Figure 1.
Demonstration of possible stimuli in different 2AFC protocols.
Each sub-figure represents a trial type. The blue bar represents the reference stimulus. The black bar represents the non-reference (comparison) stimulus. The left bar in each trial represents the stimulus in the first interval and the right bar represents the stimulus in the second interval. The ordinates denote the magnitude of the stimuli (frequency, in our experiments). A: a trial in which the reference stimulus is in the first interval, and the non-reference is higher; B: a trial in which the reference stimulus is in the second interval, and the non-reference is higher; C: a trial in which the reference stimulus is in the first interval, and the non-reference is lower; D: a trial in which the reference stimulus is in the second interval, and the non-reference is lower; In the Reference-Lower protocol only configurations A and B are used, while in the Reference protocol all 4 configurations are equally likely.
Figure 2.
Performance in trials in which the reference is first (Ref1) and trials in which the reference is second (Ref2) in Reference-Lower protocol (A), and Reference protocol (B).
Error bars represent the SEM across the participants. The insets above each bar represent the trial types that constitute that bar using the same notation as in Fig. 1. In Reference-Lower protocol performance is significantly better in Ref2 trials, while in Reference protocol it is better in Ref1 trials.
Figure 3.
Performance in trials in which first tone is higher than the second () and trials in which the second tone is higher than the first (
) in Reference-Lower protocol (A), and Reference protocol (B).
Error bars represent the SEM across the participants. The insets above each bar represent the trial types that constitute that bar using the same notation as in Fig. 1. In Reference-Lower protocol performance is significantly better in trials, while in Reference protocol it is better in
trials.
Figure 4.
A schematic explanation of the Contraction Bias and its effect on performance.
Using the same notation of Fig. 1. The horizontal dashed line representsM, the estimated value of the mean stimulus in the block. The vertical arrow presents the contraction of the first stimulus towards the mean value. The arrow is white when this contraction is beneficial to performance (A), since it increases the probability of a correct response. The arrow is red when this contraction impairs performance (B).
Figure 5.
A schematic explanation of the Interval Bias as resulting from the effect of history.
Using the same notation of Fig. 1. The horizontal dashed line represents M, the memory trace which estimates the value of the mean stimulus in the block. The value of this trace is not the global mean and is expected to vary between trials. The vertical arrow presents the contraction of the first stimulus towards the memory trace. The arrow is red when this contraction impairs performance, since it increases the probability of an incorrect response. The arrow is white when this contraction is beneficial to performance. A–D: exemplar trials from the Reference protocol; A: a Ref1, trial; B: a Ref1,
trial; C: a Ref2,
trial; D: a Ref2,
trial; E–H: exemplar trials from the Reference-Lower protocol; E: an easy Ref1 trial; F: a difficult Ref1 trial; G: an easy Ref2 trial; H: a difficult Ref2 trial. Overall, in the Reference-Lower protocol performance is expected to be higher in Ref2 trials, and in the Reference protocol performance is expected to be higher in Ref1 trials.
Figure 6.
Comparison of model simulations (white) to experimental data (blue).
A–B: Performance in trials in which the reference is first (Ref1) and trials in which the reference is second (Ref2) in Reference-Lower protocol (A) and Reference protocol (B). C–D: Performance in trials in which second tone is higher than the first () and trials in which the first tone is higher than the second (
) in Reference-Lower protocol (C), and Reference protocol (D). Note that panel C presents the same data as panel A, due to the equivalence of the Ref1 vs Ref2 and
vs.
divisions of the trials in the Reference-Lower protocol. Error bars represent the SEM across the participants. p-values are for paired t-tests, uncorrected for multiple comparisons.