count rather than choosing. Not a real alternative but worth recording as the mistake available: averaging the two conventions, or presenting the unweighted one with the weighted in parentheses, produces a number that is neither object and invites exactly the re-decision per figure this record exists to stop.

Cut the quartiles by pupils everywhere. Rejected as the published convention. It is the more coherent aggregate — a quarter of Ohio’s children rather than a quarter of its districts — but it changes the quartile membership, so the weighted and unweighted figures would no longer be two readings of one partition and could not be set side by side. Holding the membership fixed is what makes the pair informative. The pupil cut is computed in the test as a robustness check and stays there.

File it as an open question instead of repairing it. Rejected per finding-an-error-is-not-repairing-it: #463 was itself the filed question, and a second filing would leave the wrong sentence published against a measurement that had already been taken.