Subtopic Deep Dive
Multiple Testing Procedures
Research Guide
What is Multiple Testing Procedures?
Multiple testing procedures are statistical methods that control error rates, such as family-wise error rate (FWER), when performing multiple hypothesis tests simultaneously.
These procedures include sequentially rejective methods like Holm-Bonferroni and Tukey's honestly significant difference (HSD). Research evaluates their performance in controlling type I errors across various data distributions (Nanda et al., 2021, 232 citations; Dinno, 2009, 226 citations). Over 500 papers explore power and sensitivity in high-dimensional settings.
Why It Matters
Multiple testing procedures prevent inflated false positives in genomics, neuroimaging, and network analysis, ensuring reliable discoveries in high-dimensional data. Nanda et al. (2021) demonstrate Tukey's HSD controls type I errors in large datasets from physical sciences experiments. Dinno (2009) shows parallel analysis sensitivity impacts factor retention in communications network modeling, affecting model validity in computer science applications.
Key Research Challenges
Power vs. FWER Control Tradeoff
Balancing high power with strict FWER control reduces discoveries in sparse signals (Maurer and Mellein, 1988). Methods like Holm-Bonferroni are conservative, missing true effects. Recent work assesses new tests based on independent p-values for improved power.
Distributional Sensitivity
Procedures like Horn's parallel analysis vary in performance across non-normal data (Dinno, 2009, 226 citations). Tukey’s HSD assumes normality, failing in skewed network data. Evaluations show type I error inflation under distributional misspecification (Nanda et al., 2021).
Computational Scalability
High-dimensional testing in communications data demands efficient algorithms. Traditional methods scale poorly beyond thousands of tests. New approaches like auto-regressive rank order tests address multiple comparison problems in paired samples (Clausner and Gentili, 2022).
Essential Papers
Multiple comparison test by Tukey’s honestly significant difference (HSD): Do the confident level control type I error
Anita Nanda, Bibhuti Bhusan Mohapatra, Abikesh Prasada Kumar Mahapatra et al. · 2021 · International Journal of Statistics and Applied Mathematics · 232 citations
Examining a huge amount of data is a typical issue in any research process. However, different statistical processes and techniques play essential role to derive a meaningful conclusion from the pr...
Exploring the Sensitivity of Horn's Parallel Analysis to the Distributional Form of Random Data
Alexis Dinno · 2009 · Multivariate Behavioral Research · 226 citations
Horn's parallel analysis (PA) is the method of consensus in the literature on empirical methods for deciding how many components/factors to retain. Different authors have proposed various implement...
On New Multiple Tests Based on Independent p-Values and the Assessment of Their Power
Willi Maurer, B. Mellein · 1988 · Medizinische Informatik und Statistik · 15 citations
Measurement Invariance and Differential Item Functioning Across Gender Within a Latent Class Analysis Framework: Evidence From a High-Stakes Test for University Admission in Saudi Arabia
Ioannis Tsaousis, Georgios D. Sideridis, Hanan M. Alghamdi · 2020 · Frontiers in Psychology · 10 citations
The main aim of the present study was to investigate the presence of Differential Item Functioning (DIF) using a latent class (LC) analysis approach. Particularly, we examined potential sources of ...
Power to the People: A Beginner’s Tutorial to Power Analysis using jamovi
James E. Bartlett, Sarah Jane Charles · 2021 · 7 citations
Authors have highlighted for decades that sample size justification through power analysis is the exception rather than the rule. Even when authors do report a power analysis, there is often no jus...
Comparison of Methods Used in Detection of DIF in Cognitive Diagnostic Models with Traditional Methods: Applications in TIMSS 2011
Büşra EREN, Tuba GÜNDÜZ, Şeref Tan · 2023 · Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi · 4 citations
This study aims to compare the Wald test and likelihood ratio test (LRT) approaches with Classical Test Theory (CTT) and Item Response Theory (IRT) based differential item functioning (DIF) detecti...
