statistical analysis

This study addresses the limited power of conventional two-way ANOVA for testing interaction, simple, and main effects under heteroscedasticity. The authors propose a novel approach based on likelihood ratio tests combined with simultaneous comparison procedures, employing a hill-climbing algorithm with convergence guarantees to compute constrained maximum likelihood estimates and using parametric bootstrap to determine critical values. The method achieves a 30%–50% gain in power for main effect tests while maintaining robustness under non-normal errors. Simulation studies demonstrate that it also provides well-controlled Type I error rates and comparable power for interaction and simple effect tests. Practical utility is illustrated through analyses of four real-world datasets, and an open-source R package is provided to facilitate implementation.

This study investigates cross-disciplinary trends in statistical software adoption across economics, political science, and statistics. Method: We systematically replicated and coded open-source code and data files from over 10,000 peer-reviewed papers, integrating web-crawled metadata, manual annotation, qualitative coding, and frequency analysis to construct the first student-led, interdisciplinary database of statistical software usage. Contribution/Results: We introduce the “multi-platform collaborative analysis” paradigm, revealing that Stata remains dominant in economics, while R has become the preferred tool in political science and statistics; moreover, over 30% of social science studies employ two or more software packages synergistically. The project significantly enhances students’ reproducibility capacity and data literacy, fostering concurrent updates in pedagogy and research practice.

Misuse of statistical hypothesis tests severely undermines scientific reliability. This paper proposes a formal verification methodology for statistical programs: preconditions—such as normality, independence, and homoscedasticity—are explicitly encoded as logical assertions in source code; static verification is then performed on OCaml implementations using the Why3 platform to automatically detect missing or conflicting assumptions. The approach innovatively integrates contract-based programming with formal verification, distinguishing between formalizable preconditions (amenable to automated checking) and non-formalizable ones (requiring expert judgment), thereby establishing a human-in-the-loop verification paradigm. Evaluated on canonical statistical tests—including Student’s *t*-test and ANOVA—the method successfully identifies widespread misuses, such as applying the *t*-test to non-normal data or neglecting homoscedasticity checks. Results demonstrate significant improvements in the correctness, auditability, and reproducibility of statistical software.

This study addresses longstanding challenges in agricultural experimentation, where traditional statistical analyses often suffer from a disconnect between experimental design and computational implementation, leading to subjective model specification, mischaracterized error structures, and biased interpretation of interaction effects. To resolve these issues, the authors propose the first declarative Python framework that deeply embeds experimental design semantics into the analytical workflow. The framework automatically translates complex designs—such as randomized complete blocks, split-plots, and multi-environment trials—into valid linear or mixed-effects models, accurately identifies error strata, performs hypothesis tests and mean comparisons, and unifies ANOVA, mixed-model inference, and stability analysis. By rigorously enforcing correct interpretation of hierarchical and interaction effects, the approach maintains consistency with classical methodologies while substantially enhancing inferential accuracy, reproducibility, and reliability.

Normality of error terms in ANOVA models is frequently overlooked and lacks tailored diagnostic tools. This paper proposes a smoothness-based normality test specifically designed for general ANOVA models. The method constructs an asymptotically χ²-distributed test statistic—ensuring consistency—and employs orthogonal polynomial bases, with a data-driven criterion for selecting the optimal basis dimension. Theoretical analysis and Monte Carlo simulations demonstrate that the proposed test substantially outperforms classical methods (e.g., Shapiro–Wilk and Anderson–Darling) in small-sample and multi-factor ANOVA settings, exhibiting superior statistical power and robustness. The key innovation lies in the theoretical integration of ANOVA’s error structure with smoothness-based testing, yielding a principled, ready-to-use inferential framework for residual normality assessment.

This work addresses the widespread misuse of statistical methods—often stemming from implicit or ambiguous assumptions—which exacerbates the reproducibility crisis in scientific research, particularly in hypothesis testing and meta-analysis where formal verification mechanisms are lacking. To bridge this gap, the authors propose the first formal verification framework tailored for Python-based statistical programs. By developing a Why3-py frontend, they translate dynamically typed, runtime-polymorphic Python code into the WhyML intermediate representation and extend the StatWhy tool to support meta-analysis verification. Integrating program transformation, static analysis, and formal verification techniques, this approach enables, for the first time, automated correctness verification of statistical programs written in Python, effectively uncovering overlooked assumptions and misuses, thereby filling a critical void in the formal verification of statistical software.

This study addresses the limitations of traditional residual plot diagnostics—namely, their reliance on subjective human interpretation, low efficiency, and poor scalability—by introducing computer vision techniques for the first time to automate the assessment of residual plots in linear models. The authors develop the R package autovi and an accompanying Shiny-based interactive web application, autovi.web. Their approach leverages deep visual models to quantify the strength of structural signals in residual plots and produces interpretable diagnostic metrics. This methodology significantly enhances the consistency and efficiency of model fit evaluation, offering statisticians and data analysts a robust, objective, and scalable tool for automated diagnostic assessment in statistical modeling.

This study addresses the computational complexity associated with calculating quantiles of the inverse normal distribution, Student’s t-distribution, and outlier rejection criteria in hypothesis testing. To overcome the reliance on table lookups or iterative numerical methods, the paper proposes concise and highly accurate analytical approximations formulated as closed-form expressions. These approximations significantly reduce computational overhead while maintaining precision sufficient for practical statistical applications. The resulting method offers substantial gains in computational efficiency, making it particularly well-suited for resource-constrained environments or scenarios requiring rapid statistical inference. By bridging theoretical rigor with practical utility, the approach delivers both methodological insight and real-world applicability.

This study addresses the inflation of false positive rates in multiple hypothesis testing by systematically reviewing error rate control criteria—such as the family-wise error rate (FWER) and the false discovery rate (FDR)—and integrating both classical and contemporary correction methods. The work provides reproducible implementations of these approaches in R, offering a theoretically rigorous yet practice-oriented resource for teaching and applied research. By unifying methodological foundations with hands-on computational examples, this contribution fills a critical gap in existing textbooks, which often lack comprehensive integration of techniques and practical guidance. The resulting framework serves as a complete and efficient reference for graduate-level instruction and real-world data analysis, enhancing both pedagogical clarity and analytical reliability in high-dimensional statistical inference.

This work addresses the lack of intuitive, programming-free interactive tools for introductory statistics learners by developing three open-source web applications built with R and Shiny, focusing respectively on probability distributions, confidence intervals and hypothesis testing, and simple linear regression. These applications innovatively integrate dynamic visualizations, real-time statistical computations, and inline mathematical derivations within a unified interface, structured according to pedagogical progression to enable learners without programming experience to simultaneously grasp conceptual and operational aspects. High-quality rendering of graphics and equations is achieved through ggplot2 and MathJax. All applications are freely accessible online, and their source code is released under the CC-BY-4.0 license, thereby effectively supporting the teaching and learning of core statistical concepts.