Test against random groups: when selecting this option GraphVar performs a non-parametric
permutation test with a user defined amount of repetitions. For permutation
testing, in each repetition, the network measures (or connectivity values in case of “The Raw Matrix (link wise) panel”
calculations) of each subject are randomly reassigned to one of the
groups so that each randomized group obtains the same number of subjects as the original groups.
Then, the differences in network measures between randomized groups are calculated
resulting in a permutation distribution of difference under the null hypothesis
(for ANOVA also the F value deriving from each repetition is computed). The actual
between-group difference in network measures (and for ANOVA also the F value) is then
placed in the corresponding permutation distribution and a p-value is calculated based on
its percentile position. For how to correct the result by applying the non-parametric p-values
please refer to the “Results” section under “Correction”.


It is also possible to perform group comparison analyses on the “raw” correlation/association
matrices (i.e., association-matrix based statistics, where no graph topological measures
are involved). For this feature you have to check this box and also check the “Raw Matrix (link wise)” option.


As described in the “The Raw Matrix (link wise) panel” introduction, it is necessary to
determine whether a Graph-Component with a certain size as a result of the
correlational analysis is non-random. Thus, amount and size of Graph-Components
resulting from “random data” are needed to be compared against the true Graph-Components.
For group comparisons on the raw matrix GraphVar produces these
“random data” by performing non-parametric permutation tests with the subjects
underlying connectivity values for the respective groups. Thus, to produce this random data you need to select the “Test against random groups”
option in the group comparison panel and enter the amount of repetitions. When selecting
this option GraphVar simultaneously performs parametric testing of the group
difference on each link, which gives you the option to choose between parametric
and non-parametric p-values for determining for inspection of single links. However,
significant links in the Graph-Components are determined by the parametric p-values
as it would be circular to create p-values from random data and then use the same
random data again for Graph-Components (please refer to the “Network Inspector”
section for determining the significance value of links considered for Graph-Components
and for more info about p-values for true Graph-Components).