A statistical investigation of the errors associated with the minimum variance analysis of directional discontinuity normal components has been performed. This study consisted of both computer simulation of discontinuities with controlled properties and examination of actual discontinuities (current sheets) observed by the Mariner 10 spacecraft. The simulated discontinuities were created by adding fluctuations, represented by isotropic random noise, to exactly known but vaying (in a plane) magnetic field components. an empirical expression for the magnitude of the error ‖ΔBz‖ in an estimated discontinuity normal component, relative to the total field across the discontinuity, was derived, as well as other relevant statistical properties. This formula resulted from studies of the relation between precisely known values of the error and the minimum variance eigenvalues &lgr;, rotation angle in the discontinuity plane &ohgr;, and magnitude of the normal component B cos &bgr; relative to the total field B. The formula is ‖ΔBz‖=3/4 B sin &bgr; &Lgr;(3.60+244log&Lgr;) {exp[120 ¿-&ohgr;/120 ¿>3}, where &Lgr;≡&lgr;3(1/&lgr;1+1/&lgr;2) and where the subscripts 1, 2, and 3 on the eigenvalues refer to maximum, intermediate, and minimum values, respectively. It is found to give significantly more accurate estimates of the error in the normal component over a wide range of simulated conditions than the formula derived by Sonnerup (1971). Use of this empirical relation in the analysis of Mariner 10 discontinuities has provided a more precise estimate of an upper bound on the relative normal component value for tangential discontinuities that can be used to separate them from rotational discontinuities in studies using only magnetic field data from a single spacecraft in the region of space considered. This upper bound is ‖ΔBz‖/B=0.30.