Abstract
AbstractPopulation 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.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Statistics and Probability
Reference51 articles.
1. Adiar L (2007) Size at birth and growth trajectories to young adulthood. Am J Hum Biol 19:327–337
2. Bathke A, Schabenberger O, Tobias R, Madden L (2009) Greenhouse-Geisser adjustment and the ANOVA-type statistic: cousins or twins? Am Stat 63:239–246
3. Beyerlein A (2014) Quantile regression-opportunities and challenges from a user’s perspective. Am J Epidemiol 180(3):330–331
4. Bhargava S, Sachdev H, Fall C, Osmond C, Lakshmy R, Barker D, Biswas S, Ramji S, Prabhakaran D, Reddy K (2009) Relation of serial changes in childhood body-mass index to impaired glucose tolerance in young adulthood. N Engl J Med 250:865–875
5. Bonett D (2006) Confidence interval for a coefficient of quartile variation. Comput Stat Data Anal 50:2953–2957
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