基于Matlab实现Cochran检验 上传.zip

function [Cochtest]=Cochtest(X,alpha) %Cochran's test for homogeneity of variances for equal or unequal sample sizes. %[It calls to the Cochran's cunulative distribution function cochcdf(C,k,v).] % The use of the function. Let C is a set of k Chi-squared % distributed sums of squares (or the corresponding variances), % each of v degrees of freedom. To accept at a significance % level (alpha) that the maximum variance differ from the other ones, % one should examine: % P <= alpha % where, P=1-cochpdf(C,k,v) and C=max(s2)/sum(s2). % % % Syntax: function [Cochtest]=Cochtest(X,alpha) % % Inputs: % X - data matrix (Size of matrix must be n-by-2; data=column 1, sample=column 2). % alpha - significance level (default = 0.05). % Outputs: % - Sample variances vector. % - Whether or not the homoscedasticity was met. % % Example: From the example 10.13 of Zar (1999, p. 202-203), to test the Cochran's % homoscedasticity of data with a significance level = 0.05. % % Diet % --------------------------------- % 1 2 3 4 % --------------------------------- % 60.8 68.7 102.6 87.9 % 57.0 67.7 102.1 84.2 % 65.0 74.0 100.2 83.1 % 58.6 66.3 96.5 85.7 % 61.7 69.8 90.3 % --------------------------------- % % Data matrix must be: % X=[60.8 1;57.0 1;65.0 1;58.6 1;61.7 1;68.7 2;67.7 2;74.0 2;66.3 2;69.8 2; % 102.6 3;102.1 3;100.2 3;96.5 3;87.9 4;84.2 4;83.1 4;85.7 4;90.3 4]; % % Calling on Matlab the function: % Cochtest(X) % % Answer is: % % The number of samples are: 4 % % Sample Size Variance % 1 5 9.3920 % 2 5 8.5650 % 3 4 7.6567 % 4 5 8.3880 % % Cochran's Test for Equality of Variances C = 0.2762 % Probability associated to the Cochran's statistic = 0.4719 % The associated probability for the Cochran' test is equal or larger than 0.05 % So, the assumption of homoscedasticity was met. % % Created by A. Trujillo-Ortiz and R. Hernandez-Walls % Facultad de Ciencias Marinas % Universidad Autonoma de Baja California % Apdo. Postal 453 % Ensenada, Baja California % Mexico. % atrujo@uabc.mx % % April 21, 2003. % % To cite this file, this would be an appropriate format: % Trujillo-Ortiz, A. and R. Hernandez-Walls. (2003). Cochtest: Cochran's test for % homogeneity of variances for equal or unequal sample sizes. A MATLAB file. % [WWW document]. URL http://www.mathworks.com/matlabcentral/fileexchange/ % loadFile.do?objectId=3292&objectType=FILE % % References: % % Zar, J. H. (1999), Biostatistical Analysis (2nd ed.). % NJ: Prentice-Hall, Englewood Cliffs. p. 202-203. % if nargin < 2, alpha = 0.05; end k=max(X(:,2)); fprintf('The number of samples are:%2i\n\n', k); n=[];n2=[];s2=[]; indice=X(:,2); for i=1:k Xe=find(indice==i); eval(['X' num2str(i) '=X(Xe,1);']); eval(['n' num2str(i) '=length(X' num2str(i) ') ;']); eval(['n2' num2str(i) '=(length(X' num2str(i) ').^2);']); eval(['s2' num2str(i) '=(std(X' num2str(i) ').^2) ;']); eval(['xn= n' num2str(i) ';']); eval(['xn2= n2' num2str(i) ';']); eval(['xs2= s2' num2str(i) ';']); n=[n;xn];n2=[n2;xn2];s2=[s2;xs2]; end disp(' Sample Size Variance') for i=1:k fprintf(' %d %2i %.4f\n',i,n(i),s2(i)) end disp(' ') %Cochran's test procedure. C=max(s2)/sum(s2); %Cochran's C statistic. v=k-1; no=(1/v)*(sum(n)-(sum(n2)/sum(n))); %procedure for equal or unequal sample sizes. v=round(no)-1; %sample degrees of freedom. P=1-cochcdf(C,k,v); %probability associated to the Cochran's C statistic. fprintf('Cochran''s Test for Equality of Variances C = %3.4f\n', C); fprintf('Probability associated to the Cochran''s statistic = %3.4f\n', P); if P >= alpha; fprintf('The associated probability for the Cochran'' test is equal or larger than% 3.2f\n', alpha); fprintf('So, the assumption of homoscedasticity was met.\n'); else fprintf('The associated probability for the Cochran''s test is smaller than% 3.2f\n', alpha); fprintf('So, the assumption of homoscedasticity was not met.\n'); end