A correlation coefficient measures the strength of the linear relationship between two variables. However, if the two variables do not have the same probability distributions, they are not likely related linearly. Under such circumstances, the correlation coefficient calculated on their raw values has little meaning.
If you calculate the correlation coefficient using rank values instead of actual values, the correlation coefficient is meaningful even for variables with different distributions.
You determine rank values by arranging the actual values in ascending order and replacing the values with their rankings. For example, the lowest actual value will have a rank of 1; the next-lowest actual value will have a rank of 2; and so on.
Crystal Ball uses rank correlation to correlate assumptions. The slight loss of information that occurs using rank correlation is offset by two advantages:
First, the correlated assumptions need not have similar distribution types. In effect, the correlation function in Crystal Ball is distribution-independent. The rank correlation method works even when a distribution has been truncated at one or both ends of its range.
Second, the values generated for each assumption are not changed; they are merely rearranged to produce the desired correlation. In this way, the original distributions of the assumptions are preserved.