This paper discusses theorems from the mathematical statistics literature on confidence regions for an estimated rotation. The theorems can be used to analyze pairs of homologous intersections of fracture zones with magnetic anomaly lineations on opposing plates. Two classes of probability models on the data are considered: The ''fixed u'' and the ''random u'' models, corresponding to, in the geophysical context, whether error is attributed to the measurements on one or on both plates. For each model, large sample and concentrated error approximate confidence regions are given. It is found that the geometric features of the confidence regions are in rough agreement with the analysis of partial uncertainty rotations by Stock and Molnar. The paper concludes with some rudimentary small sample, diffuse error distribution theory. For illustrative purposes, a data set from the Gulf of Aden is repeatedly analyzed using a variety of probabilistic models. ¿American Geophysical Union 1987