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ft_statfun_indepsamplesZcoh.m
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ft_statfun_indepsamplesZcoh.m
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function [s, cfg] = ft_statfun_indepsamplesZcoh(cfg, dat, design)
% FT_STATFUN_INDEPSAMPLESCOHZ calculates the independent samples coherence
% Z-statistic on the biological data in dat (the dependent variable), using the
% information on the independent variable (ivar) in design.
%
% Use this function by calling one of the high-level statistics functions as
% [stat] = ft_timelockstatistics(cfg, timelock1, timelock2, ...)
% [stat] = ft_freqstatistics(cfg, freq1, freq2, ...)
% [stat] = ft_sourcestatistics(cfg, source1, source2, ...)
% with the following configuration option
% cfg.statistic = 'ft_statfun_indepsamplesZcoh'
%
% The samples-dimension of the dat-variable must be the result of a reshaping
% operation applied to a data structure with dimord chan_(freq_time) or
% pos_(freq_time). The configuration must contain channel labels in cfg.label or
% position information in cfg.pos. This information is used to determine the number
% of channels. The dimord of the output fields is [prod(nchancmb,nfreq,ntime),1]. The
% channel combinations are the elements of the lower diagonal of the cross-spectral
% density matrix.
%
% You can specify the following configuration options:
% cfg.computestat = 'yes' or 'no', calculate the statistic (default='yes')
% cfg.computecritval = 'yes' or 'no', calculate the critical values of the test statistics (default='no')
% cfg.computeprob = 'yes' or 'no', calculate the p-values (default='no')
%
% The following options are relevant if cfg.computecritval='yes' and/or cfg.computeprob='yes':
% cfg.alpha = critical alpha-level of the statistical test (default=0.05)
% cfg.tail = -1, 0, or 1, left, two-sided, or right (default=1)
% cfg.tail in combination with cfg.computecritval='yes'
% determines whether the critical value is computed at
% quantile cfg.alpha (with cfg.tail=-1), at quantiles
% cfg.alpha/2 and (1-cfg.alpha/2) (with cfg.tail=0), or at
% quantile (1-cfg.alpha) (with cfg.tail=1)
%
% The experimental design is specified as:
% cfg.ivar = independent variable, row number of the design that contains the labels of the conditions to be compared (default=1)
%
% The labels for the independent variable should be specified as the number 1 and 2.
%
% See also FT_TIMELOCKSTATISTICS, FT_FREQSTATISTICS or FT_SOURCESTATISTICS
% Copyright (C) 2006, Eric Maris
%
% This file is part of FieldTrip, see http://www.fieldtriptoolbox.org
% for the documentation and details.
%
% FieldTrip is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% FieldTrip is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with FieldTrip. If not, see <http://www.gnu.org/licenses/>.
%
% $Id$
% set the defaults
cfg.computestat = ft_getopt(cfg, 'computestat', 'yes');
cfg.computecritval = ft_getopt(cfg, 'computecritval', 'no');
cfg.computeprob = ft_getopt(cfg, 'computeprob', 'no');
cfg.alpha = ft_getopt(cfg, 'alpha', 0.05);
cfg.tail = ft_getopt(cfg, 'tail', 1);
cfg.ivar = ft_getopt(cfg, 'ivar', 1);
% perform some checks on the configuration
if strcmp(cfg.computeprob,'yes') && strcmp(cfg.computestat,'no')
ft_error('P-values can only be calculated if the test statistics are calculated.');
end
% if ~isfield(cfg, 'label') && ~isfield(cfg, 'pos')
% ft_error('the configuration needs to contain either a label or a pos field');
% elseif isfield(cfg, 'label') && isfield(cfg, 'pos') && ~isempty(cfg.label) && ~isempty(cfg.pos)
% ft_error('the configuration needs to contain either a non-empty label or a non-empty pos field');
% elseif isfield(cfg, 'label') && ~isempty(cfg.label)
% nchan = length(cfg.label);
% elseif isfield(cfg, 'pos') && ~isempty(cfg.pos)
% nchan = size(cfg.pos,1);
% end
nchan = cfg.dim(1);
% perform some checks on the design
selc1 = find(design(cfg.ivar,:)==1);
selc2 = find(design(cfg.ivar,:)==2);
nreplc1 = length(selc1);
nreplc2 = length(selc2);
nrepl = nreplc1 + nreplc2;
if nrepl<size(design,1)
ft_error('Invalid specification of the independent variable in the design array.');
end
if nreplc1<2 || nreplc2<2
ft_error('Every condition must contain at least two trials/tapers.');
end
dfc1 = nreplc1*2;
dfc2 = nreplc2*2;
if strcmp(cfg.computestat, 'yes')
% compute the statistic
nsamples = size(dat,1);
%nchan = length(cfg.label); %this is computed earlier
chancmbsel = find(tril(ones(nchan),-1));
nfreqtim = nsamples/nchan;
nchancmb = length(chancmbsel);
nnewsamples = nchancmb*nfreqtim;
s.stat = zeros(nnewsamples,1);
for freqtimindx=1:nfreqtim
chansel=((freqtimindx-1)*nchan + 1):(freqtimindx*nchan);
csdc1=dat(chansel,selc1)*dat(chansel,selc1)'/nreplc1;
powerc1=diag(csdc1);
normmat=diag(powerc1.^(-1/2));
csdc1=normmat*csdc1*normmat;
csdc2=dat(chansel,selc2)*dat(chansel,selc2)'/nreplc2;
powerc2=diag(csdc2);
normmat=diag(powerc2.^(-1/2));
csdc2=normmat*csdc2*normmat;
biasc1=1./(dfc1-2);
biasc2=1./(dfc2-2);
denomZ=sqrt(1./(dfc1-2) + 1./(dfc2-2));
tempstat=(atanh(abs(csdc1))-biasc1-atanh(abs(csdc2))+biasc2)./denomZ;
s.stat(((freqtimindx-1)*nchancmb + 1):(freqtimindx*nchancmb))=tempstat(chancmbsel);
end
%s.stat = reshape(s.stat, [nchancmb nfreqtim]);
end
if strcmp(cfg.computecritval,'yes')
% also compute the critical values
if cfg.tail==-1
s.critval = norminv(cfg.alpha);
elseif cfg.tail==0
s.critval = [norminv(cfg.alpha/2),norminv(1-cfg.alpha/2)];
elseif cfg.tail==1
s.critval = norminv(1-cfg.alpha);
end
end
if strcmp(cfg.computeprob,'yes')
% also compute the p-values
if cfg.tail==-1
s.prob = normcdf(s.stat);
elseif cfg.tail==0
s.prob = 2*normcdf(-abs(s.stat));
elseif cfg.tail==1
s.prob = 1-normcdf(s.stat);
end
%s.prob = reshape(s.prob, [nchancmb nfreqtim]);
end
% adjust the dimord
if strcmp(cfg.dimord(1:3), 'pos')
cfg.dimord = ['poscmb',cfg.dimord(4:end)];
elseif strcmp(cfg.dimord(1:4), 'chan')
cfg.dimord = ['chancmb',cfg.dimord(5:end)];
end
% append an indexing matrix to the cfg to be able to recover the channel combinations
chanindx = tril(true(nchan), -1);
cmbindx1 = repmat((1:nchan)', [1 nchan]);
cmbindx2 = repmat((1:nchan), [nchan 1]);
cfg.chancmbindx(:,1) = cmbindx1(chanindx);
cfg.chancmbindx(:,2) = cmbindx2(chanindx);