An analysis of variance test for normality (complete samples)

1965/12/01 by S. S. SHAPIRO, S. S. Shapiro, Samuel S. Shapiro +2 · 19,610 citations
Engineering · Mathematics · #Diverse Scientific and Engineering Research #Mathematics #Normality #Normality test #Statistical hypothesis testing #Statistics #Test (biology) #Variance (accounting)

paper · doi:10.1093/biomet/52.3-4.591

published in Biometrika 52(3-4), 591-611 (Oxford University Press)

openalex publication_date 1965/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

S. S. SHAPIRO, M. B. WILK; An analysis of variance test for normality (complete samples)†, Biometrika, Volume 52, Issue 3-4, 1 December 1965, Pages 591–611

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• Party Ideologies and Political Polarization-Driven Conflicts: A Study of the Global South
• Can a domain-specific language improve program structure comprehension of data pipelines? A mixed-methods study
• Secure Position Verification for Wireless Sensor Networks in Noisy Channels
• A measure of skewness for testing departures from normality
• Efficient Speech Language Modeling via Energy Distance in Continuous Latent Space
• Determination of the masses and decay widths of the scalar-isoscalar and vector-isovector mesons below 2 GeV
• Exploring the relationship between perceived bikeability and gender-inclusive micromobility usage: A study across 53 French cities
• The effectiveness of applied learning: an empirical evaluation using role playing in the classroom
• Corruption as a barrier to sustainability
• THESEUS1 modulates cell wall stiffness and abscisic acid production in Arabidopsis thaliana
• THESEUS1 modulates cell wall stiffness and abscisic acid production in Arabidopsis thaliana
• Sustained Increases in Lower-Tropospheric Subsidence over the Central Tropical North Pacific Drive a Decline in High-Elevation Rainfall in Hawaii
• Speed breeding in pea (Pisum sativum L.), an efficient and simple system to accelerate breeding programs
• Benchmarking cross-project defect prediction approaches with costs metrics
• The shift to 3D growth during embryogenesis of kelp species, atlas of cell division and differentiation of Saccharina latissima
• A comparative analysis of functional traits in semi-natural grasslands under different grazing intensities
• Synthetic Code Surgery: Repairing Bugs and Vulnerabilities with LLMs and Synthetic Data
• Real Faults in Model Context Protocol (MCP) Software: a Comprehensive Taxonomy
• Comprehensive study of tests for normality and symmetry: extending the Spiegelhalter test
• Transportation Modes Classification Using Feature Engineering
• Reconnecting to the Biosphere
• Brain Network Analysis in Alzheimer's Disease and Mild Cognitive Impairment using High-Density Diffuse Optical Tomography
• Subchronic Inhalation Toxicity of the Chlorinated Propane 1,1,1,3,3,3-Hexachloropropane (HCC-230fa)
• Morphological and molecular variation in Synaphobranchus eels (Anguilliformes: Synaphobranchidae) of the Mid-Atlantic Ridge in relation to species diagnostics
• Experimental evidence of quantum randomness incomputability
• Experimentally probing the algorithmic randomness and incomputability of quantum randomness
• Profile-Likelihood and Baseline-Sensitivity Diagnostics for Digitized Radiation-Sensor Decay Datasets
• A Psychometric and Practical Comparison of Standard Moodle-Based and STACK-Based Step-by-Step Tests in University Calculus
• Diversity of decapod crabs (Crustacea: Brachyura) in two islands of Ubatuba, southeast of Brazil
• Perceptual Implications of Automatic Anonymization in Pathological Speech
• Sketches and Diagrams in Practice
• Longevity of Cane Corso Italiano dog breed and its relationship with hair colour
• Habitat filters mediate successional trajectories in bacterial communities associated with the striped shore crab
• An Empirical Likelihood Ratio Test for Normality
