a=cronbach(X)

function a=cronbach(X)
%Syntax: a=cronbach(X)
%_____________________
%
% Calculates the Cronbach's alpha of a data set X.
%
% a is the Cronbach's alpha.
% X is the data set.
%
%
% Reference:
% Cronbach L J (1951): Coefficient alpha and the internal structure of
% tests. Psychometrika 16:297-333
%
%
% Alexandros Leontitsis
% Department of Education
% University of Ioannina
% Ioannina
% Greece
%
% e-mail: [e-mail]
% Homepage: http://www.geocities.com/CapeCanaveral/Lab/1421
%
% June 10, 2005.


if nargin<1 | isempty(X)==1
   error('You shoud provide a data set.');
else
   % X must be a 2 dimensional matrix
   if ndims(X)~=2
      error('Invalid data set.');
   end
end


% Calculate the number of items
k=size(X,2);

% Calculate the variance of the items' sum
VarTotal=var(sum(X'));

% Calculate the item variance
SumVarX=sum(var(X));

% Calculate the Cronbach's alpha
a=k/(k-1)*(VarTotal-SumVarX)/VarTotal;