Correlation: A Stand-Alone Implementation
Druker, E.¹; Coleman, R.²; Braxton, P.¹; Hughes, J.^3
1Northrop Grumman - TASC; ²Northrop Grumman; ³Northrop Grumman Shipbuilding

Correlation has always been one of the hottest topics in the arena of Cost-Risk Analysis. Statistical correlation is defined as "the degree to which two or more attributes or measurements on the same group of elements show a tendency to vary together." The problem is how to take this statistical measure, and apply it meaningfully to one's risk analysis. Commercial tools such as Crystal Ball and @Risk allow correlation matrices as inputs, and then use them to correlate the user defined random variables. Most users, however, are unaware as to what exactly adding correlation to their analysis accomplishes other than "spreading the S-Curve". This paper will act as a primer in correlation algorithms. Building upon papers published over the past twenty years and filling in gaps where necessary, it will walk the reader step by step through the process to implement correlation on their own, stopping to discuss the algorithms on the way. Along the way it will touch on such topics such as: Spearman's Rank Correlation vs. Pearson's Correlation Producing Viable Correlation Matrices from User Inputted Matrices Producing Correlated Uniform Random Variables Implementing a Lurie-Goldberg-like Optimization Algorithm in Excel The Cost-Risk Correlation Module

Finally, this paper will end with a discussion of the effects of applying top level coefficients of variation to lower level estimates as well as the implications of correlating Bernoulli risks using Pearson’s Correlation.