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.

总体均值和标准差是量化因子布局中影响的最常见估计。实际上，这种设计中的大多数统计程序都是建立在推断手段或其对比之上的。为了进行更可靠的分析，我们将总体中位数，四分位数间距（IQR）和更一般的分位数组合视为估计值，在其中我们制定了无效假设并计算了相容的置信区域。基于同时的多元中心极限定理和相应的重采样结果，我们得出了具有单变量端点的一般，潜在的异方差，阶乘设计中的渐近正确过程。特殊情况包括针对人口中位数或IQR在任意交叉的单向，两向和高速公路布局中进行的稳健测试，这些布局可能具有异方差误差分布。