Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / repanova.m

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+## Copyright (C) 2011 Kyle Winfree <kyle.winfree@gmail.com>
+##
+## This program 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.
+##
+## This program 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
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{pval}, @var{table}, @var{st}] =} repanova (@var{X}, @var{cond})
+## @deftypefnx {Function File} {[@var{pval}, @var{table}, @var{st}] =} repanova (@var{X}, @var{cond}, ['string' | 'cell'])
+## Perform a repeated measures analysis of variance (Repeated ANOVA).
+## X is formated such that each row is a subject and each column is a condition.
+##
+## condition is typically a point in time, say t=1 then t=2, etc
+## condition can also be thought of as groups.
+##
+## The optional flag can be either 'cell' or 'string' and reflects
+## the format of the table returned.  Cell is the default.
+##
+## NaNs are ignored using nanmean and nanstd.
+## 
+## This fuction does not currently support multiple columns of the same
+## condition!
+## @end deftypefn
+
+function [p, table, st] = repanova(varargin)
+
+switch nargin
+     case 0
+         error('Too few inputs.');
+     case 1
+               X = varargin{1};
+               for c = 1:size(X, 2)
+                       condition{c} = ['time', num2str(c)];
+               end
+               option = 'cell';
+     case 2
+         X = varargin{1};
+         condition = varargin{2};
+         option = 'cell';
+     case 3
+         X = varargin{1};
+         condition = varargin{2};
+         option = varargin{3};
+     otherwise
+         error('Too many inputs.');
+end
+     % Find the means of the subjects and measures, ignoring any NaNs
+     u_subjects = nanmean(X,2);
+     u_measures = nanmean(X,1);
+     u_grand = nansum(nansum(X)) / (size(X,1) * size(X,2));
+     % Differences between rows will be reflected in SS subjects, differences
+     % between columns will be reflected in SS_within subjects.
+     N = size(X,1); % number of subjects
+     J = size(X,2); % number of samples per subject
+     SS_measures = N * nansum((u_measures - u_grand).^2);
+     SS_subjects = J * nansum((u_subjects - u_grand).^2);
+     SS_total = nansum(nansum((X - u_grand).^2));
+     SS_error = SS_total - SS_measures - SS_subjects;
+     df_measures = J - 1;
+     df_subjects = N - 1;
+     df_grand = (N*J) - 1;
+     df_error = df_grand - df_measures - df_subjects;
+     MS_measures = SS_measures / df_measures;
+     MS_subjects = SS_subjects / df_subjects;
+     MS_error = SS_error / df_error; % variation expected as a result of sampling error alone
+     F = MS_measures / MS_error;
+     p = 1 - fcdf(F, df_measures, df_error); % Probability of F given equal means.
+
+     if strcmp(option, 'string')
+         table  = [sprintf('\nSource\tSS\tdf\tMS\tF\tProb > F'), ...
+                   sprintf('\nSubject\t%g\t%i\t%g', SS_subjects, df_subjects, MS_subjects), ...
+                   sprintf('\nMeasure\t%g\t%i\t%g\t%g\t%g', SS_measures, df_measures, MS_measures, F, p), ...
+                   sprintf('\nError\t%g\t%i\t%g', SS_error, df_error, MS_error), ...
+                   sprintf('\n')];
+     else
+         table  = {'Source', 'Partial SS', 'df', 'MS', 'F', 'Prob > F'; ...
+                   'Subject', SS_subjects, df_subjects, MS_subjects, '', ''; ...
+                   'Measure', SS_measures, df_measures, MS_measures, F, p};
+     end
+
+     st.gnames = condition'; % this is the same struct format used in anova1
+     st.n = repmat(N, 1, J);
+     st.source = 'anova1'; % it cannot be assumed that 'repanova' is a supported source for multcompare
+     st.means = u_measures;
+     st.df = df_error;
+     st.s = sqrt(MS_error);
+end
+
+% This function was created with guidance from the following websites:
+% http://courses.washington.edu/stat217/rmANOVA.html
+% http://grants.hhp.coe.uh.edu/doconnor/PEP6305/Topic%20010%20Repeated%20Measures.htm