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Genetic algorithms have been extensively used and studied in computer science, yet there is no generally accepted methodology for exploring which parameters significantly affect performance, whether there is any interaction between parameters, and how performance varies with respect to changes in parameters. This paper presents a rigorous yet practical statistical methodology for the exploratory study of genetic and other adaptive algorithms. This methodology addresses the issues of experimental design, blocking, power calculations, and response curve analysis. It details how statistical analysis may assist the investigator along the exploratory pathway. As a demonstration of our methodology, we describe case studies using four well-known test functions. We find that the effect upon performance of crossover is pre-dominantly linear, while the effect of mutation is predominantly quadratic. Higher order effects are noted but contribute less to overall behavior. In the case of crossover, both positive and negative gradients are found suggesting the use of a maximum crossover rate for some problems and its exclusion for others. For mutation, optimal rates appear higher compared with earlier recommendations in the literature, while supporting more recent work. The significance of interaction and the best values for crossover and mutation are problem specific.