Human monitoring behavior in a multiple-instrument setting: Independent sampling, sequential sampling or arrangement-dependent sampling

acta psychologica Acta Psychologica

ELSEVIER

86 (1994131-55

Human monitoring behavior in a multiple-instrument setting: Independent sampling, sequential sampling or arrangement-dependent sampling * Mieke Donk Vakgroep Psychonomie, Vrije Uniuersiteit, De Boelelaan I Ill, 1081 HVAmsterdam, Received

24 December

1991; revised 9 August

The Netherlands

1993

Abstract This study aims at contributing to the understanding of human monitoring behavior in multiple instrument settings. Eye movements were recorded so as to test whether sampling behavior is more consistent with traditional normative models (Senders, 1983) or with alternative approaches that emphasize heuristics and strategies rather than quantitative modelling. A core assumption of normative modelling concerns the premise that sampling one instrument is independent of the other instruments in an array. This assumption was tested in three experiments. In a first experiment, subjects monitored four independent continuous stochasts so as to detect critical situations. In a fast condition, two instruments were paired with two relatively fast changing instruments. In a slow condition, the two instruments were paired with two relatively slow changing instruments. Sampling one instrument appeared to be independent of the rates of change of the other instruments in the array. Furthermore, sampling was a function of the information generation rates of the individual instruments. This is in accordance with normative modelling. However, the spatial arrangement of the instruments on the display as well as the presence of a central fixation point strongly affected sampling behavior. In a second experiment, subjects monitored six instruments. In addition, there was no central fixation point. The results indicated again that a perceptual heuristic was used in that the spatial arrangement of the instruments on the display affected sampling behavior. Horizontal transitions occurred more often than would be predicted on the basis of independent sampling. Diagonal transitions occurred less often than would be predicted. Finally, a third experiment tested whether this preference

* This research Germany.

was carried

out while the author

was at the Institut

fiir Psychologie,

The author would like to thank A.F. Sanders, F.L. van Nes, and two anonymous comments and suggestions on an earlier draft of this article. OOOl-6918/94/$07.00 0 1994 Elsevier SSDI OOOl-6918(93)E0045-4

Science

B.V. All rights reserved

RWTH

reviewers

Aachen,

for useful

for sampling by means of horizontal eye movcmcnts at the expense of diagonal eye movements would, under conflict situations, affect the mean sampling interval of specific instruments. In a four-instrument monitoring task, sampling intervals of two slow and two fast independent instruments were compared in different spatial arrangements. Sampling intervals strongly depcndcd on the arrangement of the instruments on the display. Human monitoring seems to be biased by a tendency towards sampling by means of horizontal transitions at the cost of diagonal transitions. Under certain conditions, this tendency might make sampling intervals unrelated to the information gcncration rates of the individual instruments.

1. Introduction Modern process control can be characterized by an increasing distance between the Human Operator (HO) and the processes involved. The computer carries out many direct-control tasks resulting in a slowly reacting system whenever a HO intervenes. This state of affairs requires that the operator anticipates what forthcoming processes will be like. In order to collect knowledge about a system’s state, the HO has to monitor the instruments that reflect the state of the process under control. This monitoring or sampling usually occurs by successive fixations of the various instruments (Senders, 1983). During the last few decades, various mathematical models have been developed to account for human performance in monitoring tasks (KvHlseth, 1978; Senders, 1983; Sheridan, 1970; Stein and Wewerinke, 1983). These models are normative in that they start by considering some optimal way in which monitoring might be carried out, followed by a prediction of what the HO should do if he or she were an optimal rational processor of information. Quantitative normative modelling is attractive in that it enables accurate predictions concerning human monitoring behavior. Also the practical applications are straightforward: if one can quantify one can design better display panels, the laws governing scanning behavior, calculate work loads, and so on (Senders, 1983). A major attempt to model human monitoring behavior in a quantitative normative way was done by Senders (19.55, 1964, 1983). He presented in 1983 a hierarchy of normative models derived from a queueing theory of the monitoring process. Queueing theory is the mathematical analysis of systems involving one or more ‘service channels’ and some number of ‘customers’ who arrive serially at the service channels. According to the general theory, the instruments are the customers and the assumed single channel of visual attention is the service channel. An instrument arrives for the attention (service) and when the uncertainty about what is displayed on that instrument is reduced to zero or some sufficiently low value, the instrument leaves the service channel (Senders, 1983). The normative models derived from this general theory differ with respect to the strategy of the HO which determines his or her sampling behavior. According to the simplest model, the Periodic Sampling Model (PSM), the HO has the strategy to monitor multiple instruments so as to reconstruct the individual process dynamics of the instruments. To achieve full reconstruction. Information Theory (Shannon, 1948)

