Pith. sign in

REVIEW 2 major objections 33 references

Analysis of uncertain fixed-effects model for Latin square designs

T0 review · 2 major / 0 minor · reviewed 2026-06-26 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Uncertain fixed-effects models for Latin square designs estimate treatment and block effects using an uncertain measure when data lacks frequency stability.

desk verdict The paper recasts Latin square fixed-effects estimation inside uncertainty theory with three methods, simulations, and an education example, but the motivation for switching frameworks looks thin. read the letter →

arxiv 2606.20226 v1 pith:MALHM6DC submitted 2026-06-18 stat.ME stat.CO

Yaru Cheng , Zhiming Li This is my paper · ORCID
classification stat.MEstat.CO
keywords uncertainmeasurefixed-effectsmodelLatinsquaredesignestimationmethodshypothesistestingconfidenceintervalsexperimental
verification ladder T0 review T1 audit T2 compute T3 formal

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 establishes fixed-effects models for Latin square designs based on uncertain measure instead of probability. Three estimation methods are proposed for treatment and blocked effects, along with methods to construct confidence intervals. Uncertain homogeneity and common tests are developed to check the significance of treatment effects. Numerical simulations compare the methods using bias, mean squared error, and other metrics, and the model is applied to real education data.

What carries the argument

The uncertain fixed-effects model for Latin square designs, which uses uncertain measure to model observations and derive estimators for effects and tests for significance.

What would settle it

A simulation or dataset where the uncertain estimators fail to recover known effects or where confidence intervals do not achieve the claimed coverage under the uncertain measure axioms.

Watch

Extended reading notes

Core claim

Based on an uncertain measure, uncertain fixed-effect models are established for Latin-square designs. Three methods estimate the treatment and blocked effects and construct their confidence intervals. Uncertain homogeneity and common tests assess the significance of treatment effects.

Load-bearing premise

The experimental observations obey the axioms and operational laws of an uncertain measure rather than a probability measure, with the Latin square blocking structure remaining valid.

Editorial extensions

If this is right

  • Three estimation methods allow computation of treatment and block effects with associated confidence intervals.
  • Uncertain homogeneity and common tests provide ways to evaluate if treatment effects are significant under uncertainty.
  • Simulation studies show performance on bias, MSE, MAE, and coverage probability metrics.
  • The model can be applied to real-world experimental data such as education studies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The approach could extend to other experimental designs like randomized blocks if the uncertain measure framework holds.
  • Practitioners in fields with sparse or unstable data might prefer these methods over classical ones when frequency stability is absent.
  • Further work could compare these uncertain methods directly to Bayesian or robust alternatives in statistics.
Share X Bluesky LinkedIn Reddit HN

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 / 0 minor

Summary. The manuscript proposes uncertain fixed-effects models for Latin square designs based on uncertainty theory rather than probability. It introduces three estimation methods for treatment and block effects together with associated confidence intervals, develops uncertain homogeneity and common tests for treatment significance, compares the estimators via simulation on bias/MSE/MAE/standard deviation/coverage/interval length, provides illustrative examples, and demonstrates the approach on real education data.

Significance. If the derivations hold and the uncertain-measure framework is justified for this setting, the work would supply an alternative analysis route for experimental data lacking frequency stability. The simulation study and real-data example supply concrete empirical content, but the departure from Kolmogorov axioms and the preservation of Latin-square orthogonality under uncertain operational laws remain unexamined in the provided description.

major comments (2)
  1. [Abstract / Introduction] The abstract states that classical fixed-effects models 'can only analyze precise experimental data,' yet provides no supporting argument or reference; this motivational claim is load-bearing for preferring uncertainty theory and requires explicit justification or comparison with existing robust or imprecise-data methods in the introduction or §2.
  2. [Methods (unspecified section)] No equations, derivations, or measurability conditions are visible for the three estimation methods or the uncertain homogeneity/common tests. Consequently it is impossible to verify whether the additive row-column-treatment structure and its orthogonality are preserved under the uncertain-measure axioms (normality, duality, subadditivity, product axiom) cited in the skeptic note; this is central to every subsequent result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and will revise the manuscript accordingly to improve clarity and justification.

read point-by-point responses

  1. Referee: [Abstract / Introduction] The abstract states that classical fixed-effects models 'can only analyze precise experimental data,' yet provides no supporting argument or reference; this motivational claim is load-bearing for preferring uncertainty theory and requires explicit justification or comparison with existing robust or imprecise-data methods in the introduction or §2.

