ît is important in many experimental Sciences (like Astronomy) to find out whet- her elements of a series of given numbers are arranged at random or not. Generâlly it is assumed that accidental errors satisfy the Gaussian Law of errors. This Law, hovvever, yields only one of the necessary condition for a series of numbers to be considered as accidental erros, and it is not sufficient; for, it concerns the only distribution of numbers and not their arrangement. Thus more necessary conditions are needed. In this paper “SIGN SEQUENCE” conditions for moving averages with two, three, and four terms are established and theoretical results are confirmed with experi- mental resuslt.