• Erfassung von individuellem Beanspruchungserleben bei kognitiven Belastungssituationen mittels Mustererkennung im Lidschlagverhalten
• Internal dynamics of the massive cluster Abell 697: a multiwavelength analysis
• Cluster Abell 520: a perspective based on member galaxies
• A wide-field spectroscopic survey of the cluster of galaxies Cl0024+1654
• NOVA: Symbolic Regression Discovery of Interpretable Car-Following and Lane-Change Models with Driver Heterogeneity
• Sex estimation from morphology in living animals and dinosaurs
• Influence of Cognitive Ability on Therapy Outcomes for Anomia in Adults With Chronic Poststroke Aphasia
• Efficacy of biological agents and compost on growth and resistance of tomatoes to late blight
• On dynamic multi-agent pathfinding methods: review, simulations and modifications
• Moments or L Moments? An Example Comparing Two Measures of Distributional Shape
• The Invisible Hand of AI Libraries Shaping Open Source Projects and Communities
• xEEGNet: Towards Explainable AI in EEG Dementia Classification
• A closer look at ChatGPT's role in concept map generation for education
• Six transiting planets and a chain of Laplace resonances in TOI-178
• The SOPHIE search for northern extrasolar planets. XVI. HD 158259: A compact planetary system in a near-3:2 mean motion resonance chain
• Residential status and seasonal movements of wild orang-utans in the Gunung Leuser Reserve (Sumatera, Indonesia)
• Photosensitive and Photostable Pigments in the Retinae of Old World Monkeys
• Taxon characteristics that promote survivorship through the Permian–Triassic interval: transition from the Paleozoic to the Mesozoic brachiopod fauna
• Voting Islamist or voting secular? An empirical analysis of voting outcomes in Egypt’s “Arab Spring”
• Kardashev's Conundrum: Statistical Falsification of Exponential Energy Growth, the Non-Observation of Type II Technosignatures, and the Kardashev-Sagan-Nakamoto Resolution
• Effects of biodiversity dimensions (phylogenetic, functional, and taxonomic) of frugivorous bats on the structure of ecological networks
• NFISiS: New Perspectives on Fuzzy Inference Systems for Renewable Energy Forecasting
• Robotic Trail Maker Platform for Rehabilitation in Neurological Conditions: Clinical Use Cases
• Powerful Goodness-of-fit Tests Based on the Likelihood Ratio
• Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy
• The Influence of Environmental Variables on the Distribution and Abundance of Three Elasmobranchs in Tomales Bay, California
• Multiple colonist pools shape fiddler crab-associated bacterial communities
• High‐speed video observations of positive lightning flashes to ground
• Atmospheric BTEX concentrations in the vicinity of the crude oil refinery of the Baltic region
• Using Random Forest Machine Learning Algorithms in Binary Supernovae Classification
• Modelling financial volatility in the presence of abrupt changes
• Treatment of bimodality in proficiency test of pH in bioethanol matrix
• Gender trends in computer science authorship
• Attachment Style and Gender as Predictors of Communicative Responses to Infidelity
• Optical analysis of the poor clusters Abell 610, Abell 725, and Abell 796, containing diffuse radio sources
• Remark AS R94: A Remark on Algorithm AS 181: The W-test for Normality
• Forecasting Equity Correlations with Hybrid Transformer Graph Neural Network
• An approach based on metaheuristic algorithms to the timetabling problem in deregulated railway markets
• THE BHB STARS IN THE SURVEY FIELDS OF RODGERS ET AL. (1993): NEW OBSERVATIONS AND COMPARISONS WITH OTHER RECENT SURVEYS
• Spatial variability of organic layer thickness and carbon stocks in mature boreal forest stands—implications and suggestions for sampling designs
• Structural refinement, morphology and photocatalytic properties of β-(Ag2−2xZnx)MoO4 microcrystals synthesized by the sonochemical method
