Figure 5.

Intrinsic correlation between variables. The 30 variables defined in Table 1 were often correlated with each other. To estimate the typical correlation between any two variables X and Y, we computed for each session the correlation coefficient $\underset{\text{session}}{{\displaystyle \rho }}\left(\text{X},\text{Y}\right)=\overrightarrow{x}·\overrightarrow{y}/\sqrt{{\overrightarrow{x}}^2·{\overrightarrow{y}}^2}$, where x⃗ and y⃗ are vectors of values taken by variables X and Y for different trial types. The correlation coefficient varied between −1 and +1. Most informative for our purposes was the absolute value, which we computed and average across sessions: $\rho \left(\text{X},\text{Y}\right)={\langle \left|\underset{\text{session}}{{\displaystyle \rho }}\left(\text{X},\text{Y}\right)\right|\rangle }_{\text{sessions}}$. Repeating for all pairs of variables, we obtained a symmetric matrix ρ of elements ρ(X, Y) that varied between 0 and 1. The figure depicts in gray scale the correlation coefficient between each pair of variables. Pairs for which the correlation was >0.8 are indicated with an X. The scale is indicated on the bottom right.