Pearson.m

function varargout = Pearson(x, y, numSides)
% [pearsonCoef, pVal] = Pearson(x, y, numSides)
% Calculates the Pearson product-momentum correlation coefficient
%  INPUTS:
%   -x,y:  1D arrays of equal length
%  OPTIONAL:
%   -numSides: (defaults to 1)
%    Set to 1 if only positive correlations are significant,
%           2 if either positive or negative correlations are significant
%  OUTPUTS:
%   -pearsonCoef: value between -1 and 1, characterizing correlation
%   OPTIONAL
%    -pVal: probability pearsonCoef generated by uncorrelated
%           data.  If length(x) < 4, PVal will be NaN

% Because this routine is often called from deep within other routines,
% must perform many sanity checks to ensure that garbage isn't being fed in
if nargin < 2 || nargin > 3
  help Pearson
  error('Invalid number of input arguments')
elseif nargout < 1 || nargout > 2
  help Pearson
  error('Invalid number of returned arguments')
end
if nargin == 2
  numSides = 1;
end
numX = size(x, 1);
if numX == 1
  x = x';
  numX = size(x, 1);
elseif numX == 0 || size(x, 2) ~= 1
  fprintf(2, 'Size of X = (%g, %g)\n', numX, size(x, 2));
  error('X and Y must be 1D arrays with equal length')
end
numY = size(y, 2);
if numY == 1
  y = y';
  numY = size(y, 2);
elseif numY == 0 || size(y, 1) ~= 1
  fprintf(2, 'Size of Y = (%g, %g)\n', numY, size(y, 2));
  error('X and Y must be 1D arrays with equal length')
end
if numY ~= numX
  fprintf(2, 'Length(X)=%d, length(Y)=%d\n', numX, numY);
  error('X and Y must have equal length')
end
% end of sanity checks

% compute the Pearson correlation coefficient by performing a dot product
% on z-scored data
ind = find(isfinite(y') & isfinite(x));
numX = length(ind);
x = x(ind);
y = y(ind);
pearsonCoef = (zscore(y) * zscore(x)) / (numX - 1);

if nargout == 1
  % only the Pearson coefficient was requested, return
  varargout = {pearsonCoef};
  return
end

% compute a p-value on observing this data
if numX < 4
  % insufficient numX to compute a p-value
  pVal = NaN;
else
  if pearsonCoef >= 1
    % perfect correlation (occasionally round-off produces coef = 1 + eps)
    % corresponds to Z = Inf;
    pVal = 0.0;
  elseif pearsonCoef <= -1
    % perfect anti-correlation
    % corresponds to Z = -Inf;
    if numSides == 1
      pVal = 1.0;
    else
      pVal = 0.0;
    end
  else
    % the typical case. Compute a p-value by assuming Gaussian distribution
    
    Z = sqrt(numX - 3) * atanh(pearsonCoef);
    if numSides == 1
      pVal = 0.5 * erfc(Z / sqrt(2));
    else
      pVal = erfc(abs(Z) / sqrt(2));
    end
  end
end
varargout = {pearsonCoef, pVal};
return