• Exploring Cross-Reality Transitions between Projections and Head-Mounted Displays for Immersive Digital Art
• SONAR: Task-Aware Code Summary Evaluation for LLM Consumers Without References
• Type II supernovae as distance indicators at near-IR wavelengths
• BCI learning induces core-periphery reorganization in M/EEG multiplex brain networks
• Open Source Software Lifecycle Classification: Developing Wrangling Techniques for Complex Sociotechnical Systems
• Hard X-ray view on intermediate polars in theGaiaera
• The Effect of Hydration and Dynamics on the Mass Density of Single Proteins
• Constructing the Truth: Text Mining and Linguistic Networks in Public Hearings of Case 03 of the Special Jurisdiction for Peace (JEP)
• CostMAP: An open-source software package for developing cost surfaces
• A joint text mining-rank size investigation of the rhetoric structures of the US Presidents’ speeches
• Longitudinal Study on Social and Emotional Use of AI Conversational Agent
• Fast and Accurate Reconstruction of Pan-Tilt RGB-D Scans via Axis Bound Registration
• Surface Electromyography-controlled Pedestrian Collision Avoidance: A Driving Simulator Study
• Managing Spodoptera frugiperda (Lepidoptera: Noctuidae) resistant to Vip3Aa20: The importance of combining Bt cotton and insecticides
• Cobalt and molybdenum stimulate compounds of primary metabolism, nitrogen forms, and photosynthetic pigments in peanut plants (Arachis hypogaea L.)
• Evaluating DAO Sustainability and Longevity Through On-Chain Governance Metrics
• Eigenvalue-Based Randomness Test for Residual Diagnostics in Panel Data Models
• E-Predict: a computational strategy for species identification based on observed DNA microarray hybridization patterns. [europepmc]
• How repetitive are genomes? [europepmc]
• Affect-focused psychodynamic psychotherapy for depression and anxiety through the Internet: a randomized controlled trial. [europepmc]
• Music reduces pain and increases functional mobility in fibromyalgia. [europepmc]
• Cosinor-based rhythmometry. [europepmc]
• Arabidopsis genes, AtNPR1, AtTGA2 and AtPR-5, confer partial resistance to soybean cyst nematode (Heterodera glycines) when overexpressed in transgenic soybean roots. [europepmc]
• Rapidly increasing methyl mercury in endangered ivory gull (Pagophila eburnea) feathers over a 130 year record. [europepmc]
• Neonicotinoid-Coated Zea mays Seeds Indirectly Affect Honeybee Performance and Pathogen Susceptibility in Field Trials. [europepmc]
• Understanding Bland Altman analysis. [europepmc]
• Characterization of the Vaginal Microbiota of Ewes and Cows Reveals a Unique Microbiota with Low Levels of Lactobacilli and Near-Neutral pH. [europepmc]
• Convolutional Neural Network for Multi-Category Rapid Serial Visual Presentation BCI. [europepmc]
• Reduced diversity and altered composition of the gut microbiome in individuals with myalgic encephalomyelitis/chronic fatigue syndrome. [europepmc]
• Presence of Vaccine-Derived Newcastle Disease Viruses in Wild Birds. [europepmc]
• RBioplot: an easy-to-use R pipeline for automated statistical analysis and data visualization in molecular biology and biochemistry. [europepmc]
• A microbial signature for Crohn's disease. [europepmc]
• Hyaluronan Nanoparticles Selectively Target Plaque-Associated Macrophages and Improve Plaque Stability in Atherosclerosis. [europepmc]
• Genome Analysis of Conserved Dehydrin Motifs in Vascular Plants. [europepmc]
• Expression profiling across wild and cultivated tomatoes supports the relevance of early miR482/2118 suppression for Phytophthora resistance. [europepmc]
• Both Basal and Acute Restraint Stress-Induced c-Fos Expression Is Influenced by Age in the Extended Amygdala and Brainstem Stress Centers in Male Rats. [europepmc]
• Heat Stress Tolerance in Rice ( Oryza sativa L.): Identification of Quantitative Trait Loci and Candidate Genes for Seedling Growth Under Heat Stress. [europepmc]