    Authors: We agree that the claim requires explicit support. In the revised version we will expand the introduction (and §2) with a discussion of the limitations of classical fixed-effects models when data lack frequency stability, together with references to uncertainty-theory applications in experimental design and comparisons to robust or imprecise-probability approaches. revision: yes

  2. Referee: [Methods (unspecified section)] No equations, derivations, or measurability conditions are visible for the three estimation methods or the uncertain homogeneity/common tests. Consequently it is impossible to verify whether the additive row-column-treatment structure and its orthogonality are preserved under the uncertain-measure axioms (normality, duality, subadditivity, product axiom) cited in the skeptic note; this is central to every subsequent result.

    Authors: We apologize that the submitted version did not make the derivations sufficiently visible. Section 3 contains the three estimation methods (least-squares, maximum-likelihood, and moment estimators) expressed via uncertain variables, together with the homogeneity and common tests. In the revision we will insert an explicit subsection that states the measurability conditions, reproduces the key uncertain operational laws, and demonstrates that the additive row-column-treatment decomposition and the associated orthogonality relations are preserved under the cited axioms (normality, duality, subadditivity, and product axiom). revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity detected

full rationale

The paper introduces uncertain fixed-effects models for Latin square designs grounded in uncertain measure axioms (distinct from probability), proposes three estimation methods for treatment/blocked effects plus confidence intervals, and derives homogeneity/common tests for significance. No equations or steps are exhibited that reduce any prediction, estimator, or test statistic to a fitted input by construction, nor do self-citations load-bear the central framework choice. The derivation chain remains self-contained with independent content from the uncertain-measure operational laws and Latin-square blocking structure.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The central claim rests on the standard axioms of uncertainty theory (normality, duality, subadditivity) and the modeling assumption that Latin square data can be represented by uncertain variables. No free parameters or invented entities are identifiable from the abstract.

assumptions (2)
  • standard math Uncertain measure satisfies normality, duality, and subadditivity axioms of uncertainty theory
    Invoked as the foundation for the uncertain fixed-effects model in the abstract.
  • domain assumption Latin square blocking structure remains valid when observations are uncertain variables
    Required for the fixed-effects model to apply to the design.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Analysis of uncertain fixed-effects model for Latin square designs." pith.science (2026). https://pith.science/paper/MALHM6DC

@misc{pith2026260620226,
  author       = {Pith},
  title        = {Pith review of: Analysis of uncertain fixed-effects model for Latin square designs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MALHM6DC}},
  note         = {Machine review of arXiv:2606.20226}
}
read the original abstract

Uncertain data without frequency stability often arises in experimental design. Classical fixed-effects models can only analyze precise experimental data. Based on an uncertain measure, this paper establishes uncertain fixed-effect models for Latin-square designs. First, we propose three methods with uncertainty to estimate the treatment and blocked effects and construct their confidence intervals. Then, uncertain homogeneity and common tests are conducted to assess the significance of treatment effects. In the numerical simulations, the three estimation methods are compared based on bias, mean squared error, mean absolute error, overall standard deviation, coverage probability, and average interval length. Several examples are given to illustrate the process of estimation and hypothesis. Finally, the uncertain fixed-effects model is applied to real education data, demonstrating its practical value.

Figures

Figures reproduced from arXiv: 2606.20226 by the authors.

Figure 1
Figure 1. Comprehensive performance comparison of the three estimation methods under varying noise levels. [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Comparison of the three estimation methods under contaminated noise levels. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

33 extracted references · 5 canonical work pages

  1. [1]

    The design of experiments [M]

    Fisher R A. The design of experiments [M]. Edinburgh: Oliver & Boyd, 1935

    1935

  2. [2]

    Latin square design for selection of excipients in the development of the composition of medical sponges based on the cryoliophylized xenoderm [J]

    Pavliuk B, Chubka M, Spetsialna H, Diadiun T. Latin square design for selection of excipients in the development of the composition of medical sponges based on the cryoliophylized xenoderm [J]. Pharmakeftiki, 2024, 36(1): 40–52

    2024

  3. [3]

    Orthogonal Latin square theory based group and batch verification for digital signatures [J]

    Wang H, Lai C Z, Liu X Y, Zeng H. Orthogonal Latin square theory based group and batch verification for digital signatures [J]. Journal of Communications, 2022, 43(2): 44–54

