data_outliers3.m

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        % location parameter of the columns of a matrix
        % X. If X is a vector, it returns the LMS
        % location parameter of its components. If X
        % is a scalar, it returns X."
        [gm]=LMSloc(rtb);   

        % calculate standard deviation
        stdrt=std(rtb);  

        if length(rtb) > 3 && isequal(sod, 0)
            pts=intersect( find(rtb > gm - num_std*stdrt), find(rtb < gm + num_std*stdrt)); % find all values within num_std std of geometric mean
            npts=setdiff( 1:num_cols, pts); % find the indices of the outliers
        else
            pts=1:num_cols;
            npts=[];
        end
        
        if isempty(pts)
            pts=1:num_cols;
            npts=[];
        end

        % Determine the maximum number of outliers in any rta data row
        max_num_out=max([max_num_out, length(npts)]);
        
        % indices of set of non-outliers (i.e. values kept)
        ptsa{e1, 1}=pts;   
        
        % indices of set of outliers (i.e. values discarded from 
        % descriptive statistics)
        nptsa{e1, 1}=npts; 

        % select the set of non-outliers data for calculating descriptive statistics
        if isequal(abs_rta, 1)
            rts=abs(rt(pts));
        else
            rts=rt(pts);
        end

        % Calculate the arithmetic mean.
        [mn_rt1]=mean(rts);

        % Calculate the robust estimate of the mean
        [mn_rt2]=LMSloc(rts);

        % calculate standard deviation
        stdrt=std(rts);

        % calculate 95% confidence interval of
        % the standard error of the
        % t-distribution with a two-sided test
        [ci_int]=t_confidence_interval(rts, 0.95);

        % Calculate the median
        medianrt=median(rts);

        % Calculate the median index
        % (data point closest ot the median value)
        [mbuf ix]=min(abs(rts-medianrt));

        % Calculate the minimum
        minrt=min(rts);

        % Calculate the maximum
        maxrt=max(rts);


        mn_rt1a(e1,1)=      m_round(mn_rt1,   round_kind(1), round_digits(1));
        mn_rt2a(e1,1)=      m_round(mn_rt2,   round_kind(1), round_digits(1));
        stdrta(e1,1)=       m_round(stdrt,    1, 3);
        ci_inta(e1,1)=      m_round(ci_int,   1, 3);
        median_indexa(e1,1)=m_round(ix,       0, 0);
        median_val(e1,1)=   m_round(medianrt, round_kind(1), round_digits(1));
        min_rta(e1,1)=      m_round(minrt,    round_kind(1), round_digits(1));
        max_rta(e1,1)=      m_round(maxrt,    round_kind(1), round_digits(1));

        if ~isequal(sod, 1) && ~isempty(npts)
            % select the set of outliers data for calculating descriptive statistics
            if isequal(abs_rta, 1)
                rts=abs(rt(npts));
            else
                rts=rt(npts);
            end

            % Calculate the arithmetic mean.
            [mn_rt1]=mean(rts);

            % Calculate the robust estimate of the mean
            [mn_rt2]=LMSloc(rts);

            % calculate standard deviation
            stdrt=std(rts);

            % calculate 95% confidence interval of
            % the standard error of the
            % t-distribution with a two-sided test
            [ci_int]=t_confidence_interval(rts, 0.95);

            % Calculate the median
            medianrt=median(rts);

            % Calculate the median index
            % (data point closest ot the median value)
            [mbuf ix]=min(abs(rts-medianrt));
            
            % Convert to Median Index of the original data array
            ix=npts(ix);
            
            % Calculate the minimum
            minrt=min(rts);

