In the case of moving average schemes or what are termed them-dependent stochastic processes, the successive observations in the series are not stochastically independent. As a result, the usual sign test, the test based on the rank correlation τ (for randomness against trend alternatives), and the test proposed by Moore and Wallis [9] and further developed by Goodman and Grunfeld [2] (for the comovement between two time series) are not valid and require some modifications. Accordingly, the modified forms of these non-parametric tests are studied here in detail, and their applications considered.