kendtauz.m

function z = kendtauz(varargin)
% kendtauz  - give approximate z-score for kendall tau (via formula)
%
% FORMAT:       z = kendtauz(v, m [, d])
%
% Input fields:
%
%       v           vector for which tau was computed
%       m           matrix (either VxM or MxV)
%       d           dim of m to use to build pairs, default: first match
%
% Output fields:
%
%       z           approximate z-score
%
% Notes: See references of
%        http://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient
%        for further explanations
%
% See also kendtau

% Version:  v0.9b
% Build:    11050712
% Date:     Apr-09 2011, 2:11 PM EST
% Author:   Jochen Weber, SCAN Unit, Columbia University, NYC, NY, USA
% URL/Info: http://neuroelf.net/

% Copyright (c) 2010, 2011, Jochen Weber
% All rights reserved.
%
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions are met:
%     * Redistributions of source code must retain the above copyright
%       notice, this list of conditions and the following disclaimer.
%     * Redistributions in binary form must reproduce the above copyright
%       notice, this list of conditions and the following disclaimer in the
%       documentation and/or other materials provided with the distribution.
%     * Neither the name of Columbia University nor the
%       names of its contributors may be used to endorse or promote products
%       derived from this software without specific prior written permission.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
% ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
% WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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% try to pass input to kendtau first
try
    [tau, z, nn] = kendtau(varargin{:});
catch ne_eo;
    rethrow(ne_eo);
end

% then compute z
nn = (1 / nn) .* z;
z = 0.5 + sqrt(2 .* z + 0.25);
z = tau ./ sqrt((10 + 4 .* z) ./ (9 .* z .* (z - 1) .* nn));