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prescribes that the sampling frequency of an instrument (15;) should be at least twice its bandwidth frequency (FI(). Thus, in this model, the frequency of sampling should be a linear function of the signal’s information generation rate. In addition, sampling is supposed to be periodic and independent of the preceding readout of a signal. The sampling duration is supposed to be a function of the ratio of the signal’s amplitude to the size of the permissible error of readout. This implies that the sampling duration is a constant over time and independent of the bandwidth of the process. In his Conditional Sampling Models (CSMs), the sampling rate is also supposed to be a linear function of a signal’s information generation rate. In addition, the timing of a next sample from an instrument is a rational function of the reading of the preceding sample. According to the CSMs, the HO tries to estimate when a signal exceeds a critical limit. Consequently, the sampling frequency is supposed to increase as a signal approaches a critical limit. The duration of sampling might be either constant or varying as a function of the time elapsed since a previous observation. In the latter case, the model predicts sampling duration to increase as the time since the last observation increases. Basically, Senders’ models apply to visual sampling of time-varying, bandwidthlimited signals. In either model, the number of inspections is assumed to be a direct function of the information generation rates of the individual instruments; i.e., high-bandwidth processes will be sampled more than low-bandwidth processes. A basic assumption of either model of Senders concerns sampling independence. Sampling one instrument is supposed to be dependent on the dynamics of only that instrument and, consequently, independent of the dynamics of the other instruments in the array. Therefore, the transition probabilities between instruments only depend on the information generation rates of the individual instruments. If two instruments both have a large sampling frequency, there will be a large number of transitions; if two instruments both have a small sampling frequency, there will be a small number of transitions. Thus, according to Senders (1983), the information generation rate of an instrument determines the rate of sampling. In a multiple instrument array, the required rate of sampling of each individual instrument determines the transition probabilities between these various instruments. Senders recognized that scanning patterns in real-life situations might be dictated by couplings in the system. It is reasonable to assume, that when observing the altimeter, an error is observed between desired and displayed state, the next observation should be on the vertical speed indicator in order to observe the cause of the change in altitude (Senders, 1983). However, Senders (1983) assumes that ‘logical’ scanning patterns will occur when there is no clear interdependency in sampling the various instruments. ‘Logical’ means in accordance with some scheme of information intake, related to the nature of the information presented on each instrument (Senders, 1983). The sequence of scanning is then only a product of the individual instrument sampling rates. A different non-quantitative approach is offered by Van Delft (1987). According to Van Delft, sampling of multiple instruments is based on qualitative decision heuristics (Hogarth, 1980) and not on independent sampling decisions. The mean

34

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/Am

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sampling interval of either individual instrument is a function of the total array of instruments. The supervisor structures the monitoring task through fixed sampling sequences which dictate the order in which sources are regularly scanned. The sampling rate is determined by the instrument with the smallest desired sampling interval in that the choice of the common time base of sampling is determined by the instrument which is sampled with the smallest interval. Thus, the decision to sample is thought to take place at a higher level of task structuring than the individual instruments. Indeed, Hannen (1987) found that the sampling rate of two instruments was significantly larger in a condition in which these instruments occurred in combination with relatively fast changing instruments than when combined with relatively slow changing instruments. This effect occurred under both unrestricted conditions in which subjects were allowed to sample as often as they wanted, and restricted conditions in which subjects were limited in the maximum number of samples that were permitted. It was concluded that sampling one process depends on the bandwidths of the other processes in the array. This is in clear contrast to Senders’ independent sampling assumption. It needs to be remarked, though, that Van Delft based his conclusions on experiments in which the instruments were binary stochasts whereas Senders used continuous displays. In addition, a process was sampled by a manual observing response instead of eye fixation; i.e., a subject pushed a button in order to observe the desired instrument. These differences with the experiments of Senders render a direct comparison doubtful. On the other hand, there is nothing in the sequential sampling model of Van Delft which limits its application to the case of sampling binary stochasts by way of manual observing responses. Although Van Delft’s hypothesis of a common time base of sampling was supported, he did not carry out a direct test of the extent sampling actually occurs in a fixed sequence. The deduction from a common time base to a predetermined sampling sequence is logical but not necessary. In addition, Van Delft is vague about the determinants of the fixed sampling sequences: ‘With what sequence the supervisor will scan his sources is expected to be a function of the relative estimate of source dynamics’ (Van Delft, 1987). An alternative determinant of a fixed sequence might be the relative arrangement of the instruments on the display. Fitts et al. (1950) found that the transition probability of fixation from one instrument to another was a function of the arrangement of the instruments on a panel. However, Fitts et al. (1950) measured pilot eye movements during actual flights. Their data on transition probabilities might therefore not be free from confounding factors like existing couplings between different instruments. It needs to be remarked though, that neither Senders (1983) nor Van Delft (1987) predict any dependency of sampling on instrument arrangement. The present experiments aim at contributing to the discussion of whether visual sampling is better described by a rational normative rule (Senders, 1983) or by sequential sampling heuristics (Van Delft, 1987). Experiment 1 is basically a replication of Hannen’s study on the mutual effects of the instruments’ dynamics

