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.