A methodology to determine quantitatively the dimensionality of the dominant conducting structures and the resolution of the structural parameters in magnetotelluric data is presented. In addition, the method recovers the regional impedance responses when the regional structure can be characterized, at least approximately, as one or two dimensional. The methodology is based upon three general models of the MT tensor, each of which has a distinct parameterization and physical interpretation. A weighted statistical residual describes quantitatively the fit of the model response to the data within the scatter of the measured data and hence permits (i) tests of dimensionality, (ii) determination of the appropriate strike angle, and (iii) recovery of the regional responses. The method has been tested extensively with synthetic data, and proven to be successful. These synthetic studies give insight into the different physical parameterizations and the stability of the parameters determined. We describe and illustrate some of these synthetic studies. With field data, the methodology is not always as straight-forward, but its application to a great many sites has proven valuable. Data from two closely spaced sites, which are both affected by strong but very different three-dimensional effects, are analyzed to illustrate the geological significance of the results. The analyses reveal and recover regional responses within the data which indicate the presence of electrical anisotropy located deep in the crust and upper mantle. Analyses of the entire data set, of which these two form a part, confirm this finding.