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.