    2022

  4. [4]

    Latin-square-based key negotiation protocol for a group of UAVs [J]

    Kou G Y, Wei G H, Yuan Z M, Li S L. Latin-square-based key negotiation protocol for a group of UAVs [J]. Electronics, 2023, 12(14): 3131

    2023

  5. [5]

    Comparative evaluation of completely randomized design, randomized complete block design, and Latin square design: A simulation study [J]

    Osuagwu C U, Mbachu H I. Comparative evaluation of completely randomized design, randomized complete block design, and Latin square design: A simulation study [J]. International Journal of Scientific Research in Multidisciplinary Studies, 2024, 10(11): 75–81. 18 Yaru Cheng, Zhiming Li*

    2024

  6. [6]

    Some matrix constructions of L2-type Latin square designs [J]

    Saurabh S, Sinha K. Some matrix constructions of L2-type Latin square designs [J]. Bulletin of the Institute of Combinatorics and its Applications, 2022, 95: 93–104

    2022

  7. [7]

    Further results on large sets plus of partitioned incomplete Latin squares[J]

    Lu H, Cao H. Further results on large sets plus of partitioned incomplete Latin squares[J]. Discrete Mathematics, 2025, 348(1): 114215

    2025

  8. [8]

    Construction of partial diallel crossing system using Latin square designs [J]

    Singh P, Sharma R. Construction of partial diallel crossing system using Latin square designs [J]. International Journal of Agricultural and Statistical Sciences, 2023, 19(2): 851–858

    2023

Show all 33 references
  1. [9]

    Latin squares and their applications [M]

    Dnes J, Keedwell A D. Latin squares and their applications [M]. New York: Academic Press, 1974

    1974

  2. [10]

    A generalized model for a Latin square design [J]

    Tar L. A generalized model for a Latin square design [J]. Alkalmazott Matematikai Lapok, 1980, 27: 309–325

    1980

  3. [11]

    On the randomization in Latin-square design under the Neyman model [J]

    Ogawa J. On the randomization in Latin-square design under the Neyman model [J]. Proceedings of the Institute of Statistical Mathematics, 1962, 10: 1–16

    1962

  4. [12]

    Statistical design and analysis of experiments [M]

    John P W M. Statistical design and analysis of experiments [M]. New York: Macmillan, 1971

    1971

  5. [13]

    Regression models for randomized complete block, Latin squares, and Graeco-Latin square designs[M]//Design and Analysis of Experiments: Classical and Regression Approaches with SAS

    Onyiah L C. Regression models for randomized complete block, Latin squares, and Graeco-Latin square designs[M]//Design and Analysis of Experiments: Classical and Regression Approaches with SAS. Boca Raton: Chapman and Hall/CRC, 2008: 341–419

    2008

  6. [14]

    How to use analysis of variance correctly: an analysis of variance for the univariate quantitative data collected from the Latin square design [J]

    Hu C, Hu L. How to use analysis of variance correctly: an analysis of variance for the univariate quantitative data collected from the Latin square design [J]. Journal of Southern Medical University, 2012, 32(5): 709–713

    2012

  7. [15]

    Augmented Latin square designs for imprecise data [J]

    Al-Aita A, Talebi H. Augmented Latin square designs for imprecise data [J]. Communications in Statistics–Theory and Methods, 2015, 44(12): 2533–2547

    2015

  8. [16]

    Enhancing experimental efficiency in uncertain data: a comparative analysis of neutrosophic and classical Latin square designs [J]

    Kumari S, Shahabudheen A. Enhancing experimental efficiency in uncertain data: a comparative analysis of neutrosophic and classical Latin square designs [J]. Neutrosophic Sets and Systems, 2020, 31: 125–136

    2020

  9. [17]

    Uncertainty theory [J]

    Liu B. Uncertainty theory [J]. Studies in Fuzziness and Soft Computing, 2007, 154: 205–234

    2007

  10. [18]

    Uncertainty theory [M]

    Liu B. Uncertainty theory [M]. 6th ed. Berlin: Springer-Verlag, 2026

    2026

  11. [19]

    Uncertain regression analysis: an approach for imprecise observations [J]

    Yao K, Liu B. Uncertain regression analysis: an approach for imprecise observations [J]. Soft Computing, 2018, 22(17): 5579– 5582

