Change-detection algorithms are often tested on real-world datasets where changes are synthetically introduced. While this common practice allows generating multiple datasets to obtain stable performance measures, it is often quite arbitrary since the change magnitude is seldom controlled. Thus, experiments { in particular those on multivariate and high-dimensional data. We here present a rigorous framework for introducing changes having a controlled magnitude in multivariate datasets. In particular, we introduce changes by directly roto-translating the data, and we measure the change magnitude by the symmetric
Kullback-Leibler divergence between pre- ad post-change distributions. We present an iterative algorithm that identities the roto-translation parameters yielding the desired change magnitude, and we prove its convergence analytically. We also illustrate our MATLAB framework that introduces changes having a controlled magnitude in real-world datasets, which is made publicly available for download.