Analysis of covariance is a crucial method for improving precision of statistical tests for factor effects in randomized experiments. However, existing solutions suffer from one or more of the following limitations: (i) they are not suitable for ordinal data (as endpoints or explanatory variables); (ii) they require semiparametric model assumptions; (iii) they are inapplicable to small data scenarios due to often poor type-I error control; or (iv) they provide only approximate testing procedures and (asymptotically) exact test are missing. In this paper, we investigate a resampling approach to the NANCOVA framework, which is a fully nonparametric model based on relative effects that allows for an arbitrary number of covariates and groups, where both outcome variable (endpoint) and covariates can be metric or ordinal. Thereby, we evaluate novel NANCOVA tests and a nonparametric competitor test without covariate adjustment in extensive simulations. Unlike approximate tests in the NANCOVA framework, our resampling version showed good performance in small sample scenarios and maintained the nominal type-I error well. Resampling NANCOVA also provided consistently high power: up to 26% higher than the test without covariate adjustment in a small sample scenario with 4 groups and two covariates. Moreover, we prove that resampling NANCOVA provides an asymptotically exact testing procedure, which makes it the first one in the NANCOVA framework. In summary, resampling NANCOVA can be considered a viable tool for analysis of covariance that overcomes issues (i) - (iv).

翻译：协方差分析是提高随机实验中因子效应统计检验精度的关键方法。然而，现有解决方案存在以下一个或多个局限：(i) 不适用于有序数据（作为终点或解释变量）；(ii) 需要半参数模型假设；(iii) 由于Ⅰ类错误控制不佳，不适用于小数据场景；或 (iv) 仅提供近似检验程序，缺乏（渐近）精确检验。本文研究NANCOVA框架的重采样方法，该框架是基于相对效应的完全非参数模型，允许任意数量的协变量和组别，其中结果变量（终点）和协变量均可为度量或有序类型。通过大量模拟实验，我们评估了新的NANCOVA检验方法以及未进行协变量调整的非参数竞争检验。与NANCOVA框架中的近似检验不同，我们的重采样版本在小样本场景中表现出良好性能，并能有效维持名义Ⅰ类错误水平。重采样NANCOVA还提供了持续的高检验功效：在包含4个组别和两个协变量的小样本场景中，其功效比未调整协变量的检验高出26%。此外，我们证明重采样NANCOVA提供了渐近精确的检验程序，这使其成为NANCOVA框架中的首个此类方法。综上所述，重采样NANCOVA可被视为克服问题(i)-(iv)的有效协方差分析工具。