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arxiv: 2606.31418 · v1 · pith:EY5QA3SHnew · submitted 2026-06-30 · 📊 stat.ME

On the choice of using raw or demographically-corrected scores

Ignacio Gonzalez-Perez , Mats Julius Stensrud , Marco Piccininni This is my paper

Pith reviewed 2026-07-01 04:33 UTC · model grok-4.3

classification 📊 stat.ME
keywords demographic correctionz-score standardizationclassification accuracycognitive screeningMini-Mental State Examinationfairnessthreshold classifiers
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The pith

Raw scores outperform demographically corrected scores for classification under specific data conditions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that demographic corrections such as z-score standardization can reduce accuracy when classifying individuals from cognitive screening tests. It derives sufficient conditions on the joint distributions of demographics, scores, and class labels that make the raw score the better classifier for threshold rules. These conditions receive a substantive interpretation, and the result is checked against the claim that corrections produce fairer decisions. The analysis is applied to the Mini-Mental State Examination in the OASIS-3 data.

Core claim

Under sufficient conditions on the joint distribution of demographic variables, test scores, and the binary class label, a threshold classifier based on the raw score achieves strictly higher accuracy than the same threshold applied to the demographically corrected score.

What carries the argument

Sufficient conditions on the relationship among demographics, raw scores, and labels that guarantee higher accuracy for raw-score classification.

If this is right

  • Accuracy of threshold-based decisions can improve by retaining raw scores rather than applying demographic corrections.
  • Claims that demographic correction increases fairness require separate verification against the actual decision rule.
  • The choice between raw and corrected scores depends on the joint distribution of demographics, scores, and the target outcome.
  • For the MMSE, raw scores are preferable when the data satisfy the derived conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Practitioners could test the sufficient conditions on their own data before deciding whether to correct scores.
  • The same logic may extend to other threshold-based screening instruments that adjust for age, education, or sex.
  • Alternative correction methods could be evaluated by checking whether they violate or satisfy analogous conditions.

Load-bearing premise

The observed data distributions match the sufficient conditions derived for the classification task.

What would settle it

Empirical comparison on a new dataset in which the corrected scores produce measurably higher classification accuracy than raw scores while satisfying the stated conditions would refute the central claim.

Figures

Figures reproduced from arXiv: 2606.31418 by Ignacio Gonzalez-Perez, Marco Piccininni, Mats Julius Stensrud.

Figure 1
Figure 1. Figure 1: DAG representing the causal structure of the variables in our system. strong assumptions: it does not allow raw and corrected ROC curves to cross. For example, it is possible that ROC curves cross and still AUC(X) ≥ AUC(Z). This is considered a disadvantage of the AUC as a comparative tool [43]. However, our previous results like Theorems 1 and 2 are not affected by this caveat, as they perform local (at a… view at source ↗
Figure 2
Figure 2. Figure 2: Example of a causal DAG for the scenario introduced in Sec￾tion 3 (A) and its associated extended causal DAG (B). Definition 3 (Strong demographic insensitivity). We say that a score S is insen￾sitive to the demographics V in the strong sense if the distribution of S vS | {V = v, D = d} does not depend on vS for all (v, d) in V × {0, 1}. Yet, in our screening problem we are not necessarily interested in th… view at source ↗
Figure 3
Figure 3. Figure 3: Extended causal DAG introduced in [PITH_FULL_IMAGE:figures/full_fig_p030_3.png] view at source ↗
read the original abstract

Demographic corrections are routinely performed in many disciplines, including psychology. Yet, there are ongoing debates about whether these corrections are appropriate and improve classification accuracy. Here, we focus on cognitive screening tests, and show that common demographic corrections, like the z-score standardization, can be detrimental for classification in some settings. Formally, we present sufficient conditions ensuring that raw scores outperform the demographically-corrected ones, and give a substantive interpretation of this result. We also investigate the claim that using demographically-corrected scores results in more fair decisions compared to using raw scores. We apply our results to the Mini-Mental State Examination in the OASIS-3 dataset.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that common demographic corrections such as z-score standardization can be detrimental to classification performance in some settings, including cognitive screening tests. It derives sufficient conditions under which raw scores strictly outperform demographically corrected scores, provides a substantive interpretation of those conditions, examines implications for fairness, and applies the results to the Mini-Mental State Examination (MMSE) in the OASIS-3 dataset.

