Estimation of rms target position accuracy for radar is of great importance to radar manufacturers and customers alike. With increasing frequency customers insist on direct measurement with small RCS aircraft on radial flight paths. Too often, however, a colocated precision reference radar is unavailable from which to accurately define the true target flight path. In these cases the total error can be tested in two parts: the bias component can be estimated from static measurements and the random component (jitter and thermal error) is estimated as a variance. Here the true target flight path is traditionally modelled as entirely radial. Unfortunately even small deviations from a true radial can lead to large errors in variance estimation, particularly when the target is close to the radar where the radar error is expected to be small. If the customer requires proof of theoretical accuracy then the model error can be larger than the radar error and the radar will falsely fail the test. In addition to unbiased optimal estimation of variance, expressions are developed for the uncertainty in the estimate and related to the producer's and consumer's risks of falsely failing or falsely passing a tri-coordinate position accuracy test. Considerable development is accorded sound test design with these principles, and expressions are developed for confidence limits to infer bounds or true variance given the test results.