--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/m-toolbox/classes/+utils/@math/spcorr.m	Wed Nov 23 19:22:13 2011 +0100
@@ -0,0 +1,101 @@
+% SPCORR calculate Spearman Rank-Order Correlation Coefficient
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Description:
+% 
+% SPCORR calculates Spearman Rank-Order Correlation Coefficient
+% 
+% CALL:
+%       [rs,pValue,TestRes] = spcorr(y1,y2,alpha)
+% 
+% INPUT: 
+%       - y1 and y2 are data series
+%       - alpha is the significance level. Default 0.05
+% 
+% OUTPUT:
+%       - rs: Spearman rank-order correlation coefficient
+%       - pValue: Probability associated with the calculated rs in the
+%       hypothesis that the correlation between y1 and y2 is zero
+%       - TestRes: True or false on the basis of the test results. The null
+%       hypothesis for the test is that the two series y1 and y2 are
+%       uncorrelated.
+%         TestRes = 0 => Do not reject the null hypothesis at significance
+%         level alpha. (pValue >= alpha)
+%         TestRes = 1 => Reject the null hypothesis at significance level
+%         alpha. (pValue < alpha)
+% 
+% NOTE: 
+%       The statistic of Spearman rank-order correlation coefficient is
+%       well approximated by a Student t distribution. Hypothesis test is
+%       then based on such statistic.
+% 
+%   References:
+%      [1] W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery,
+%      Numerical Recipes 3rd Edition: The Art of Scientific Computing,
+%      Cambridge University Press; 3 edition (September 10, 2007)
+% 
+%
+% L Ferraioli 06-12-2010
+%
+% $Id: spcorr.m,v 1.2 2011/07/06 14:42:26 luigi Exp $
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function [rs,pValue,TestRes] = spcorr(y1,y2,alpha)
+  
+  % check size
+  if size(y1)~=size(y2)
+    error('y1 and y2 must have the same size')
+  end
+  
+  % check input
+  if isempty(alpha)
+    alpha = 0.05;
+  elseif alpha > 1
+    alpha = alpha/100;
+  end
+    
+  
+  % calculate rank for y1 and y2
+  [r1,s1] = utils.math.crank(y1);
+  [r2,s2] = utils.math.crank(y2);
+  
+  n = numel(y1);
+  
+  dv = (r1-r2).^2;
+  
+  dd = sum(dv);
+  
+  en = n*n*n-n;
+  
+  sq1 = sqrt(1-s1/en);
+  sq2 = sqrt(1-s2/en);
+  
+  % calculate Spearman rank-order correlation coefficient
+  rs = (1 - 6*(dd + s1/12 + s2/12)/en)/(sq1*sq2);
+  
+  % transform rs in t which is according Student's distribution with n-2
+  % degrees of freedom
+  t = rs*sqrt((n-2)/(1-rs^2));
+  
+  % Indicated with f(x) the prob. distribution function (Student's t in the
+  % present caase). The probability Pr(k <= t) is proportional to the
+  % integral Int_(-t,t)[f(x)dx]. For a Student's distribution such integral
+  % is represeted by the Beta incomplete function
+  % Pr(k <= t) = betainc(df/(df+t^2),df/2,1/2,'upper')
+  % As a consequence Pr(k > t) = 1 - Pr(k <= t) which in Matlab can be
+  % effectively calculated as
+  % Pr(k > t) = betainc(df/(df+t^2),df/2,1/2,'lower')
+  % Which provides the probability of finding a value grater than t if our
+  % variable k is distributed according to a Student's distribution with df
+  % degrees of freedom. Such a value represent the required pValue for the
+  % test in the hypothesis that the two input data series are uncorrelated
+  fac = (rs+1)*(1-rs);
+  if fac>0
+    df = n-2;
+    pValue = betainc(df/(df+t*t),0.5*df,0.5,'lower');
+  else
+    pValue = 0;
+  end
+  
+  TestRes = (pValue < alpha);
+  
+  
+end
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