Significance. If the derived sufficient conditions are shown to be satisfied by the relevant data distributions, the work supplies a formal, distribution-dependent argument against routine demographic correction and identifies concrete settings where raw scores are preferable. The explicit statement of conditions and the real-data application constitute a strength; however, the practical impact hinges on verification that the OASIS-3 joint distributions meet the stated inequalities.

major comments (2)
  1. [Abstract / sufficient-conditions section] Abstract and the section stating the sufficient conditions: the central claim rests on distribution-dependent inequalities between conditional densities of the raw score given disease status and demographics. The manuscript applies the result to MMSE in OASIS-3, yet provides no explicit check that the observed empirical conditional distributions satisfy the required relationships (e.g., the location or scale shifts induced by demographics). Without this verification the formal guarantee does not transfer and the empirical comparison stands alone.
  2. [OASIS-3 application] Application section (OASIS-3 analysis): the load-bearing empirical step is whether the data satisfy the inequalities; if the parametric assumptions implicit in the conditions are violated by the MMSE score distributions, the reported performance comparison becomes the sole evidence and requires accompanying sensitivity or bootstrap analysis that is not described.
minor comments (2)
  1. Notation for the conditional densities and the precise statement of the sufficient conditions could be clarified with an accompanying diagram or table of the required inequalities.
  2. The fairness discussion would benefit from an explicit definition of the fairness metric used and a side-by-side numerical comparison with the classification-performance results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments highlighting the link between the theoretical conditions and the empirical application. We address each major comment below and outline revisions where appropriate.

read point-by-point responses

  1. Referee: The manuscript applies the result to MMSE in OASIS-3, yet provides no explicit check that the observed empirical conditional distributions satisfy the required relationships (e.g., the location or scale shifts induced by demographics). Without this verification the formal guarantee does not transfer and the empirical comparison stands alone.

    Authors: The sufficient conditions identify theoretical settings where raw scores strictly dominate. The OASIS-3 section is an independent empirical demonstration that raw MMSE scores can yield higher classification accuracy than z-scores in this dataset; we do not claim the data satisfy the inequalities. The direct performance comparison therefore stands on its own. To improve clarity we will add a brief discussion of the empirical conditional distributions and note that verification of the inequalities is not required for the reported results. revision: partial

  2. Referee: the load-bearing empirical step is whether the data satisfy the inequalities; if the parametric assumptions implicit in the conditions are violated by the MMSE score distributions, the reported performance comparison becomes the sole evidence and requires accompanying sensitivity or bootstrap analysis that is not described.

    Authors: The OASIS-3 results are obtained via direct, non-parametric evaluation (cross-validated AUC or accuracy) of classifiers trained on raw versus corrected scores; they do not rely on the parametric form of the sufficient conditions. Nevertheless, we agree that quantifying uncertainty in the performance difference would strengthen the empirical claim and will add bootstrap confidence intervals for the reported metrics in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

Derivation of sufficient conditions is self-contained and non-circular

full rationale

The paper's core contribution is a set of formally derived sufficient conditions on conditional densities under which raw scores strictly outperform demographically corrected scores for classification. These conditions are presented as mathematical statements rather than empirical fits or self-referential definitions. No load-bearing step reduces to a fitted parameter renamed as a prediction, a self-citation chain, or an ansatz smuggled via prior work. The OASIS-3 application functions as an empirical check of the conditions rather than the source of the result itself. The derivation chain therefore remains independent of its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on abstract; no explicit free parameters, axioms, or invented entities are described.

pith-pipeline@v0.9.1-grok · 5636 in / 847 out tokens · 31124 ms · 2026-07-01T04:33:03.211817+00:00 · methodology

discussion (0)

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Reference graph

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