<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">DEFINITION MODULE Correl2;

   (* EXPORT QUALIFIED Kendl1, Kendl2, Spear; *)

   FROM NRVect IMPORT Vector;
   FROM NRMatr IMPORT Matrix;

   PROCEDURE Kendl1(    DATA1, DATA2: Vector; 
                    VAR tau, z, prob: REAL); 
   (*
     Given data arrays DATA1[0, n-1] and DATA2[0, n-1],
     this program returns Kendall's "tau" as tau, its number
     of standard deviations from zero as z, and its two-sided significance
     level as prob. Small values of prob indicate a significant
     correlation (tau positive) or anticorrelation (tau negative).
   *)

   PROCEDURE Kendl2(    TAB: Matrix; 
                    VAR tau, z, prob: REAL); 
   (*
     Given a two-dimensional table TAB[I, J], such that TAB[K,L]
     contains the number of events falling in bin K of one
     variable and bin L of another, this program returns Kendall's "tau" as 
     tau, its number of standard deviations from zero as z, and its two-sided 
     significance level as prob.  Small values of prob indicate a significant
     correlation (tau positive) or anticorrelation (tau negative)
     between the two variables.  Although TAB is a real array, it
     will normally contain integral values.
   *)

   PROCEDURE Spear(    DATA1, DATA2: Vector; 
                   VAR d, zd, probd, rs, probrs: REAL); 
   (*
     Given two data arrays, DATA1[0, n-1] and DATA2[0, n-1],
     this routine returns their sum-squared difference of ranks as d,
     the number of standard deviations by which d deviates from its 
     null-hypothesis expected value as zd, the two-sided significance 
     level of this deviation as PROBD, Spearman's rank correlation rs as rs, 
     and the two-sided significance level of its deviation from zero as probs.
     The external routine Sort2 (section 8.2) is used. A small value of either 
     probd or probrs indicates a significant correlation (rs positive) or 
     anticorrelation (rs negative).
   *)
END Correl2.
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