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ANOVA and rank tests when the number of treatments is large

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  • Boos, Dennis D.
  • Brownie, Cavell

Abstract

In this paper we consider the analysis of variance (ANOVA) F-tests, and rank statistic analogs, for testing equality of treatment means in the one-way and two-way experimental layouts. The rank-based procedures include the Kruskal-Wallis and Friedman statistics with chi-squared critical values, and the "ANOVA on ranks" or F-versions of these procedures. We provide proofs of asymptotic normality for these statistics under the nonstandard assumption that the number of treatments converges to infinity while the number of replications per treatment remains finite. These results confirm the robustness of F-distribution critical values for nonnormal data in situations which have a large number of treatments.

Suggested Citation

  • Boos, Dennis D. & Brownie, Cavell, 1995. "ANOVA and rank tests when the number of treatments is large," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 183-191, May.
    • Handle: RePEc:eee:stapro:v:23:y:1995:i:2:p:183-191
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    Citations

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    Cited by:

    1. Solomon Harrar & Arne Bathke, 2012. "A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 135-165, February.
    2. Badi Baltagi & Chihwa Kao & Sanggon Na, 2013. "Testing for cross-sectional dependence in a panel factor model using the wild bootstrap $$F$$ test," Statistical Papers, Springer, vol. 54(4), pages 1067-1094, November.
    3. Junyong Park, 2019. "Testing homogeneity of proportions from sparse binomial data with a large number of groups," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 505-535, June.
    4. Calhoun, Gray, 2011. "Hypothesis testing in linear regression when k/n is large," Journal of Econometrics, Elsevier, vol. 165(2), pages 163-174.
    5. Chun-Lung Su, 2021. "Bayesian multi-way balanced nested MANOVA models with random effects and a large number of the main factor levels," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 663-692, July.
    6. Jiménez-Gamero, M. Dolores & Franco-Pereira, Alba M., 2021. "Testing the equality of a large number of means of functional data," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    7. Bathke, Arne C. & Harrar, Solomon W. & Wang, Haiyan & Zhang, Ke & Piepho, Hans-Peter, 2010. "Series of randomized complete block experiments with non-normal data," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1840-1857, July.
    8. Lyubchich, Vyacheslav & Gel, Yulia R., 2016. "A local factor nonparametric test for trend synchronism in multiple time series," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 91-104.

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