A distribution-free test for the relationship between model input and output when using Latin hypercube sampling

A test for the detection of non-monotone relationships between the inputs and outputs of computer simulation models is described for use in sensitivity analyses employing Latin hypercube sampling. The test is based on the squared differences of the consecutive ranks of the output variable when the values of the output variable have been ordered by the corresponding values of an input variable. The test is distribution-free and does not require the values of the output variable to be independent of one another. Instead, the weaker assumption of exchangeability is used. The resulting test statistic is shown to be independent of Spearmanʹs rank correlation coefficient, and a simple method for combining the two statistics is discussed. The test is illustrated with an example from a recent performance assessment for the Waste Isolation Pilot Plant.