Table 1 Summary of the estimated coefficients (with 95% HDIs) of the polynomial for the choice and no-choice conditions, along with the estimated difference (95% HDI) between conditions for Experiment 1. Coefficients are standardized to make the scales comparable—raw coefficients can be obtained by dividing \(b_n\) by the standard deviation of the time points for the corresponding term, \(SD(t^ {\circ n})\) with \(t = [3,6,9,12,18,30,45]\) (where \(t^{\circ n}\) is element-wise power function, raising the values in t to the nth power) . Differences between choice and no-choice conditions that exclude zero are highlighted in bold.
Polynomial coefficient | No choice | Choice | Difference |
|---|---|---|---|
Intercept (\(b_0\)) | 17.06 [14.82, 19.04] | 16.59 [14.72, 18.21] | 0.47 [0.06, 0.83] |
Slope (\(b_1\)) | 9.33 [0.90, 18.05] | 9.33 [2.71, 16.10] | \(-0.00\) [\(-1.95\), 1.96] |
Quadratic (\(b_2\)) | \(-39.90\) [\(-67.24\), \(-0.74\)] | \(-31.84\) [\(-51.86\), \(-7.39\)] | \(-7.98\) [\(-15.88\), 2.22] |
Cubic (\(b_3\)) | 36.97 [10.08, 61.51] | 23.53 [5.04, 40.67] | 13.34 [4.81, 21.41] |
Quartic (\(b_4\)) | 30.23 [3.64, 51.65] | 27.80 [4.25, 46.80] | 2.58 [\(-0.61\), 4.86] |
Quintic (\(b_5\)) | \(-36.73\) [\(-58.84, -8.51\)] | \(-28.90\) [\(-47.44, -5.77\)] | \({\mathbf {-7.82}} {\mathbf {[-11.74, -2.54]}}\) |
