Keywords

1 Introduction

Digitization of the working environment leads to tasks with high demands on cognitive capacity and impose high mental workload on employees. The cognitive demands even increase when the tasks include high goal ambiguity that is particular prominent in the highly digitized working environment. Here, the final goals are often hard to be reached at once and must be split into a series of sub-goals that should be completed in a particular order. Tasks where the correct sequential ordering of the sub-goals is obvious from the final goal are referred to as low ambiguous. However, the complexity of the final goals of present-day’s tasks often leads to ambiguous ordering of the sub-goals. This high goal ambiguity may result in a suboptimal sequence of the sub-goals, ineffective and needless steps, or even dead ends, where people have to go back to the initial state and start over again.

In previous studies researchers reported that tasks with high goal ambiguity resulted in suboptimal planning with more steps and bad performance ([11], [2]), more errors [17], and prolonged planning and solution times ([10], [17]). Studies related to the effects of goal ambiguity were conducted with children ([11], [2], [12]) and adults ([10], [17], [1], [9]).

The goal ambiguity could also affect mental workload. Mental workload describes the relation between task demands and personal capacity. Cognitive resources for human information processing are limited and thus, mental workload represents the amount of task demands placed on a person’s limited resources [8].

Although research already showed that the degree of goal ambiguity is crucial for planning and problem solving, it remains unclear how the ambiguity influences the mental workload. In our study we aimed to bridge this gap. We investigated whether the goal ambiguity affects mental workload and task performance during planning and problem solving. We hypothesized that problems with higher ambiguity of goal structure require higher mental workload.

2 Methods

2.1 Procedure and Subjects

Our sample consisted of 21 subjects between the ages of 22 and 64 years (2 female, 19 male, mean age 38 ± 11, Table 1). The investigation took place in a non-shielded office. The experiment was fully carried out with each subject in a single day. It consisted of a training phase where the subjects were familiarized with the tasks and the main experiment. The training task was identical with the main task but shorter and easier. It was repeated until the subject reported to be confident in the proceeding. During the training phase, we did not register any data.

Table 1. Sample set.
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During the main experiment, we registered several workload-relevant parameters for consolidating our findings. In particular, we registered the electroencephalogram (EEG), heart rate, errors, and planning time before the first move of the trial. As an error we defined a suboptimal move that led to more steps for reaching the goal state. At the beginning of the task, we conducted a resting measurement as a baseline for the analysis of the heart rate.

The Federal Institute for Occupational Safety and Health (BAuA) in Berlin was in charge of the project. All of the investigations acquired were approved by the local review board of the BAuA and the experiments were conducted in accordance with the Declaration of Helsinki. All procedures were carried out with the adequate understanding and written consent of the subjects.

2.2 Tower of Hanoi

For our study, we employed the Tower of Hanoi (ToH) as a classic task in cognitive science. The ToH was widely used in studies of executive functioning and problem solving, involving various levels of planning to achieve a goal [13].

The computerized version of ToH was realized through the implementation in the E-Prime application suite. Our ToH task consisted of three pegs and three or four discs of graduated size. Subjects were asked to transform a given start state into a goal state (Fig. 1) by taking the upper disk from one peg and placing it on another peg at a time. A larger disc could not be placed on a smaller disc. Subjects were requested to plan their actions before their first movement for reaching the goal with the least number of moves. In case of a non-optimal move, a feedback about the occurrence of an error was shown on the screen and the trial started over again. For avoiding the tendency of a speed and accuracy trade-off, there was no time limit for task solving. In general, subjects needed around 10 min to complete the ToH.

The tower-ending goal state, where all disks were stacked on one peg, provided an unambiguous goal state. Hereby, the disk at the bottom had to be in its goal position first, followed by the second from the bottom, and so on. In contrast, in the flat-ending goal state, where the disks were distributed over the pegs, the prioritization of moves was completely ambiguous. Subjects had to solve six trials with tower-ending and six trials with flat-ending goal state. The task design is presented in Fig. 2.

Fig. 1.
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Tower of Hanoi task. Subjects were required to transform the starting configuration into a goal configuration with low ambiguity (the tower-ending goal state) or high ambiguity (the flat-ending goal state).

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Fig. 2.
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Task design for the Tower of Hanoi task.

