Rank tests for ANOVA with large number of factor levels

Haiyan Wang, Michael G. Akritas

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Recent papers (Boos, D. D and Brownie, C. (1995). ANOVA and rank tests when the number of treatments is large. Statist. Probab. Lett., 23, 183-191; Akritas, M. G. and Arnold, S. (2000). Asymptotics for ANOVA when the number of levels is large. Journal of the American Statistical Association, 95, 212-226; Bathke, A. (2002). ANOVA for a large number of treatments. Mathematical Methods of Statistics, 11(1), 118-132; Akritas and Papadatos 2004; Wang and Akritas 2003) have studied asymptotic properties of ANOVA F-statistics, under general distribution assumptions, when the number of levels is large. Most of these results pertain to statistics based on the original observations, which require strong moment assumptions and are sensitive to outliers. In this paper, we study the use of rank statistics as robust alternatives. Balanced and unbalanced, homoscedastic and heteroscedastic ANOVA models are considered. The main asymptotic tools are the asymptotic rank transform and Hájek's projection method. Simulation results show that the present rank statistics outperform those based on the original observations, in terms of both Type I and Type II errors.

Original languageEnglish (US)
Pages (from-to)563-589
Number of pages27
JournalJournal of Nonparametric Statistics
Issue number3-4
StatePublished - 2004

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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