The paper under review is devoted to the comparison of linear models and linear normal models. The first part deals with the case when the covariances are known. It is pointed out that the ordering of two linear models \(L_ 1,L_ 2\) with \(L_ 1\geq L_ 2\) by variances of best linear estimators coincides with the concept of factorization into independent models, more precise: there exists a linear model \(L_ 3\) such that \(L_ 1\) is equivalent in Le Cam's sense to \(L_ 2\times L_ 3\). If the models are normal then the ordering ''\(\geq ''\) is equivalent to the ordering ''\(\leq ''\) of the Hellinger transforms and the affinity of binary subexperiments. In the second part linear models are treated when the covariances are known except for an unknown multiplicative factor. The paper includes a nice introduction into the theory of linear models where for instance some results for best linear unbiased estimators are recalled. The main tools are elements of convex functions of R. T. Rockafellar and an earlier paper of \textit{O. H. Hansen} and the author [Ann. Stat. 2, 367--373 (1974; Zbl 0289.62011)].