## 3 Results
### External Validation of Algorithmically Extracted Workload Measure  
As explained, the algorithmic cognitive-load measure provides a continuous simulation of the pupil response to the current task that is free of a luminance-created contribution to the same pupillary response. To externally validate the cognitive-load algorithm, we looked at the observed correlations between ground truth and algorithmically derived cognitive-load measures. Ground truth was calculated in the conventional way, by subtracting average baseline pupillary size from the pupillary size at a precisely defined point in time during the manipulation phase. Note: This ground-truth method aims to eliminate the influence of luminance on the pupillary response in the manipulation phases and, thus, corresponds in conventional offline calculations of pupillary responses to what the cognitive-load algorithm does online. To calculate these observed correlations, we first selected the strongest maxima (or highest local peaks) in the modeled cognitive-load responses. In this way, we targeted points in time of assumedly highest signal-to-noise ratio and strongest change in cognitive load across time. In addition, to generalize the insights gained by correlations between the algorithmic model and the ground truth measure, we repeated this method for 20 time points randomly selected from a period of 250 ms before and after a local maximum of the algorithmic impulses. For the pupil response to each answer of each participant, we correlated the algorithmic cognitive-load measure and baseline corrected pupil-size changes (for example, see Figures 9 and 10). After calculating a correlation per individual question and for each participant, mean correlations for each participant (see Supplementary Table S6) and for each group were calculated: NEUL: \(R^{2}=0.634\); NEUH: \(R^{2}=0.652\); NEGL: \(R^{2}=0.565\), NEGH: \(R^{2}=0.648\). To statistically assess the presence or absence of significant correlations in our observed correlations, we applied a nonparametric resampling procedure. To this end, we randomly reshuffled individual samples of ground truth and algorithmic measures of all used pupillary responses per each participant and, thus, separately per group. We then calculated correlations on the reshuffled data described above for the observed data and repeated this procedure 10,000 times. This created a distribution of 10,000 correlations per participant, from which we determined the statistical thresholds (\(p=0.0125\); i.e., Bonferroni corrected for tests in four separate groups). In other words, only observed correlations exceeding 98.75% of the surrogate correlations were deemed significant. The assessment showed a significant difference between observed measurements and randomly shuffled measurements in each participant and for each answer. The same nonparametric resampling procedure was conducted to assess a difference in correlation between all four groups. Here, we observed a significantly reduced correlation between ground truth and cognitive load in the NEGL group: (NEUL-NEGL: \(p=0.004\); NEUH-NEGL: \(p<0.001\); NEGH-NEGL: \(p=0.001\)). This loss in correlation might also be related to the missing evidence for a clear cognitive-load-dependent pupil-size effect in the NEGL group compared to the NEGH group. Figure 10: Correlation between modeled cognitive load according to the algorithm (\(y\) axis) and ground truth (i.e., pupil size during manipulation minus pupil size during baseline; \(x\) axis) of 20 points in a window from 250 ms before to 250 ms after peaks (or local maxima) in the modeled measure of cognitive load during a single answer of one participant. The red line reflects assumption of perfect correlation, the blue dots reflect the actual correlation between measured pupil sizes and cognitive load. Figure 9: Example data and modeled cognitive load from a single participant’s pupil response (size change in pixels) during a single answer of the interviewee (here, to Question No. 5).