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QANOVA: quantile-based permutation methods for general factorial designs

Author

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  • Marc Ditzhaus

    (TU Dortmund University)

  • Roland Fried

    (TU Dortmund University)

  • Markus Pauly

    (TU Dortmund University)

Abstract

Population means and standard deviations are the most common estimands to quantify effects in factorial layouts. In fact, most statistical procedures in such designs are built toward inferring means or contrasts thereof. For more robust analyses, we consider the population median, the interquartile range (IQR) and more general quantile combinations as estimands in which we formulate null hypotheses and calculate compatible confidence regions. Based upon simultaneous multivariate central limit theorems and corresponding resampling results, we derive asymptotically correct procedures in general, potentially heteroscedastic, factorial designs with univariate endpoints. Special cases cover robust tests for the population median or the IQR in arbitrary crossed one-, two- and higher-way layouts with potentially heteroscedastic error distributions. In extensive simulations, we analyze their small sample properties and also conduct an illustrating data analysis comparing children’s height and weight from different countries.

Suggested Citation

  • Marc Ditzhaus & Roland Fried & Markus Pauly, 2021. "QANOVA: quantile-based permutation methods for general factorial designs," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 960-979, December.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:4:d:10.1007_s11749-021-00758-y
    DOI: 10.1007/s11749-021-00758-y
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    References listed on IDEAS

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    Cited by:

    1. Sattler, Paavo & Zimmermann, Georg, 2024. "Choice of the hypothesis matrix for using the Wald-type-statistic," Statistics & Probability Letters, Elsevier, vol. 208(C).
    2. Baumeister, Marléne & Ditzhaus, Marc & Pauly, Markus, 2024. "Quantile-based MANOVA: A new tool for inferring multivariate data in factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    3. Yuichi Goto & Koichi Arakaki & Yan Liu & Masanobu Taniguchi, 2023. "Homogeneity tests for one-way models with dependent errors under correlated groups," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 163-183, March.
    4. Ditzhaus, Marc & Smaga, Łukasz, 2022. "Permutation test for the multivariate coefficient of variation in factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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