Statistical Analyses of Scatterplots to Identify Important Factors in Large-Scale Simulations

The robustness of procedures for identifying patterns in scatterplots generated in Monte Carlo sensitivity analyses is investigated. These procedures are based on attempts to detect increasingly complex patterns in the scatterplots under consideration and involve the identification of (1) linear relationships with correlation coefficients, (2) monotonic relationships with rank correlation coefficients, (3) trends in central tendency as defined by means, medians and the Kruskal-Wallis statistic, (4) trends in variability as defined by variances and interquartile ranges, and (5) deviations from randomness as defined by the chi-square statistic. The following two topics related to the robustness of these procedures are considered for a sequence of example analyses with a large model for two-phase fluid flow: the presence of Type I and Type II errors, and the stability of results obtained with independent Latin hypercube samples. Observations from analysis include: (1) Type I errors are unavoidable, (2) Type II errors can occur when inappropriate analysis procedures are used, (3) physical explanations should always be sought for why statistical procedures identify variables as being important, and (4) the identification of important variables tends to be stable for independent Latin hypercube samples.