Figure 1.
Results of the multiple-thresholds-approach of the example with the real data.
Mean values for the small-world parameters clustering coefficient, path length, and number of edges. We thresholded the correlation matrix 10, 15, and 35 times; this resulted in different statistical results. For the version with 10 increments, t-tests revealed no statistical differences. For the version with 15 increments, the clustering coefficient and number of edges was significantly increased in the high IQ group compared to the low IQ group. In the version with 35 different thresholds, the comparison between the high and low IQ groups revealed significant effects for all small-world parameters. The high IQ group showed a significantly enhanced small-world topology. For an optimized display, the numbers of edges were scaled (number of edges divided by 1000).
Figure 2.
Procedure of the multiple-thresholds-approach with artificial data.
Networks of two groups based on artificial data. The networks were thresholded over a set of thresholds.
Figure 3.
Results of the multiple-thresholds-approach of the example with the artificial data.
Displayed are the results of the second example, which used artificial data. The comparison of the two networks, based on artificial data, revealed several significant differences. Depending on the number of thresholds (defining the different measurement units within each group) and the threshold range used for the comparison, completely distinct results could be obtained. For an optimized display, the numbers of edges were scaled (number of edges divided by 1000).
Figure 4.
Results of the group-level-permutation-statistics-approach of the example with the real data.
Displayed are the distributions of the randomly generated group pair differences. The red arrow indicates where the differences of the real data ( = empirical difference between high and low IQ groups) are located within the distribution. The results show that the high IQ group revealed increased small-world network parameters.
Figure 5.
Results of the group-level-permutation-statistics-approach of the example with the artificial data.
Displayed are the distributions of the randomly generated group pair differences. The red arrow indicates where the differences of the original data are located within the distribution. The results show, that there are no significant differences regarding the clustering coefficient or the characteristic path length.