Comparing Individual Means in the Analysis of Variance
1949/06/01 by John W. Tukey · 79 citations
Mathematics · Computer Science · #Advanced Statistical Methods and Models #Statistical and Computational Modeling
paper · doi:10.2307/3001913
Abstract
The practitioner of the analysis of variance often wants to draw as many conclusions as are reasonable about the relation of the true means for individual treatments, and a statement by the F-test (or the z-test) that they are not all alike leaves him thoroughly unsatisfied. The problem of breaking up the treatment means into distinguishable groups has not been discussed at much length, the solutions given in the various textbooks differ and, what is more important, seem solely based on intuition. After discussing the problem on a basis combining intuition with some hard, cold facts about the distributions of certain test quantities (or statistics) a simple and definite procedure is proposed for dividing treatments into distinguishable groups, and for determining that the treatments within some of these groups are different, although there is not enough evidence to say which is which. The procedure is illustrated on examples.
Cited by
- Multiple Range and Multiple F Tests
- A Cluster Analysis Method for Grouping Means in the Analysis of Variance
- Contextual Effects on Choice Reaction Time and Accuracy in Acute and Chronic Schizophrenics Impairment in Selective Attention or in the Influence of Prior Learning?
- Efficacy of Common Decontamination Methods for Cleaning Contaminated Wounds
- Minimizing aviation lighting duration reduces bat attraction to wind turbines
- To adjust or not to adjust? Matching statistical choices to scientific questions in exercise physiology and sport science
- Molecule auto-correction to facilitate molecular design
- Exploring the effect of installing collars on snow crab (Chionoecetes opilio) pots in Newfoundland and Labrador: Do collars improve size selectivity?
- One Persona, Many Cues, Different Results: How Sociodemographic Cues Impact LLM Personalization
- Global system errors to simultaneously improve the identification of subsystems with mixed data Gaussian process regression
- Bioinformatic discovery of type 11 secretion system (T11SS) cargo across the Proteobacteria
- Probing the Influence of the Protein Scaffold on H-Cluster Reactivity via Gain-of-Function Studies─Improved H<sub>2</sub> Evolution and O<sub>2</sub> Tolerance through Rational Design of [FeFe] Hydrogenase
- Catalytic p <i>K</i> <sub>a</sub> Attenuation in a Hydrolytic Metalloenzyme by Genetic Code Expansion
- Effortless Data Exploration with zenvisage: An Expressive and Interactive Visual Analytics System
- Assessing Test Case Prioritization on Real Faults and Mutants
- How different thinning can improve carbon sequestration, carbon stock and mechanical stability in peri-urban mixed forest stands: a study case in Mediterranean environment
- Automated Statistical and Machine Learning Platform for Biological Research
- Assessing crosstalk in simultaneous multicolor single-molecule localization microscopy
- Multi-objective Hyperparameter Optimization in the Age of Deep Learning
- An Exploratory Eye Tracking Study on How Developers Classify and Debug Python Code in Different Paradigms
- Genomics of Experimental Adaptive Radiation in the Cryptic Coloration of Feather Lice
- Who Speaks to Whom? An LLM-Based Social Network Analysis of Tragic Plays
- Arctic migrating barnacle geese utilize accommodation fields in a new agricultural staging area
- A round-robin exercise for the precise prediction of aqueous solubility of organic chemicals using chemometric, machine learning, and stacking ensemble of deep learning models
- Quantity of SARS-CoV-2 RNA copies exhaled per minute during natural breathing over the course of COVID-19 infection
- Experimental degradation of polystyrene via three-dimensional surface texture analysis after UV radiation and mechanical abrasion
- Multiplicity Considerations in the Design and Analysis of Clinical Trials
- Monitoring the Colonisation Dynamics of <i>Rugulopteryx okamurae</i> on Algal Communities in the Northwestern Mediterranean Sea
- Unintended Memorization of Sensitive Information in Fine-Tuned Language Models
- Disentangling Shared and Private Neural Dynamics with SPIRE: A Latent Modeling Framework for Deep Brain Stimulation
- A methodology for multi-label algorithm selection in constrained multiobjective optimization
- BASELINE HEALTH AND DISEASE ASSESSMENT OF FOUNDER EASTERN QUOLLS (DASYURUS VIVERRINUS) DURING A CONSERVATION TRANSLOCATION TO MAINLAND AUSTRALIA
- The Power of Log-Sum-Exp: Sequential Density Ratio Matrix Estimation for Speed-Accuracy Optimization
- Digitized dataset of aqueous acid dissociation constants
- Two residues reprogram immunity receptors for nitrogen-fixing symbiosis
- Structure of presented stimuli influences gazing behavior and choice
- Temporal and spatial variation in personal ambient temperatures for outdoor working populations in the southeastern USA
- Network entropy as a key to the past: A quantitative approach to complex social networks
- An Acoustic Analysis of Speech Motor Performance in Autistic Children
- Antibiotics adsorb to polyester microplastic fibers and alter bacterial communities in stream mesocosms
- AI‐Assisted Morphometric Analysis and Molecular Phylogeny for a Dactylogyrid (Monopisthocotyla) Skin Parasite of an Ornamental Crenuchid Fish From Brazil
- Exploring crop health and its associations with fungal soil microbiome composition using machine learning applied to remote sensing data
- Characterizing developmental changes in infant habituation using functional change point detection
- Pollution gradient leads to local adaptation and small-scale spatial variability of communities and functions in an urban marine environment
- The statistical impact of ROI referencing on quantitative susceptibility mapping
- Assessing the genetic composition of invasive knotweeds (<i>Reynoutria</i>, Polygonaceae) using data from the first intron and second exon of the nuclear <i>LEAFY</i> gene
- How good does a Defect Predictor need to be to guide Search-Based Software Testing?