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2.3 EEG, Heart Rate, and Performance Data

The EEG was registered by 25 electrodes placed at positions according to the 10–20 system. It was recorded with reference to Cz and at a sample rate of 500 Hz. For signal registration we used the g.LADYbird/g.Nautilus device by g.tec GmbH and their Matlab interface for the recording. Subsequently, the recorded EEG signal was filtered with a bandpass filter (order 100) between 0.5 and 40 Hz. Independent component analysis (ICA, Infomax algorithm [14]) was used for artifact rejection. For increasing topographical localization a simple Hjorth-style surface Laplacian filter using 8 neighbors [7] was applied. Next, we transformed the artifact-free EEG to average reference and cut it into segments of 1 s length, overlapping by 0.5 s. We computed the workload relevant frequency bands (theta: 4–8 Hz, alpha: 8–12 Hz) over the segments by means of Fast Fourier Transformation (FFT) and generated the Dual Frequency Head Maps (DFHM) as outlined in the article by Radüntz [15]. For classifying the DFHM of each subject from the EEG segments as low, moderate, or high workload, we used the already trained SVM classifiers from the laboratory study [15] and obtained a value every 0.5 s. Finally, we applied a moving-average time window of 6 s and adjusted the result in order to gain a DFHM-workload index as percentage value between 0 (all DFHM classified as low) and 100 (all DFHM classified as high). For each ToH trial, a mean value of the DFHM-workload index was computed.

We registered the pulse signal by means of a plethysmographic pulse sensor at the earlobe using g.tec’s g.PULSEsensor coupled with g.tec’s mobile amplifier g.Nautilus. The pulse signal was windowed with a Hamming function and filtered with a bandpass filter (order 100) between 0.5 and 3.5  Hz. Peak detection was performed in order to determine the heart rate and the inter-beat intervals. Artifacts were automatically detected by means of statistical analysis, corrected using linear interpolation of the values at neighboring points, and equidistantly resampled with a time resolution of 0.5 s. Heart rate was determined in beats per minute in the time domain. The mean values for each trial were baseline-corrected according to the mean value measured during the resting state.

For performance evaluation, we used the number of errors and the planning time of each trial and person. Biosignal processing and all calculations were done with MATLAB.

2.4 Statistical Analysis

For each dependent variable (i.e., DFHM-workload index, heart rate, number of errors, and planning time), we averaged the corresponding values from the six trials with tower-ending goal state and the six trials with flat-ending goal state, respectively. Based on these values, we calculated the means for the two levels of goal ambiguity (Fig. 2) over the 21 subjects for each dependent variable.

The Shapiro-Wilk test showed a normal distribution for the differences between tower-ending and flat-ending goal state for the DFHM-index and planning time but not for heart rate and errors. Thus, comparisons between tower-ending and flat-ending trials related to the DFHM-workload index and planning time were conducted using paired-sample t-test, while for heart rate and errors we used the Wilcoxon test. Statistical calculations were conducted using SPSS with a significance threshold of 5%.

3 Results

The DFHM-workload index, planning time, and number of errors showed significant differences between the two levels of ambiguity as represented by the tower-ending and flat-ending goal states. Planning time was significantly higher during the flat-ending goal state (t(20) \(=\) −5.544, p \(\le \) .001, \(\left| d\right| \) \(=\) 1.21) indicating that the planning demands in tasks with high goal ambiguity (M \(=\) 17.5 s, SD \(=\) 8.4 s) were significantly higher than during tasks with low goal ambiguity (M \(=\) 11.4 s, SD \(=\) 6.0 s). Accordingly, the number of errors was significantly higher during the flat-ending goal state (z \(=\) −3.63, p \(\le \) .001, r \(=\) 0.56) indicating that the performance in tasks with high goal ambiguity was significantly worse (Mdn \(=\) 0.67, range \(=\) [0, 4]) than in tasks with low goal ambiguity (Mdn \(=\) 0.17, range \(=\) [0, 1]).

The DFHM-workload index was significantly higher during the flat-ending goal state (t(20) \(=\) -2.242, p \(=\) .036, \(\left| d\right| \) \(=\) 0.49) indicating a higher mental workload as assessed by the EEG during trials with high goal ambiguity (M \(=\) 63.13, SD \(=\) 7.98) compared to trials with low goal ambiguity (M \(=\) 61.69, SD \(=\) 7.19). However, no significant difference could be found for the baseline-corrected heart rate (z \(=\) −0.226, p \(=\) .821, r \(=\) 0.04), although there was the tendency that in flat-ending trials it was higher (Mdn \(=\) 2.34, range \(=\) [−9.46, 15.87]) than in tower-ending ones (Mdn \(=\) 1.66, range \(=\) [−12.08, 14.68]). Figures 3 and 4 show the results.

Fig. 3.
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(a) Median of errors and (b) mean value of planning time computed for the ToH-goal states with low and high ambiguity over 21 subjects (\(***\): p < .001; error bars for normal-distributed data indicate 95% confidence interval).

