Robust analysis of variance with imprecise data: an ad hoc algorithm

Abstract

We present an easy to implement algorithm, which is valid to analyse the variance of data under several robust conditions. Firstly, the observations may be precise or imprecise. Secondly, the error distributions may vary within the wide class of the strongly unimodal distributions, symmetrical or not. Thirdly, the variance of the errors is unknown. The algorithm starts by estimating the parameters of the ANOVA linear model. Then, the asymptotic covariance matrix of the effects is estimated. Finally, the algorithm uses this matrix estimate to test ANOVA hypotheses posed in terms of linear combinations of the effects.