Abstract: In this paper, a simple numerical experiment of the analysis error of statistical interpolation has been made by using ideal observational network. The experimental results show that the analysis quality of "OPTIMAL" statistical interpolation can be improved when (1) the observation errors and the first guess field errors are decreased, (2) the number of the observations considered at a grid point is reasonably increased, (3) the distance between neighboring observational stations is become appropriately small, (4) the well-distributed observations are selected, and that the analysis accuracy may be greatly decreased when normal observation errors and. the character of error correlation function used in the calculation are not equal to those on the ensemble average case. Finally the scale response of analysis error has been discussed by using a technique of the eiqenvector decomposition of the prediction error correlation.