Asymptotics for Analysis of Variance When the Number of Levels is Large

Michael G. Akritas, Steven Arnold

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

We study asymptotic results for F tests in analysis of variance models as the number of factor levels goes to ∞ but the number of observations for each factor combination is fixed. Asymptotic derivations of the type discussed in this article would be relevant whenever both the numerator and denominator degrees of freedom go to ∞ (at the same rate). We consider null and alternative distributions of F, the usual F statistic, for fixed-effects and random-effects, balanced and unbalanced, one-way and two-way, and normal and nonnormal analysis of variance (ANOVA) models. The results may be most relevant for random-effects and mixed models. For example, we may have an agricultural experiment in which the number of cows is quite large but the number of measurements on each cow is small. The results would also be relevant for fixed-effects models in which there are many factor levels but not many observations for each factor level.

Original languageEnglish (US)
Pages (from-to)212-226
Number of pages15
JournalJournal of the American Statistical Association
Volume95
Issue number449
DOIs
StatePublished - Mar 1 2000

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Analysis of variance
Fixed Effects Model
F-statistics
F Test
Numerator
Fixed Effects
Random Effects Model
Mixed Model
Denominator
Random Effects
Null
Degree of freedom
Factors
Alternatives
Model
Experiment
Observation

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "We study asymptotic results for F tests in analysis of variance models as the number of factor levels goes to ∞ but the number of observations for each factor combination is fixed. Asymptotic derivations of the type discussed in this article would be relevant whenever both the numerator and denominator degrees of freedom go to ∞ (at the same rate). We consider null and alternative distributions of F, the usual F statistic, for fixed-effects and random-effects, balanced and unbalanced, one-way and two-way, and normal and nonnormal analysis of variance (ANOVA) models. The results may be most relevant for random-effects and mixed models. For example, we may have an agricultural experiment in which the number of cows is quite large but the number of measurements on each cow is small. The results would also be relevant for fixed-effects models in which there are many factor levels but not many observations for each factor level.",
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Asymptotics for Analysis of Variance When the Number of Levels is Large. / Akritas, Michael G.; Arnold, Steven.

In: Journal of the American Statistical Association, Vol. 95, No. 449, 01.03.2000, p. 212-226.

Research output: Contribution to journalArticle

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