# Why Use Rank Correlation in Simulation Methods? When performing a risk analysis using Monte Carlo simulation, there are various measures of dependence;
among them, we can name the Pearson correlation coefficient and the
non-parametric rank correlation coefficient (Spearman’s correlation
coefficient); the later being the most commonly used. The correlation represents
the co-movement of two cost components; when one is more expensive, the other
tends to cost more (or less for a negative correlation). Both correlation
measures range from a value of -1 to 1. The value of 1 indicates perfect
correlation while -1 indicates conversely perfect negative dependence. A value
of 0 means no correlation.

There is a common agreement that the rank
correlation coefficient is a better measure of dependence for construction costs
since these costs are frequently not normally distributed; in addition the
dependence between two components may be monotonic but not linear in which case
the Pearson correlation is not a suitable measure.

An important requirement for including
the correlation information in the Monte Carlo simulation (MCS) model is to
assure that the coefficients in the correlation matrix are theoretically
consistent with a functional relationship, so the variance of the variable
derived by the MCS is nonnegative. By definition, the
variance is the second moment about the expected value of the derived variable;
therefore, it has to be nonnegative. Another way to see this is that if the
consistency condition is ignored the determinant of the correlation matrix could
be negative and this will lead the decision variable to have a negative
variance. A quick way to check for consistency is to test that the Eigen values
of the correlation matrix are nonnegative.

Dr. Javier Ordóñez