Fig 1.
Schematic depiction of task designs.
(A, B) In a comparison task participants had to judge whether the second stimulus was longer or shorter (time dimension) or consisted of fewer or more dots (number dimension) than the first stimulus. Participants were cued before blocks of eight trials which dimension would be the target dimension for the next trials. Stimuli consisted of clouds of small blue dots which appeared and disappeared dynamically on the screen (Dynamic Raindrops, panel A) or stayed on screen for the whole interval (Static Raindrops, panel B). Either the first or second stimulus was always the standard stimulus, lasting for 1800 ms and consisting of 30 dots in total, while the other stimulus could take on one of six comparison magnitudes in both dimensions. (C) Here, participants only had to make a judgement based on time. Intervals were marked by a grey circle changing color to blue and back to grey. The same durations as in the Raindrops tasks were used in the temporal comparison task. (D) In the numerical Stroop task participants had to report how many items were on the screen. Three conditions were employed: 1) congruent (digit magnitude corresponded to number of items), 2) incongruent (digit magnitude did not correspond to number of items), and 3) control (letters). All tasks were self-paced, that is, the next trial only started after a response was given.
Fig 2.
Graphical illustration and numerical example of the MLE procedure.
For each of the 80 trials evidencetotal was calculated based on the stimulus parameters and the weights selected during each iteration of the MLE procedure (Formula 1). Evidencetotal was then used to compute the cumulative probability of a response (“longer”, grey curve left panel; “shorter”, grey curve right panel). In each iteration of the MLE procedure and for each trial the logarithm of the probability of the participant’s actual response (response “longer”, black curve left panel; response “shorter”, black curve right panel) given was computed with the current weights. The final weights were those for which the sum of the log-values over all trials was maximal. Dashed and dotted lines show two examples of different sets of weights and their effects on the weight-selection process on one specific incongruent trial. In the dotted line, more numerosity information was used, thus this set of weights would be superior if participant’s response was “longer” (i.e., influenced by the incongruent numerosity information and reflected in a higher log-value). On the contrary, the dashed line is an example of a set of weights in which temporal information is taken into account more than numerosity information. Here, if the participant correctly responds “shorter”, this set of weights will be favoured (higher log-value). Note however, that the weights selection was based on all trials.
Fig 3.
Vector correlations assessing stability of interference effects over time.
Vector fields show the composed ω-vectors (ωtime as x-component and ωnumber as y-component) for each participant (i.e., each square, distribution is constant over all panels) and the grand average (grey highlighted square). Correlations were computed between ω-vectors of session I and session II in the Dynamic Raindrops task (left hand side) and in the Static Raindrops tasks (right hand side).
Fig 4.
Vector correlations assessing stability of interference effects over tasks (and time).
Vector fields show the composed ω-vectors (ωtime as x-component and ωnumber as y-component) for each participant (i.e., each square, distribution is constant over all panels) and the grand average (grey highlighted square). Correlations were computed between ω-vectors of different versions of the Raindrops task.
Fig 5.
Correlations between timing performance in temporal comparison task and magnitude comparison tasks.
Testing whether being a ‘timing’ participant in a magnitude comparison task (quantified by ωtime) is correlated to performance in a comparison task which only has the time dimension and no other interfering information of a different dimension. Each dot represents one participant; grey line shows the regression line.
Fig 6.
Correlations between Stroop effect and magnitude interference effects.
To test whether participants showing larger magnitude interference effects (quantified by ωnumber) also show larger Stroop interference effects, these two scores were correlated for each task. Each dot represents one participant; grey line shows the regression line.
Fig 7.
Empirical (black) and disattenuated (grey, where relevant) correlations between sessions and versions of the Raindrops task, as well as the Numerical Stroop and Temporal Comparison task. (See main text for additional details).