Confidence ellipsoids for ASCA models based on multivariate regression theory

In analysis of variance simultaneous component analysis, permutation testing is the standard way of assessing uncertainty of effect level estimates. This article introduces an analytical solution to the assessment of uncertainty through classical multivariate regression theory. We visualize the uncertainty as ellipsoids, contrasting these to data ellipsoids. This is further extended to multiple testing of effect level differences. Confirmatory and intuitive results are observed when applying the theory to previously published data and simulations. Ellipsoids are already standard tools for assessment of variation in analysis of variance simultaneous component analysis, but these only serve as visual guides to the sample variation in score plots. We introduce confidence ellipsoids that reflect the estimated variation of the effect level means, corresponding to confidence intervals in analysis of variance. These enable more informative visualizations and pairwise comparisons of effect level means for both main effects and interactions, without the use of permutation testing.