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Fig. 4.
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(a) Mean DFHM-workload index and (b) median of baseline-corrected heart rate computed for the ToH-goal states with low and high ambiguity over 21 subjects (\(*\): .01 \(\le \) p < .05; error bars for normal-distributed data indicate 95% confidence interval).

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For the sake of completeness, we also looked for possible age differences. Subjects with an age below the median of 40 years were classified as younger (n=11), the remaining as older (n=10). For the normally distributed dependent variables DFHM-workload index and planning time, we calculated two mixed ANOVAs with age as between-subject factor. Results for the DFHM-workload index indicated neither a significant main effect for age (F(1, 19) = 0.347, p = .56, \(\eta ^2\) = .02) nor an interaction effect between age and goal ambiguity (F(1, 19) = 0.545, p = .47, \(\eta ^2\) = .03). Similarly, the planning time did not yield significant differences neither for age (F(1, 19) = 3.415, p = .08, \(\eta ^2\) = .15) nor for the interaction between age and ambiguity (F(1, 19) = 1.193, p = .29, \(\eta ^2\) = .06).

For the non-normally distributed dependent variables heart rate and errors, two Mann-Whitney-U tests were calculated to determine if there were differences between the age groups. As dependent variables for the baseline-corrected heart rate and errors, we employed the gradient between flat-ending and tower-ending goal states, respectively. There was no statistically significant difference in heart rate between younger and older subjects related to goal ambiguity (U \(=\) 52.00, Z \(=\) −0.211, p \(=\) .83, r \(=\) −.05). Finally, we were not able to find a statistically significant difference in errors between the age groups (U \(=\) 32.00, Z \(=\) −1.634, p \(=\) .10, r \(=\) −.36).

Figure 5 shows the results for the four dependent variables for each age group and goal-ambiguity level.

Fig. 5.
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(a) Mean DFHM-workload index, (b) mean value of planning time, (c) median of baseline-corrected heart rate, and (d) median of errors computed for the ToH-goal states with low and high ambiguity over subjects under (blue) and over (red) 40 years (error bars for normal-distributed data indicate 95% confidence interval). (Color figure online)

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4 Discussion and Conclusions

We hypothesized that problems with higher ambiguity of goal states affect task performance and require higher mental workload. For assessing mental workload, we used the DFHM method that was previously developed in a laboratory setting and is based on the EEG. The 21 subjects participating completed the ToH task that consisted of trials with tower-ending and flat-ending goal state representing low and high ambiguity, respectively.

The results indicated that mental workload as registered by the DFHM-workload index from EEG was significantly higher during trials with high goal ambiguity. Moreover, subjects’ performance (i.e., planning time and errors) during trials with high goal ambiguity was significantly poorer than during trials with low goal ambiguity. Heart rate did not yield any significant differences. The reason might be the small set size or the lack of time pressure during the task that is particular relevant for heart rate alterations.

In our study, we tried to address a possible interaction between ambiguity and age on workload. We have to admit that our sample set was not very appropriate. From the literature it is well known that working memory and information processing capabilities decrease with age ([3], [5]). Studies indicated significant differences in working-memory capacity and planning abilities for subjects over 60 years ([4], [6], [16]). Thus, a limitation of our study in this context was that our sample set was to young (i.e., median age of 40 years) for revealing age-related trends. Nevertheless, descriptive statistics and inspection of the results showed an increased planning time for younger compared to older subjects resulting in higher mental workload and heart rate but less errors during high-ambiguity trials. This might be an indication that younger subjects were more attached to planning tasks and thus, invested more effort. On the contrary, older subjects seemed less motivated and engaged in high-ambiguity planning tasks as linked to less planning time, decreased mental workload and heart rate, and more errors. Future studies should investigate a possible interaction between goal ambiguity and age with a suitable sample set. Furthermore, time on task and time pressure are notably relevant topics for further research as these could have an additional effect on planning performance and mental workload.

To sum up, we concluded that problems with higher goal ambiguity impose increasingly high demands on cognitive capacity, resulting in not only higher error rates, longer planning time, and suboptimal performance but also in negative consequences of inappropriate workload that could affect human’s health and the safety of persons. The issue of goal ambiguity is of particular interest for problem solving in digitized working environments that often comprise suboptimal sequences of sub-goals because of an unclear goal state. Application developers should focus on reducing ambiguity and optimizing the goal structure by predefining and communicating the sequence of the sub-goals to the users through intelligent assistance systems. This way, we await performance at its best whilst simultaneously preserve employee’s health.