A positional quality control test based on proportions

Abstract

This paper presents a new method for positional accuracy quality control of spatial data. This method is valid for 1D, 2D, 3D and nD dimensional data, where data can follow any kind of distribution function. Normality of errors, or any other assumption are not required. The method is an exact statistical hypothesis testing based on multinomial distribution. The proportions of the multinomial distribution are defined by means of several metric tolerances. The proposed statistical test is exact, so the p-value can be derived by exploring a space of solutions and summing up the probabilities of each isolated case of this space. The performance of the test has been analyzed by means of a simulation procedure. The validity and the power of the contrast seem to be good enough. An application example is presented for the 3D case of working with two tolerances. In all cases, H0 is the same, but in the first one, its hypothesis is true, in the second, the true distribution has larger errors than assumed by H0 (it is worse) and, in the third case, the true distribution implies smaller errors than that stated by H0 (it is better in the sense of the error magnitude). In all three cases, the behavior of the proposed method is acceptable.