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Function Synopsis

O = lyngby_fir_test_chi2(Y, X, B, varargin)

Help text

 lyngby_fir_test_chi2 - Chi square test for FIR filter

       lyngby_fir_test_chi2(Y, X, B, 'PropertyName', 'PropertyValue')  
       Input:    Y   Data matrix 
                 X   Design matrix
                 B   Estimated filter

       Property: RegMatrix  Regularization matrix

       Output:   O   Lower tail P-values

       A mass-univariate chi squared test with a null hypothesis of
       B=0 for the FIR filter with the model: Y = X*B+U. The test is
       performed separately for each column in B, ie, for each voxel
       if Y is a (brain scans x voxels) data matrix.

       The noise variance in U is estimated with the maximum
       likelihood regarded as independent Gaussian distributed. When
       the number of samples (eg, scans) is small and the noise
       variance is estimated this chi2 test is biased, ie, is the
       test is a large sample test.  

       It is also possible to use this function to test a regularized
       model, such as the 'smooth FIR' by inputting the
       regulatization matrix with the 'RegMethod' property. This
       introduces an other bias causing a too high estimate of the
       variance. The two biases might cancel each other somewhat. 

       Ref: Goutte, Nielsen, Hansen (2000), IEEE
              Trans. Med. Imaging. 19(12):1188-1201, Equation 13. 

         XN = randn(70, 10000);     % eg, 70 scans and 10000 voxels
         PN = randn(70, 1);
         B = lyngby_fir_main(PN, XN);
         G = lyngby_fir_paradigm2design(PN, size(B,1));
         LT = lyngby_fir_test_chi2(XN, G, B);
         hist(LT, 100), title('Histogram of lower tail area')

       See also: LYNGBY, LYNGBY_FIR_MAIN,

 $Id: lyngby_fir_test_chi2.m,v 1.4 2003/02/21 14:26:01 fnielsen Exp $

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