            % Calculate the maximum
            maxrt=max(rts);

            out_mn_rt1a(e1,1)=      m_round(mn_rt1,   round_kind(1), round_digits(1));
            out_mn_rt2a(e1,1)=      m_round(mn_rt2,   round_kind(1), round_digits(1));
            out_stdrta(e1,1)=       m_round(stdrt,    1, 3);
            out_ci_inta(e1,1)=      m_round(ci_int,   1, 3);
            out_median_indexa(e1,1)=m_round(ix,       0, 0);
            out_median_val(e1,1)=   m_round(medianrt, round_kind(1), round_digits(1));
            out_min_rta(e1,1)=      m_round(minrt,    round_kind(1), round_digits(1));
            out_max_rta(e1,1)=      m_round(maxrt,    round_kind(1), round_digits(1));

        else

            out_mn_rt1a(e1,1)=0;
            out_mn_rt2a(e1,1)=0;
            out_stdrta(e1,1)=0;
            out_ci_inta(e1,1)=0;
            out_median_indexa(e1,1)=0;
            out_median_val(e1,1)=0;
            out_min_rta(e1,1)=0;
            out_max_rta(e1,1)=0;

        end

    else
        % if the data array is empty
        ptsa{e1,1}=[];
        nptsa{e1,1}=[];

        mn_rt1a(e1,1)=0;
        mn_rt2a(e1,1)=0;
        stdrta(e1,1)=0;
        ci_inta(e1,1)=0;
        median_indexa(e1,1)=0;
        median_val(e1,1)=0;
        min_rta(e1,1)=0;
        max_rta(e1,1)=0;


        out_mn_rt1a(e1,1)=0;
        out_mn_rt2a(e1,1)=0;
        out_stdrta(e1,1)=0;
        out_ci_inta(e1,1)=0;
        out_median_indexa(e1,1)=0;
        out_median_val(e1,1)=0;
        out_min_rta(e1,1)=0;
        out_max_rta(e1,1)=0;

    end
end

% Save data to the output variable rt_stats
rt_stats=[mn_rt1a, mn_rt2a, stdrta, ci_inta, median_indexa, median_val, min_rta, max_rta];

% Calculate the number of descriptive statistics
num_stats=size(rt_stats, 2);

% % Save data to the output variable rt_outlier_stat
rt_outlier_stats=[out_mn_rt1a, out_mn_rt2a, out_stdrta, out_ci_inta, out_median_indexa, out_median_val, out_min_rta, out_max_rta];

% % Initialize the output variables other_stats and other_outlier_stats
other_stats=zeros(num_vars, num_data_rows, num_stats);
other_outlier_stats=zeros(num_vars, num_data_rows, num_stats);

for e2=1:num_vars;

    rta=varargin{e2};

    [num_data_rows, buf]=size(rta);

    for e1=1:num_data_rows;

        if iscell(rta);
            buf1=rta{e1, :};
            if iscell(buf1);
                rt=buf1{1};
            else
                rt=buf1;
            end
        else
            rt=rta(e1, :);
        end

        num_cols=length(rt);

        if num_cols > 0

            if ~isequal(dep_var, 1)
                % Calculate the robust estimate of the mean.
                %
                % Statistical language for this type of mean is
                % "calculates the Least Median of Squares (LMS)
                % location parameter of the columns of a matrix
                % X. If X is a vector, it returns the LMS
                % location parameter of its components. If X
                % is a scalar, it returns X."
                [gm]=LMSloc(rt);

                % calculate standard deviation
                stdrt=std(rt);

                if length(rt) > 3 && isequal(sod, 0)
                    pts=intersect( find(rt > gm - num_std*stdrt), find(rt < gm + num_std*stdrt)); % find all values within num_std std of geometric mean
                    npts=setdiff( 1:num_cols, pts); % find the indices of the outliers
                else
                    pts=1:num_cols;
                    npts=[];
                end

                if isempty(pts)
                    pts=1:num_cols;
                    npts=[];
                end
                
                % Determine the maximum number of outliers in any rta data row
                max_num_out=max([max_num_out, length(npts)]);

                % indices of set of non-outliers (i.e. values kept)
                ptsa{e1, e2+1}=pts;

                % indices of set of outliers (i.e. values discarded from
                % descriptive statistics)
                nptsa{e1, e2+1}=npts;
            else

                
                [mp1 np1]=size(ptsa);

                if mp1 < e1
                    pts=ptsa{1, 1};
                    ptsa{e1, e2+1}=ptsa{1, 1};
                else
                    pts=ptsa{e1, 1};
                    ptsa{e1, e2+1}=ptsa{e1, 1};
                end

            end
            
            % select the set of non-outliers data for calculating descriptive statistics
            if isequal( abs_other(e2), 1)
                rts=abs(rt(pts));
            else
                rts=rt(pts);
            end

