Resampling NANCOVA: Nonparametric analysis of covariance in small samples

Abstract

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. A resampling approach to the NANCOVA framework is investigated. NANCOVA 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. Novel NANCOVA tests and a nonparametric competitor test without covariate adjustment were evaluated in extensive simulations. Unlike approximate tests in the NANCOVA framework, the proposed 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, it is shown that resampling NANCOVA provides an asymptotically exact testing procedure, which makes it the first one with good finite sample performance in the present NANCOVA framework. In summary, resampling NANCOVA can be considered a viable tool for analysis of covariance overcoming issues (i) - (iv).