In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of the order $n^{-1/5}$ for the nth iteration is achieved using suitable parameters. The novelty with respect to previous studies is that we allow the stochastic representation to be discontinuous and to consist of possibly dependent random variables (satisfying a mixing condition).

The independence assumption, although reasonable when examining cross-sectional data using single-factor experimental designs, is seldom verified by investigators. A Monte Carlo type simulation experiment was designed to examine the relationship between true Types I and II error probabilities in six multiple comparison procedures. Various aspects, such as patterns of means, types of hypotheses, and degree of dependence of the observations, were taken into account. Results show that, if independence is violated, none of the procedures control a using the error rate per comparison. At the same time, as the correlation increases, so does the per-comparison power.