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Record W1519593092 · doi:10.1002/0470013192.bsa433

Multivariate Normality Tests

2005· other· en· W1519593092 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueEncyclopedia of Statistics in Behavioral Science · 2005
Typeother
Languageen
FieldMathematics
TopicAdvanced Statistical Methods and Models
Canadian institutionsUniversity of Manitoba
Fundersnot available
KeywordsMultivariate statisticsUnivariateKurtosisStatisticsMultivariate analysisMultivariate analysis of varianceNormalityMathematicsSkewnessEstimatorMultivariate normal distributionNormality testMultivariate kernel density estimationEconometricsStatistical hypothesis testingComputer scienceArtificial intelligence

Abstract

fetched live from OpenAlex

Abstract Most classical multivariate procedures (e.g., multivariate analysis of variance, multivariate measures of effect size, classification procedures, maximum likelihood factor analysis) require that the data follow a multivariate normal density function. Behavioral science researchers risk committing many more Type I errors, quantifying inaccurately the magnitude of effect sizes, missing treatment effects, establishing inaccurate confidence intervals, and so on by failing to consider whether their data conform to multivariate normality. This paper discusses a number of options for assessing and dealing with nonnormal multivariate data including: (a) testing for univariate normality among the p measures, (b) transforming the data to achieve normality, (c) univariate normal probability plots, (d) multivariate measures of skewness and kurtosis, (e) computing squared distance statistics to locate outlying values, and (f) adopting robust estimators with robust test statistics to circumvent the biasing effects of nonnormality.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.326
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.001
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.094
GPT teacher head0.464
Teacher spread0.369 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it