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# lyngby_fir_test_chi2

## (export/lyngby/lyngby_fir_test_chi2.m)

### 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.
Example:
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,
LYNGBY_FIR_PARADIGM2DESIGN, LYNGBY_FIR_REGMATRIX.
$Id: lyngby_fir_test_chi2.m,v 1.4 2003/02/21 14:26:01 fnielsen Exp $

### Cross-Reference Information

This function calls

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