CompareSlopes

CompareSlopes - Perform linear regression y = ax on two groups and compare slopes.

  USAGE

    % To compare two slopes:
    [p,t,df,slope1,slope2,sem1,sem2] = CompareSlopes(x1,y1,x2,y2)

    % To compare a slope to a theoretical value:
    [p,t,df,slope,sem] = CompareSlopes(x,y,s)

    x1,y1          data for group 1
    x2,y2          data for group 2
    s              expected (theoretical) slope

  OUTPUT

    p              test probability (e.g. p<0.05 => significant)
    t              t-test statistics
    df             degrees of freedom
    slope1,slope2  regression slopes

0001 function [p,t,df,slope1,slope2,sem1,sem2] = CompareSlopes(x1,y1,x2,y2)
0002 
0003 %CompareSlopes - Perform linear regression y = ax on two groups and compare slopes.
0004 %
0005 %  USAGE
0006 %
0007 %    % To compare two slopes:
0008 %    [p,t,df,slope1,slope2,sem1,sem2] = CompareSlopes(x1,y1,x2,y2)
0009 %
0010 %    % To compare a slope to a theoretical value:
0011 %    [p,t,df,slope,sem] = CompareSlopes(x,y,s)
0012 %
0013 %    x1,y1          data for group 1
0014 %    x2,y2          data for group 2
0015 %    s              expected (theoretical) slope
0016 %
0017 %  OUTPUT
0018 %
0019 %    p              test probability (e.g. p<0.05 => significant)
0020 %    t              t-test statistics
0021 %    df             degrees of freedom
0022 %    slope1,slope2  regression slopes
0023 
0024 % Copyright (C) 2011-2013 by Michaël Zugaro
0025 %
0026 % This program is free software; you can redistribute it and/or modify
0027 % it under the terms of the GNU General Public License as published by
0028 % the Free Software Foundation; either version 3 of the License, or
0029 % (at your option) any later version.
0030 
0031 if nargin < 3,
0032     error('Incorrect number of parameters (type ''help <a href="matlab:help CompareSlopes">CompareSlopes</a>'' for details).');
0033 end
0034 
0035 if nargin == 3,
0036     
0037     % One sample against theoretical value
0038     
0039     % Compute linear regression
0040     s1 = regstats(y1(:),x1(:),1,'tstat');
0041 
0042     % Get N, slope and SEM
0043     n1 = length(x1);
0044     slope1 = s1.tstat.beta;
0045     sem1 = s1.tstat.se;
0046 
0047     % T-test
0048     df = n1-2;
0049     s = x2;
0050     t = (slope1-s)/sqrt(n1*sem1^2);
0051     p = 2*tcdf(-abs(t),df); % (two-tailed test)
0052     
0053     % Return sem
0054     slope2 = sem1;
0055     
0056 else
0057 
0058     % Two samples
0059     
0060     % Compute linear regressions
0061     s1 = regstats(y1(:),x1(:),1,'tstat');
0062     s2 = regstats(y2(:),x2(:),1,'tstat');
0063 
0064     % Get N, slopes and SEM
0065     n1 = length(x1);
0066     n2 = length(x2);
0067     slope1 = s1.tstat.beta;
0068     slope2 = s2.tstat.beta;
0069     sem1 = s1.tstat.se;
0070     sem2 = s2.tstat.se;
0071 
0072     % T-test
0073     df = n1+n2-4;
0074     t = (slope1-slope2)/sqrt(n1*sem1^2+n2*sem2^2);
0075     p = 2*tcdf(-abs(t),df); % (two-tailed test)
0076     
0077 end
0078 
0079 
0080 
0081 
0082 
0083 %  x = [x1(:);x2(:)];
0084 %  y = [y1(:);y2(:)];
0085 %
0086 %  group = [zeros(length(x1),1);ones(length(x2),1)];
0087 %
0088 %  X = [group x x.*group];
0089 %
0090 %  s = regstats(y,X);
0091 %
0092 %  r =  [s.tstat.beta s.tstat.se s.tstat.t s.tstat.pval];
0093 
0094 
0095 
0096 
0097 %  [slope1,u1,u2,u3,stats1] = regress(y1(:),x1(:));
0098 %  [slope2,u1,u2,u3,stats2] = regress(y2(:),x2(:));
0099 %
0100 %  n1 = length(x1);
0101 %  sse1 = stats1(end)/n1;
0102 %  n2 = length(x2);
0103 %  sse2 = stats2(end)/n2;
0104 %
0105 %  t = (slope1-slope2)/sqrt(sse1+sse2);
0106 %  p = 2*tcdf(-abs(t),n1+n2-4);
0107 %
0108 %  r = [slope1 slope2 t p];
0109 
0110 
0111 
0112 %  x = [x1(:);x2(:)];
0113 %  y = [y1(:);y2(:)];
0114 %
0115 %  group = [zeros(length(x1),1);ones(length(x2),1)];
0116 %
0117 %  X = [group x x.*group];
0118 %
0119 %  [slope2,u1,u2,u3,stats2] = regress(y,X);
0120 %  slope2, stats2