Current techniques in image-guided surgery rely on the use of localizers for the measurement of position in physical space. These measurements are prone to error due to intrinsic properties of the localizer used. The error and thus accuracy of a localizer can be determined using various techniques, many of which assume that the error is isotropic and free of bias. A bias error adds an orientation dependence to the error of measured points. Determination of the presence of a bias error is an important component in the characterization of a localizer's performance. Statistical analysis of localized points on a rigid phantom can be used to detect the presence of a bias error. In this paper, we will examine the use of statistical techniques in the characterization of a series of localizers and how that information is useful in determining localizer efficacy.