            % Calculate the arithmetic mean.
            [mn_rt1]=mean(rts);

            if isempty(rts)
                e2
            end
            % Calculate the robust estimate of the mean
            if ~isempty(rts)
                [mn_rt2]=LMSloc(rts);
            else
                mn_rt2=[];
            end
            
            % calculate standard deviation
            stdrt=std(rts);

            % calculate 95% confidence interval of
            % the standard error of the
            % t-distribution with a two-sided test
            [ci_int]=t_confidence_interval(rts, 0.95);

            % Calculate the median
            medianrt=median(rts);

            % Calculate the median index
            % (data point closest ot the median value)
            [mbuf ix]=min(abs(rts-medianrt));

            % Calculate the minimum
            minrt=min(rts);

            % Calculate the maximum
            maxrt=max(rts);


            other_stats(e2, e1, 1)=m_round(mn_rt1,   round_kind(e2+1), round_digits(e2+1));
            other_stats(e2, e1, 2)=m_round(mn_rt2,   round_kind(e2+1), round_digits(e2+1));
            other_stats(e2, e1, 3)=m_round(stdrt,    1, 3);
            other_stats(e2, e1, 4)=m_round(ci_int,   1, 3);
            other_stats(e2, e1, 5)=m_round(ix,       0, 0);
            other_stats(e2, e1, 6)=m_round(medianrt, round_kind(e2+1), round_digits(e2+1));
            other_stats(e2, e1, 7)=m_round(minrt,    round_kind(e2+1), round_digits(e2+1));
            other_stats(e2, e1, 8)=m_round(maxrt,    round_kind(e2+1), round_digits(e2+1));


            if ~isequal(sod, 1) && ~isempty(npts)

                if isequal(dep_var, 1)

                    [mp1 np1]=size(nptsa);

                    if mp1 < e1
                        npts=nptsa{1, 1};
                        nptsa{e1, e2+1}=nptsa{1, 1};
                    else
                        npts=nptsa{e1, 1};
                        nptsa{e1, e2+1}=nptsa{e1, 1};
                    end

                end

                % select the set of outliers data for calculating descriptive statistics
                if isequal( abs_other(e2), 1)
                    rts=abs(rt(npts));
                else
                    rts=rt(npts);
                end

                % Calculate the arithmetic mean.
                [mn_rt1]=mean(rts);

                % Calculate the robust estimate of the mean
                [mn_rt2]=LMSloc(rts);

                % calculate standard deviation
                stdrt=std(rts);

                % calculate 95% confidence interval of
                % the standard error of the
                % t-distribution with a two-sided test
                [ci_int]=t_confidence_interval(rts, 0.95);

                % Calculate the median
                medianrt=median(rts);

                % Calculate the median index
                % (data point closest ot the median value)
                [mbuf ix]=min(abs(rts-medianrt));
                
                % Convert to Median Index of the original data array
                ix=npts(ix);
            
                % Calculate the minimum
                minrt=min(rts);

                % Calculate the maximum
                maxrt=max(rts);

                other_outlier_stats(e2, e1, 1)=m_round(mn_rt1,   round_kind(e2+1), round_digits(e2+1));
                other_outlier_stats(e2, e1, 2)=m_round(mn_rt2,   round_kind(e2+1), round_digits(e2+1));
                other_outlier_stats(e2, e1, 3)=m_round(stdrt,    1, 3);
                other_outlier_stats(e2, e1, 4)=m_round(ci_int,   1, 3);
                other_outlier_stats(e2, e1, 5)=m_round(ix,       0, 0);
                other_outlier_stats(e2, e1, 6)=m_round(medianrt, round_kind(e2+1), round_digits(e2+1));
                other_outlier_stats(e2, e1, 7)=m_round(minrt,    round_kind(e2+1), round_digits(e2+1));
                other_outlier_stats(e2, e1, 8)=m_round(maxrt,    round_kind(e2+1), round_digits(e2+1));

            else

                other_outlier_stats(e2, e1, 1:8)=0;

            end

        else

            % if the data is empty
            other_stats(e2, e1, 1:8)=[];

            other_outlier_stats(e2, e1, 1:8)=[];

        end
    end

end

% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Write the descriptive statistics to the tab delimited outfile
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%