Accounting for the potential false absences in the dataset allows the possibility that the presences of hybrids and P. eos were either positively or negatively correlated (maximum negative correlation: odds ratio = 0, p<0.001; maximum positive correlation: odds ratio = infinite, p<0.001).
Shubina and Lee (2004) showed that the maximum positive correlation of (5) is effected by concentrating all its mass on the (NE-SW) quadrants: {(x,y):(x - x0)(y - y0) ≥ 0}, and for the negative, on the (NW-SE) quadrants: {(x,y):(x - x0)(y - y0) ≤ 0}, for some real numbers x0 and y0.
The correlation plots reveal a wide range of correlation coefficients among all of the measured metabolites, ranging from 1.0 (maximum positive correlation) to −1.0 (maximum anticorrelation) and 0 indicating no correlation.
There was also no significant correlation between the presences of hybrids and P. neogaeus, regardless of how the false absences are accounted for (maximum negative correlation: odds ratio = 0.63, p = 0.3104; maximum positive correlation: odds ratio = 2.01, p = 0.0999).
There was a negative correlation between the presences of P. eos and P. neogaeus (odds ratio = 0.20, p = 0.0238), and accounting for false absences allows only the possibility of a negative correlation (maximum negative correlation: odds ratio = 0, p<0.001; maximum positive correlation: odds ratio = infinite, p = 0.5728).
For the value of bicor from −1 to 1, −1 represents the maximum negative correlation and 1 represents the maximum positive correlation.
Note −1 ≤ r ≤ 1, thus, r = 0 corresponds to no interaction, r = −1 is the maximum negative correlation, and r = 1 is the maximum positive correlation.
The maximum positive correlation (0.84) was observed between grain volume and horizontal deviation from ellipse (HDFE), followed by r = 0.81 between horizontal area and composite 1 (Comp1).
The second LV showed a task main effect (singular value = 152.44, P < 0.016, task demands LV, Fig. 6, see Table 2 for a list of local maxima), with positive correlations for temporal sequencing tasks and negative for comparison tasks.
It is thus flexible enough to accommodate nearly the maximum positive (negative) correlation.
