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REVIEW 2 major objections 2 minor 78 references

Standard hypothesis tests are invalid under models of generative surveying that include prompt perturbations.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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Standard hypothesis tests fail for generative surveys under realistic prompt perturbations; a permutation test is valid and practical guidance on budget allocation is given.

T0 review reviewed 2026-06-29 challenge →

load-bearing objection The paper shows standard tests fail under a generative survey model with prompt perturbations and offers a permutation test plus budget advice, but the model's match to real LLMs is untested. the 2 major comments →

arxiv 2605.27463 v1 pith:AZZ4Q7OZ submitted 2026-05-26 stat.ME cs.AIstat.AP

When prompt perturbations break your A/B test: A valid statistical test for generative surveying

Hayden Helm , Carey Priebe This is my paper
classification stat.ME cs.AIstat.AP
keywords generative surveyingprompt perturbationshypothesis testingpermutation testA/B testingLLM feedbackstatistical validity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper shows that standard tests such as the sign test and Wilcoxon signed-rank test do not control type I error when applied to generative surveys that account for sensitivity to prompt phrasing. It introduces a permutation test that is valid under a model incorporating realistic perturbation structure. The work also examines how effect estimates vary with model choice and offers guidance on allocating experimental resources across personas, perturbations, and replicates. A sympathetic reader would care because many current applications of LLMs for market research rely on these invalid tests.

Core claim

Under a statistical model for generative surveying that includes realistic perturbation structure, standard hypothesis tests including the sign test and Wilcoxon signed-rank test are invalid, whereas a permutation test is valid. The paper formally characterizes the conditions under which the standard tests fail and demonstrates that both the magnitude and direction of estimated effects are sensitive to the choice of model.

What carries the argument

A permutation test that respects the perturbation structure in the generative surveying model.

Load-bearing premise

The statistical model for generative surveying with realistic perturbation structure accurately describes how LLMs respond to semantically equivalent prompt variations.

What would settle it

Collect data from an LLM survey with multiple perturbations per persona and compare the p-values from the standard sign test and the proposed permutation test; if they frequently disagree on significance, the invalidity claim is supported.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The sign test and Wilcoxon signed-rank test fail to maintain correct type I error rates when perturbations are present.
  • Effect estimates in generative surveys depend on the specific LLM used, even within the same family.
  • Budget should be allocated across personas, perturbations, and replicates to achieve desired power.
  • Conditions for failure of standard tests can be characterized in terms of the perturbation model parameters.

Where Pith is reading between the lines

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

  • Existing generative survey results that used standard tests may need to be reanalyzed with the permutation test.
  • The approach could be extended to other settings where input variations affect statistical conclusions, such as in robustness testing for machine learning models.
  • Power calculations under this model can inform minimal sample sizes for future generative surveys.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper claims that standard hypothesis tests (sign test, Wilcoxon signed-rank) are invalid for A/B testing in generative surveying because LLM responses exhibit dependence induced by prompt perturbations. It derives a permutation test that is valid under the proposed generative model, formally characterizes the conditions under which standard tests fail, applies the framework to estimate model parameters in a simple surveying example, analyzes the power of the permutation test, and supplies guidance on allocating budget across personas, perturbations, and replicates. It also shows that effect magnitude and direction can be sensitive to model choice even within the same LLM family.

Significance. If the perturbation model accurately captures the dependence structure of real LLM responses to semantically equivalent prompts, the work supplies a practically important correction to inference in generative surveying. The valid permutation test and budget-allocation results would directly improve the reliability of LLM-based market research. The formal characterization of test failure conditions is a methodological contribution; the parameter estimation and power analysis add concrete guidance. These strengths are tempered by the absence of external validation that the assumed perturbation structure matches observed LLM behavior.

major comments (2)
  1. [§2] §2 (generative model): the invalidity result for the sign and Wilcoxon tests is derived under a specific perturbation dependence structure; without an explicit equation or proof sketch showing how the covariance between perturbed responses violates the exchangeability or independence assumptions of those tests, the central claim cannot be verified.
  2. [§4–5] §4–5 (application and power): parameters are estimated and power is characterized under the model, yet no comparison of the fitted perturbation distribution to empirical LLM output distributions (e.g., response similarity across prompt variants) is reported; this leaves the practical guidance conditional on an untested modeling assumption.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'realistic perturbation structure' is used without a one-sentence gloss of the key dependence assumption.
  2. [Model section] Notation: the distinction between persona-level, perturbation-level, and replicate-level random effects is not always visually clear in the displayed equations.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and for identifying points that will improve the clarity and transparency of the manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [§2] §2 (generative model): the invalidity result for the sign and Wilcoxon tests is derived under a specific perturbation dependence structure; without an explicit equation or proof sketch showing how the covariance between perturbed responses violates the exchangeability or independence assumptions of those tests, the central claim cannot be verified.