• Reliability and Validity of Fall Efficacy Scale-International in People with Parkinson's Disease during On- and Off-Drug Phases. [europepmc]
• Combined transcriptome and proteome profiling reveals specific molecular brain signatures for sex, maturation and circalunar clock phase. [europepmc]
• Isolated, small, and large hospitals have fewer nursing resources than urban hospitals: Implications for rural health policy. [europepmc]
• Azospirillum brasilense promotes increases in growth and nitrogen use efficiency of maize genotypes. [europepmc]
• Medical Diagnostic Tests: A Review of Test Anatomy, Phases, and Statistical Treatment of Data. [europepmc]
• Genome-Wide Association Mapping for Agronomic and Seed Quality Traits of Field Pea ( Pisum sativum L.). [europepmc]
• The Abbreviated Maslach Burnout Inventory Can Overestimate Burnout: A Study of Anesthesiology Residents. [europepmc]
• Nutrient Level Determines Biofilm Characteristics and Subsequent Impact on Microbial Corrosion and Biocide Effectiveness. [europepmc]
• Machine learning can predict survival of patients with heart failure from serum creatinine and ejection fraction alone. [europepmc]
• Temporal, Environmental, and Biological Drivers of the Mucosal Microbiome in a Wild Marine Fish, Scomber japonicus. [europepmc]
• Students' Trait Emotional Intelligence and Perceived Teacher Emotional Support in Preventing Burnout: The Moderating Role of Academic Anxiety. [europepmc]
• Wearable monitoring of sleep-disordered breathing: estimation of the apnea-hypopnea index using wrist-worn reflective photoplethysmography. [europepmc]
• Effectiveness of blended learning versus lectures alone on ECG analysis and interpretation by medical students. [europepmc]
• Using the Standardized Root Mean Squared Residual (SRMR) to Assess Exact Fit in Structural Equation Models. [europepmc]
• Evaluating Growth Patterns of Abdominal Aortic Aneurysm Diameter With Serial Computed Tomography Surveillance. [europepmc]
• Anthropogenic nitrate in groundwater and its health risks in the view of background concentration in a semi arid area of Rajasthan, India. [europepmc]
• A diagnostic miRNA signature for pulmonary arterial hypertension using a consensus machine learning approach. [europepmc]
• Coordination of fungal biofilm development by extracellular vesicle cargo. [europepmc]
• Comparison of seven modelling algorithms for γ-aminobutyric acid-edited proton magnetic resonance spectroscopy. [europepmc]
• Single leg vertical jump performance identifies knee function deficits at return to sport after ACL reconstruction in male athletes. [europepmc]
• Co-optimization of therapeutic antibody affinity and specificity using machine learning models that generalize to novel mutational space. [europepmc]
• Accuracy of EEG Biomarkers in the Detection of Clinical Outcome in Disorders of Consciousness after Severe Acquired Brain Injury: Preliminary Results of a Pilot Study Using a Machine Learning Approach. [europepmc]
• Carboxylesterase 2a deletion provokes hepatic steatosis and insulin resistance in mice involving impaired diacylglycerol and lysophosphatidylcholine catabolism. [europepmc]
• Effect of Brief Interpersonal Therapy on Depression During Pregnancy: A Randomized Clinical Trial. [europepmc]
• Effect of long-term caloric restriction on DNA methylation measures of biological aging in healthy adults from the CALERIE trial. [europepmc]
• Environmental gradients reveal stress hubs pre-dating plant terrestrialization. [europepmc]
• Multimodal assessment of brain fluid clearance is associated with amyloid-beta deposition in humans. [europepmc]
• Encrypted federated learning for secure decentralized collaboration in cancer image analysis. [europepmc]
• Prevalence of persistent SARS-CoV-2 in a large community surveillance study. [europepmc]
• Fibrin drives thromboinflammation and neuropathology in COVID-19. [europepmc]

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