Biomedical Engineering Reference
In-Depth Information
level gets lower than necessary to protect against rejections of null hypothesis due to
fluctuations.
In special, but very common cases of comparison of a set of mean values it is
suggested to consider Tukey's HSD (honestly significant difference) test. Tukey's
method considers the pairwise differences. Scheffe's method applies to the set of
estimates of all possible contrasts among the factor level means. An arbitrary contrast
is a linear combination of two or more means of factor levels whose coefficients add
up to zero. If only pairwise comparisons are to be made, the Tukey method will
result in a narrower confidence limit, which is preferable. In the general case when
many or all contrasts might be of interest, the Scheffe method tends to give narrower
confidence limits and is therefore the preferred method [Armitage et al., 2002].
1.5.3.2
Parametric and nonparametric statistical maps
The multiple comparison problem is critical for comparison of images or vol-
ume data collected under different experimental conditions. Usually such images or
volumes consist of a huge number of elements: pixels, voxels, or resels (resolution
elements). For each element statistical models (parametric or non-parametric) are
assumed. Hypotheses expressed in terms of the model parameters are assessed with
univariate statistics.
In case of the parametric approach (statistical parametric mapping) the general lin-
ear models are applied to describe the variability in the data in terms of experimental
and confounding effects, and residual variability. In order to control the FWER ad-
justments are made, based on the number of resels in the image and the theory of
continuous random fields in order to set a new criterion for statistical significance
that adjusts for the problem of multiple comparisons [Friston et al., 2007]. This
methodology, with application to neuroimaging and MEG/EEG data, is implemented
in SPM—a MATLAB software package, written by members and collaborators of
the Wellcome Trust Centre for Neuroimaging. SPM is free but copyright software,
distributed under the terms of the GNU General Public Licence. SPM homepage:
http://www.fil.ion.ucl.ac.uk/spm/ .
In case of the non-parametric approach (statistical non-parametric mapping,
SnPM) the idea is simple: if the different experimental conditions do not make any
different effect on the measured quantity, then the label assignment to the condi-
tions is arbitrary. Any reallocation of the labels to the data would lead to an equally
plausible statistic image. So, considering the statistic images associated with all pos-
sible re-labelings of the data, we can derive the distribution of statistic images pos-
sible for this data. Then we can test the null hypothesis of no experimental effect
by comparing the statistic for the actual labeling of the experiment with this re-
labeled distribution. If, out of N possible relabelings the actual labeling gives the
r th most extreme statistic, then the probability of observing that value under the
null hypothesis is r
N . The details are worked out in [Holmes et al., 1996, and
Nichols and Holmes, 2002]. SnPM is implemented as a free MATLAB toolbox:
http://www.sph.umich.edu/ni-stat/SnPM/#dox .
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