For a given variable, say, each of the observations, , has associated with it an additional number, the ‘rank’ of the observation, which indicates the magnitude of that observation relative to the magnitudes of the other observations on that same variable.
The smallest observation for variable is assigned the rank , the second smallest observation for variable the rank , the third smallest the rank , and so on until the largest observation for variable is given the rank .
If a number of cases all have the same value for the given variable, , then they are each given an ‘average’ rank, e.g., if in attempting to assign the rank , observations were found to have the same value, then instead of giving them the ranks
all observations would be assigned the rank
and the next value in ascending order would be assigned the rank
The process is repeated for each of the variables.
Let be the rank assigned to the observation when the th variable is being ranked. The actual observations are replaced by the ranks .
|(b)||Nonparametric rank correlation coefficients
Program Text (g02bnfe.f90)
Program Data (g02bnfe.d)
Program Results (g02bnfe.r)