Two-way heteroscedastic anova when the number of levels is large

Lan Wang, Michael G. Akritas

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

We consider testing for main treatment effects and interaction effects in crossed two-way layouts when one or both factors have large number of levels. Random errors are allowed to be nonnormal and heteroscedastic. In the heteroscedastic case, we propose new test statistics. The asymptotic distributions of our test statistics are derived under both the null hypothesis and local alternatives. The sample size per treatment combination can either be fixed or tend to infinity. Numerical simulations indicate that the proposed procedures have good power properties and maintain approximately the nominal α-level with small sample sizes. A data set from a study evaluating forty varieties of winter wheat in a large-scale agricultural trial is analyzed.

Original languageEnglish (US)
Pages (from-to)1387-1408
Number of pages22
JournalStatistica Sinica
Volume16
Issue number4
StatePublished - Oct 1 2006

Keywords

  • Heteroscedasticity
  • Large number of factor levels
  • Local alternatives
  • Projection method
  • Quadratic forms
  • Unbalanced designs

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    Wang, L., & Akritas, M. G. (2006). Two-way heteroscedastic anova when the number of levels is large. Statistica Sinica, 16(4), 1387-1408.