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The paper develops a simple theory to account for the magnetoresistance influence on Van der Pauw-type experiments (i.e. resistivity and Hall coefficient RH measurements in arbitrarily shaped samples). In particular, it is proved that the voltage developed between two nonsuccessive contacts includes not only the usual Hall term (involving the magnetic field and RH) but also an additional term proportional to the magnetoresistance coefficient. This term is especially important under high magnetic fields and in anisotropic or ambipolar semiconductors; if ignored, it will be responsible for misleading interpretations of the Hall coefficient behaviour. Moreover, the influence of contact dimensions is shown to result mainly in an erroneous term, proportional to the Hall voltage. In this new light averaging techniques, suitable for more accurate measurements, are proposed. The experimental results fully support the theoretical derivations. As an application, a powerful method for the characterisation of ambipolar semiconductor slabs with arbitrary geometry is presented.