Figure 5. Dimensionality of magnitude representation.

(A) Average normalized amplitudes associated with numbers 1–6, independent of task framing (report highest/lowest) or category (blue/orange) at highlighted centro-parietal electrodes. Grey shaded area shows time of greatest disparity between signals (Kruskal-Wallis, P_FDR <0.01). Scalp map inset shows response amplitude for number six during identified time window. Colored shading represents SEM. The ascending direction of the univariate responses was independent of task framing (Figure 5—figure supplement 1) (B) Equivalent analysis for bandits b1 (lowest value) to b6 (highest value) in the bandit task. Scalp map shows response amplitude for highest subjectively valued bandit b6. (C) Dimensionality of the data was iteratively reduced using SVD and the strength of cross-validation under each new dimensionality was assessed by comparing the mean cross-validation in the 350–600 ms time window (bottom plot). Each cell in the grid contains the t- and p-value of a pairwise comparison of mean CV under different dimensionalities of the data. Reduction to one (and to a lesser degree two) dimension(s) significantly reduced the size of the effect. (D) Multidimensional scaling (MDS) revealed two principal axes that describe the data: a magnitude axis approximately following the number/bandit order and a certainty axis distinguishing inlying (e.g. 3,4) from outlying (e.g. 1,6) numbers or bandits.

Figure 5—figure supplement 1. Univariate centro-parietal signals separated by task and task framing.

Grey-shaded areas show time of greatest disparity between signals (Kruskal-Wallis, P_FDR <0.01). (A-B) Centro-parietal responses for numbers followed an ascending pattern from low to high numbers, independent of whether the task instructions asked to indicate the color with the lowest or highest average. Scalp maps show response amplitude for number six at the identified time window. (C-D) Centro-parietal responses for bandits followed the same ascending pattern, going from subjectively lowest valued bandit to the highest valued bandit. The bandit task was identical for both framing groups. Scalp maps show response amplitude for the highest valued bandit b6 at the identified time window.

Figure 5—figure supplement 2. We tested whether the univariate CPP amplitude modulations could explain our multivariate findings.

The magnitude model was compared to a model RDM constructed from univariate CPP amplitude differences in a multiple regression. (A-B) CPP amplitudes were obtained by averaging the univariate centro-parietal response to each stimulus (digit or bandit) within the individually identified time windows from Figure 5A–B. CPP RDMs (inset) were constructed based on the differences between average amplitudes. Error bars represent SEM. (C) Average Euclidean distances of CPP amplitudes from both tasks combined (numerical: 1–6, bandit: b1-b6). The lower left quadrant, containing the between-task distances in CPP amplitudes, served as the CPP model RDM for the cross-validation analysis. (D-F) For each control analysis, the magnitude model significantly explained variance in the multivariate neural patterns even after entering the univariate CPP as a second regressor in a multiple regression (within-task comparison: P_cluster <0.005, bottom colored lines; cross-validation: P_cluster <0.05). Shaded colored area represents SEM.

Figure 5—figure supplement 3. Cross-validation after excluding the first principal dimension.

A more stringent test to control for univariate effects is to exclude the first dimension identified by SVD. Cross-temporal cross-validation on the reduced data revealed a smaller but significant cluster at the same time points as our main result and a previously unobserved later cluster (P_cluster <0.05). Consistent with our previous analyses (Figure 5A–C), this suggests there is a major univariate component to our multivariate findings, but the shared pattern also exists in higher dimensions of the data.