Holighi, Khalil Shafie

Committee Member

Lalonde, Trent

Committee Member

Schaffer, Jay

Committee Member

Ku, Heng-Yu


Applied Statistics and Research Methods


University of Northern Colorado

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Greeley (Colo.)


University of Northern Colorado

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101 pages

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Born digital


The functional magnetic resonance imaging (fMRI) data are known to be complex valued. The real and imaginary components are assumed to be independently and normally distributed. After image reconstructions, these components are separated into two components, namely magnitude and phase. Usually, only the magnitude component is used in the analysis and it is assumed to be normally, or Gaussian, distributed. The statistical analysis of fMRI data using random field theory also assumed that the data are Gaussian distributed. However, the magnitude component is actually Rician distributed and no work has been found on the Rician random field. In this dissertation, Rician random field was defined, in general, and simulated in a two-dimensional image. A new test statistic to detect a signal from the functional magnetic resonance image, Rmax, which follows the Rician random field, was introduced. The power of Rmax was calculated using Monte Carlo simulation, and compared to the Gaussian test statistic, Zmax. The effects of factors known to influence the power of Rmax, namely amplitude, scale and location of the signal, were also studied. The amplitude was shown to be the most influencing factor on the power of Rmax, followed by the scale of the signal. The location of the signal did not seem to affect the power of the Rmax. However, the power of Rmax did not outperform the power of Zmax. Future studies are required to provide more information on the properties and behaviors of Rmax.

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