    Authors: Section 2 introduces the generative model in which responses to semantically equivalent prompts share a common perturbation factor, inducing dependence. The text states that this structure violates the assumptions of the sign and Wilcoxon tests, but we agree that an explicit covariance equation and short proof sketch would make the violation transparent. In the revised manuscript we will insert a short derivation showing that Cov(Y_{ij}, Y_{ik}) > 0 for j ≠ k under shared perturbation, which directly breaks the exchangeability required by those tests. revision: yes

  2. Referee: [§4–5] §4–5 (application and power): parameters are estimated and power is characterized under the model, yet no comparison of the fitted perturbation distribution to empirical LLM output distributions (e.g., response similarity across prompt variants) is reported; this leaves the practical guidance conditional on an untested modeling assumption.

    Authors: We acknowledge that the paper contains no direct empirical comparison of the fitted perturbation distribution to observed LLM response similarities. The power and budget-allocation results in §§4–5 are therefore conditional on the modeling assumption. In revision we will add an explicit limitations subsection that states this assumption, motivates it from existing literature on prompt sensitivity, and outlines the empirical checks that would be needed to validate it. We cannot supply the missing comparison without new data collection outside the scope of the present work. revision: partial

standing simulated objections not resolved
  • Empirical validation of the assumed perturbation dependence structure against observed LLM output distributions.

Circularity Check

0 steps flagged

No circularity detected; derivation is model-internal but self-contained

full rationale

The paper defines a generative surveying model that incorporates prompt perturbations and derives the invalidity of sign/Wilcoxon tests (plus validity of a permutation test) strictly under that model. No equations, fitted parameters, or self-citations appear in the abstract or provided text that would reduce any claim to its inputs by construction. The load-bearing assumption that the model captures 'realistic' structure is an external modeling choice, not a definitional loop or renamed fit. This is the normal case of a paper working inside its stated assumptions without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the central model is described only at the level of 'realistic perturbation structure' without further decomposition.

reviewed 2026-06-29 · how reviews work

0 comments
Cite this review

Pith. "Pith review of When prompt perturbations break your A/B test: A valid statistical test for generative surveying." pith.science (2026). https://pith.science/paper/AZZ4Q7OZ

@misc{pith2026260527463,
  author       = {Pith},
  title        = {Pith review of: When prompt perturbations break your A/B test: A valid statistical test for generative surveying},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AZZ4Q7OZ}},
  note         = {Machine review of arXiv:2605.27463}
}
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read the original abstract

Generative surveying -- where collections of LLM-based personas provide feedback on messages -- has emerged as a cheap and scalable alternative to traditional market research. However, LLMs are sensitive to small variations in prompt design and conclusions drawn from generative surveys may depend on arbitrary phrasing choices. Controlling for this sensitivity requires including semantically equivalent perturbations in the analysis. In this paper, we show that standard hypothesis tests, including the sign test and Wilcoxon signed-rank test, are invalid under a statistical model for generative surveying that includes realistic perturbation structure. We propose a permutation test that is valid under this model and formally characterize the conditions under which standard tests fail. Applying our framework to a simple generative surveying problem, we estimate relevant parameters, characterize the power of the permutation test under realistic conditions, and provide practical guidance on budget allocation across personas, perturbations, and replicates. Finally, we show that both the magnitude and direction of the estimated effect are sensitive to the choice of model, even within the same model family.

Figures

Figures reproduced from arXiv: 2605.27463 by Carey Priebe, Hayden Helm.

Figure 1
Figure 1. Figure 1: (Left) Illustration of persona-based generative message testing for a single persona. The illustrated [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (Left) Simple statistical model for persona-based generative surveying where outcomes are binary. Light [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Empirical CDF of p-values under the null [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Power of the permutation test as a function of total query budget [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Effect size (βˆ 1) versus number of active pa￾rameters for models in the Mistral-3 and Qwen-3 fami￾lies. Effect size is non-monotonic in model scale within both families. Same scale models across families can produce estimates of opposite sign (e.g., Mistral-8B and Qwen-3-8B estimate effects in opposite directions) meaning that model choice alone can determine the con￾clusion of a generative survey. should… view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

78 extracted references · 4 canonical work pages · 2 internal anchors

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This paper was first reviewed by grok-4.3 on June 29, 2026.