NAG Fortran Library Routine Document G02BSF

G02BSF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose G02BSF computes Kendall and/or Spearman non-parametric rank correlation coefficients for a set of data omitting cases with missing values from only those calculations involving the variables for which the values are missing; the data array is preserved, and the ranks of the observations are not available on exit from the routine. 3 Description The input data consists of n observations for each of m variables, given as an array where x ij is the ith observation on the jth variable. In addition each of the m variables may optionally have associated with it a value which is to be considered as representing a missing observation for that variable; the missing value for the jth variable is denoted by xm j. Missing values need not be specified for all variables. Let w ij ¼ 0 if the ith observation for the jth variable is a missing value i.e., if a missing value, xm j , has been declared for the jth variable, and x ij ¼ xm j (see also Section 7); and w ij ¼ 1 otherwise, for The observations are first ranked, a pair of variables at a time as follows: For a given pair of variables, j and l say, each of the observations x ij for which the product w ij w il ¼ 1ði ¼ 1; 2;. .. ; nÞ has associated with it an additional number, the 'rank' of the observation, which indicates the magnitude of that observation relative to the magnitude of the other observations on variable j for which w ij w il ¼ 1. The smallest of these valid observations for variable j is assigned to rank 1, the second smallest valid observation for variable j the rank 2, the third smallest rank 3, and so on until the largest such observation is given the rank n jl , where n jl ¼ X n i¼1 w ij w il : If a number of cases all have the same value for the variable j, then they are each given an 'average' rank, e.g., if in attempting to assign the rank h þ 1, k observations for which w ij w il ¼ 1 were found to have the same value, then instead of …