QANOVA: quantile-based permutation methods for general factorial designs

Marc Ditzhaus (), Roland Fried and Markus Pauly
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Marc Ditzhaus: TU Dortmund University
Roland Fried: TU Dortmund University
Markus Pauly: TU Dortmund University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 30, issue 4, No 7, 960-979

Abstract: 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.

Keywords: Birth cohorts; IQR; Main and interaction effects; Median; Permutation tests; 62G09; 62G10; 62G20 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11749-021-00758-y

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