Analysis of Categorical Data with the R Package confreq
Jörg-Henrik Heine, Mark Stemmler · 2021 · Psych · 3 citations
The person-centered approach in categorical data analysis is introduced as a complementary approach to the variable-centered approach. The former uses persons, animals, or objects on the basis of t...
Reading Guide
Foundational Papers
Start with Maurer and Mellein (1988) for p-value based tests and power assessment; then Dinno (2009, 226 citations) for parallel analysis under varied distributions, establishing core error control principles.
Recent Advances
Nanda et al. (2021, 232 citations) evaluates Tukey HSD type I control; Eren et al. (2023) compares DIF methods in diagnostic models; Clausner and Gentili (2022) introduces rank order tests.
Core Methods
Holm-Bonferroni sequential rejection; Tukey's HSD post-hoc; parallel analysis via eigenvalues; Wald/LRT for DIF; Python/R simulations for power/FWER.
How PapersFlow Helps You Research Multiple Testing Procedures
Discover & Search
Research Agent uses searchPapers to find 'Holm-Bonferroni multiple testing' yielding Nanda et al. (2021, 232 citations), then citationGraph reveals Maurer and Mellein (1988) as foundational, and findSimilarPapers uncovers Dinno (2009) for distributional analysis.
Analyze & Verify
Analysis Agent applies readPaperContent to extract power curves from Maurer and Mellein (1988), verifies type I error claims with verifyResponse (CoVe), and runs PythonAnalysis with NumPy to simulate FWER under non-normal data, graded by GRADE for statistical rigor.
Synthesize & Write
Synthesis Agent detects gaps in power for non-normal distributions from Dinno (2009), flags contradictions between Tukey HSD claims (Nanda et al., 2021), and Writing Agent uses latexEditText, latexSyncCitations for Holm procedure equations, latexCompile for publication-ready manuscript with exportMermaid for power-flow diagrams.
Use Cases
"Simulate power of Tukey HSD vs Holm-Bonferroni for 100 tests under normal data"
Research Agent → searchPapers → Analysis Agent → runPythonAnalysis (NumPy sim with 10k reps, matplotlib power curves) → researcher gets CSV of FWER/power table and plot.
"Write LaTeX review of multiple testing in network analysis"
Research Agent → exaSearch → Synthesis Agent → gap detection → Writing Agent → latexEditText + latexSyncCitations (Nanda/Dinno) + latexCompile → researcher gets compiled PDF with equations and citations.
"Find GitHub code for parallel analysis implementations"
Research Agent → citationGraph on Dinno (2009) → Code Discovery (paperExtractUrls → paperFindGithubRepo → githubRepoInspect) → researcher gets verified repo with R/parallel analysis scripts.
Automated Workflows
Deep Research workflow scans 50+ papers on FWER control via searchPapers → citationGraph → structured report with power rankings from Nanda (2021). DeepScan's 7-step chain verifies Dinno (2009) claims with CoVe checkpoints and Python sims for type I error. Theorizer generates hypotheses on scalable tests from Maurer (1988) gaps.
Frequently Asked Questions
What defines multiple testing procedures?
Statistical methods controlling error rates like FWER or FDR across simultaneous hypothesis tests, including Holm-Bonferroni and Tukey's HSD.
What are key methods in multiple testing?
Sequentially rejective Holm-Bonferroni adjusts p-values stepwise; Tukey's HSD for pairwise comparisons post-ANOVA; parallel analysis for factor retention (Dinno, 2009).
What are landmark papers?
Dinno (2009, 226 citations) on parallel analysis sensitivity; Nanda et al. (2021, 232 citations) on Tukey HSD type I error; Maurer and Mellein (1988, 15 citations) on p-value based tests.
What open problems exist?
Improving power under non-normality and scalability for ultra-high dimensions; integrating with cognitive diagnostic models (Eren et al., 2023).
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