- Demographically-Inspired Query Variants Using an LLM
- Carbohydrate active enzymes in <i>Pectobacteriaceae</i> : coevolving enzyme sets and host adaptation
- Interstitial and recruited macrophages prevent tuberculosis relapse by limiting immune evasion
- Invisible Filters: Cultural Bias in Hiring Evaluations Using Large Language Models
- Getting off the DIME: Dimension Pruning via Dimension Importance Estimation for Dense Information Retrieval
- Which Reaction Conditions Work on Drug-Like Molecules? Lessons from 66,000 High-Throughput Experiments
- Near Optimal Inference for the Best-Performing Algorithm
- Visual evoked responses during standing and walking. [europepmc]
- Two decades of warming increases diversity of a potentially lignolytic bacterial community. [europepmc]
- Mitochondrial pleomorphy in plant cells is driven by contiguous ER dynamics. [europepmc]
- The Iflaviruses Sacbrood virus and Deformed wing virus evoke different transcriptional responses in the honeybee which may facilitate their horizontal or vertical transmission. [europepmc]
- A Comparison of Lung Nodule Segmentation Algorithms: Methods and Results from a Multi-institutional Study. [europepmc]
- Mobile Brain/Body Imaging (MoBI) of Physical Interaction with Dynamically Moving Objects. [europepmc]
- RBioplot: an easy-to-use R pipeline for automated statistical analysis and data visualization in molecular biology and biochemistry. [europepmc]
- Targeted mutagenesis in tetraploid switchgrass (Panicum virgatum L.) using CRISPR/Cas9. [europepmc]
- Case-Control Comparison of Enteric Viromes in Captive Rhesus Macaques with Acute or Idiopathic Chronic Diarrhea. [europepmc]
- Biallelic mutations in the ubiquitin ligase RFWD3 cause Fanconi anemia. [europepmc]
- Electronic cigarette user plasma nicotine concentration, puff topography, heart rate, and subjective effects: Influence of liquid nicotine concentration and user experience. [europepmc]
- Forward Genetics Approach Reveals Host Genotype-Dependent Importance of Accessory Chromosomes in the Fungal Wheat Pathogen Zymoseptoria tritici . [europepmc]
- Effects of electronic cigarette liquid solvents propylene glycol and vegetable glycerin on user nicotine delivery, heart rate, subjective effects, and puff topography. [europepmc]
- Investigation of dose-rate effects and cell-cycle distribution under protracted exposure to ionizing radiation for various dose-rates. [europepmc]
- CREBBP/EP300 bromodomains are critical to sustain the GATA1/MYC regulatory axis in proliferation. [europepmc]
- Gene flow contributes to diversification of the major fungal pathogen Candida albicans. [europepmc]
- Comparison of the Vaginal Microbiomes of Premenopausal and Postmenopausal Women. [europepmc]
- Integrating Gene Expression Data Into Genomic Prediction. [europepmc]
- Transmission of Xylella fastidiosa Subspecies Pauca Sequence Type 53 by Different Insect Species. [europepmc]
- Nutrient Level Determines Biofilm Characteristics and Subsequent Impact on Microbial Corrosion and Biocide Effectiveness. [europepmc]
- Emotions and brain function are altered up to one month after a single high dose of psilocybin. [europepmc]
- Trends in Antibiotic Resistance Among Ocular Microorganisms in the United States From 2009 to 2018. [europepmc]
- Dynamics of fMRI patterns reflect sub-second activation sequences and reveal replay in human visual cortex. [europepmc]
- Senolytics reduce coronavirus-related mortality in old mice. [europepmc]
- How Depressing Is Inbreeding? A Meta-Analysis of 30 Years of Research on the Effects of Inbreeding in Livestock. [europepmc]
Related