Impurities adsorbed on single crystal surfaces tend to form two-dimensional structures which are simply related to the substrate. Degeneracy in the registry of such structures relative to the substrate is perhaps the most characteristic feature of surface crystallography. LEED structure analysis, however, is usually based on calculations which assume the interaction of perfectly coherent plane radiation with a defect free surface. Unfortunately, analysis of the response of typical LEED systems makes it clear that the first assumption is sufficiently poor as to make the evaluation of the second difficult. In particular, we show that the limited coherence of the primary electrons necessitates the use of statistical methods in characterizing LEED. The application of the statistical approach in the analysis of LEED beam profiles is illustrated by simple adsorption models. This analysis can be used to characterize the adsorption sites and the nature and distribution of mistakes in the periodicity of surface structures. © 1969.