It has been suggested recently that point displacements in a free geodetic network traversing a strike-slip fault may be estimated from repeated surveys by minimizing only those displacement components normal to the strike. It is desirable to justify this procedure. We construct, from estimable quantities, a deformation parameter which is an F-statistic of the type occurring in the analysis of variance of linear models not of full rank. A test of its significance provides the criterion to justify the displacement solution. It is also interesting to study its behaviour as one varies the supposed strike of the fault. Justification of a displacement solution using data from a strike-slip fault is found, but not for data from a rift valley. The technique can be generalized to more complex patterns of deformation such as those expected near the end-zone of a fault in a dislocation model.