    2018

  12. [20]

    Uncertain maximum likelihood estimation with application to uncertain regression analysis [J]

    Lio W, Liu B. Uncertain maximum likelihood estimation with application to uncertain regression analysis [J]. Soft Computing, 2020, 24(13): 9351–9360

    2020

  13. [21]

    Least absolute deviations estimation for uncertain regression with imprecise observations [J]

    Liu Z, Yang Y. Least absolute deviations estimation for uncertain regression with imprecise observations [J]. Fuzzy Optimization and Decision Making, 2020, 19: 33–52

    2020

  14. [22]

    Uncertain regression model based on Huber loss function [J]

    Xie W, Wu J, Sheng Y. Uncertain regression model based on Huber loss function [J]. Journal of Intelligent and Fuzzy Systems, 2023, 45: 1169–1178

    2023

  15. [23]

    Uncertain hypothesis test with application to uncertain regression analysis [J]

    Ye T, Liu B. Uncertain hypothesis test with application to uncertain regression analysis [J]. Fuzzy Optimization and Decision Making, 2022, 21(2): 157–174

    2022

  16. [24]

    Uncertain significance test for regression coefficients with application to regional economic analysis [J]

    Ye T, Liu B. Uncertain significance test for regression coefficients with application to regional economic analysis [J]. Commu- nications in Statistics–Theory and Methods, 2023, 52(20): 7271–7288

    2023

  17. [25]

    A formula to calculate the variance of uncertain variable[EB/OL]

    Yao K. A formula to calculate the variance of uncertain variable[EB/OL]. http://orsc.edu.cn/online/130831, 2013

    2013

  18. [26]

    Analysis of hypothesis tests for multiple uncertain finite populations with applications to normal uncertainty distributions[EB/OL]

    Zhang F, Li Z M. Analysis of hypothesis tests for multiple uncertain finite populations with applications to normal uncertainty distributions[EB/OL]. https://arxiv.org/abs/2512.02832, 2025

    2025

  19. [27]

    Latin square design: A methodological innovation in educational research for improved teaching and learning [J]

    Sule A S, Lantana B, Nuhu U M, Nasir U, Amina A N. Latin square design: A methodological innovation in educational research for improved teaching and learning [J]. FUDMA Journal of Sciences, 2025, 9(5): 328–334

    2025

  20. [28]

    Estimation of unknown parameters in uncertainty distribution via the least absolute deviation principle and its application in uncertain statistics [J]

    Ning S, Liu Y. Estimation of unknown parameters in uncertainty distribution via the least absolute deviation principle and its application in uncertain statistics [J]. Communications in Statistics–Simulation and Computation, 2026:1–13

    2026

  21. [29]

    Least absolute deviation estimation for uncertain regression model via uncertainty distribution and its application in sport statistics [J]

    Dong Y. Least absolute deviation estimation for uncertain regression model via uncertainty distribution and its application in sport statistics [J]. Symmetry, 2026, 18(2):260. https://doi.org/10.3390/sym18020260

    2026 doi

  22. [30]

    Minimum relative error estimation for uncertain regression model with imprecise observations [J]

    Huang X, Sheng Y. Minimum relative error estimation for uncertain regression model with imprecise observations [J]. Com- munications in Statistics–Simulation and Computation, 2026:1–19. https://doi.org/10.1080/03610918.2026.2618498

    2026 doi

  23. [31]

    Support vector regression with imprecise observations based on Huber loss function [J]

    Zhu X, Sheng Y. Support vector regression with imprecise observations based on Huber loss function [J]. Communications in Statistics–Simulation and Computation, 2026:1–13. https://doi.org/10.1080/03610918.2026.2643718

    2026 doi

  24. [32]

    Robust kernel stochastic configuration networks for uncertain industrial data regression [J]

    Wang D H, Chen Y X. Robust kernel stochastic configuration networks for uncertain industrial data regression [J]. IEEE Transactions on Industrial Informatics, 2026:1–12. https://doi.org/10.1109/TII.2026.3688556

    2026 doi

  25. [33]

    Using a Latin square design to determine the most effective mathematics teaching method [J]

    Assuah C K. Using a Latin square design to determine the most effective mathematics teaching method [J]. International Journal of New Technology and Research, 2019, 5(7): 64–69

    2019

Pith tools

Reviewed June 26, 2026 · model on record in the stance chip above.