On the inhomogeneity of a test compounded of two Rasch homogeneous subscales

Van den Wollenberg stated a theorem specifying the conditions for a test, which is composed of two Rasch homogeneous subscales, as also behaving Rasch homogeneously. In our note, simple numerical counterexamples are given for which this theorem fails.While preparing the final version of this note, Ilse Rop passed away. The first author therefore takes sole responsibility for this final version.