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35

with two major changes: continuous rather than binary instruments were used, and sampling occurred by eye instead of by manual observing responses. The present study tested whether sampling two instruments in an array of four is affected by the information generation rates of the remaining two instruments in the array. There was a fast condition in which the two instruments were paired with two relatively fast-changing instruments and a slow condition in which the two instruments were paired with two relatively slow-changing instruments. A fixation point was provided to prevent random sampling when the observers decided that none of the instruments needed sampling. It should be mentioned that neither Senders (1983) nor Van Delft (1987) would predict any change in sampling pattern when a resting point is utilized. According to both Senders and Van Delft, sampling is a function of the dynamics of the instruments in an array. Clearly, the presence of a resting point does not affect the dynamics of the instruments. Obviously Senders (1983) would predict no difference between the sampling intervals of the two key instruments in the fast compared to the slow condition. According to the sequential sampling theory Wan Delft, 1987) it is predicted that the two key instruments will be more frequently sampled in the fast than in the slow condition. Finally, in order to investigate whether sampling patterns actually are independent of the arrangement of the instruments on the display, observed proportions of horizontal, vertical and diagonal transitions were compared with predicted proportions on the basis of the arrangement-independent sampling assumption which underlies both Senders’ and Van Delft’s approach.

2. Experiment

1

2.1. Method Subjects Four male and four female subjects participated in one three-hour session. The subjects were between 18 and 30 years of age. All reported having a normal visual acuity and having no previous experience with this type of experiment. Subjects received DMlO.- per hour for their participation and could earn an additional bonus dependent on their performance. Stimuli and task Fig. 1 shows the display which was presented. The full display consisted of a central fixation point and four pseudo-randomly moving processes in the form of four lines in four rectangles which were continuously visible. The display was projected on a white screen (1.50 m x 1.55 m), positioned 2.30 m in front of the subject (visual angle: 33.1” X 34.0”). The rectangles were horizontally and vertically 62 cm apart from each other which is about 15.1” of visual angle. They were equally sized (11 cm high and 40 cm long; 2.7” x 9.9O>. Each rectangle contained a horizontal line, the left end of which was fixed while the right end slowly extended or shrank. The right end of a line could be in either

M. Donk /Acta

Psychologica

86 (1994)

31-55

I Fig. 1. The display as presented

to the subjects.

one of 20 positions; from Position 1 at the extreme left to Position 20 at the extreme right. The positions had equal distances to each other (1/20th of the length of the rectangle) and were not marked. Line movements from one position to another were continuous and took about one second. Positions 1 to 15 were defined as belonging to the non-critical zone and Positions 15 to 20 to the critical zone of the rectangle. The boundary between the critical and the non-critical zone was indicated by two vertical lines perpendicular to the horizontal axes of each rectangle. The processes in the non-critical zone could not be affected by the subjects; the lines extended with a probability of 2/3 and shrank with a probability of l/3. Thus, given a line movement, the likelihood that a line moved from Position X to X-t 1 was 2/3 and from Position X to X - 1 was l/3. In the critical zone, lines could only extend; i.e., from Position X to X+ 1. When a line entered a critical zone, subjects responded by pressing a key. This had the effect that the line length immediately reduced to a random position in the non-critical zone. The processes within one display only differed with respect to their mean rate of change. The mean rates of change of the four processes were 1.00 cm/s, 0.50 cm/s, 0.33 cm/s, and 0.25 cm/s in the fast condition, and 0.33 cm/s, 0.25 cm/s, 0.20 cm/s, and 0.17 cm/s in the slow condition (1 cm equals 0.25” of visual angle). The instruments with rates of change of 0.33 cm/s and 0.25 cm/s (key instruments) occurred in both conditions. The task was to detect ‘critical’ situations defined as occasions on which the right end of a horizontal line entered the critical zone. A button press indicated a detection and resulted in the immediate return of the line to a random position in the non-critical zone. There was only one button in order to avoid too much involvement in response selection. Thus, no selection of response was required for different instruments. The main data of interest were eye movements and fixations of subjects whereas detection performance was only included to provide subjects with feedback between sessions. Subjects were instructed to fixate the resting point in the middle of the screen when they felt no need of inspecting an instrument. This was done to present subjects with a full load in order to avoid sampling without reason. While fixating the resting point, changes in the rectangles could

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31

not be detected. Fixating one rectangle excluded detection of critical situations in other rectangles. Extra money could be earned by a combination of maximizing the time spent on the resting point and minimizing the time a process was in a critical zone. Apparatus The stimuli were generated by a program on a PDP 11/23 computer connected to a graphical terminal (Digital VT220). A TV-projector (Electrohome, Model: 38-B02304-60) was connected to this terminal and projected its display on a white screen in front of the subject. Eye movements were registered by the Debit 84 system (Demel) which operates according to the ‘point of regard’ method (Young and Sheena, 1975). This method enables the determination of the eye position on the basis of two reflection sources of the eye; i.e., the cornea1 and the pupil reflection, resulting from an infrared lightbeam (800-900 nm) which is projected onto the eye. The reflections were recorded by a TV-camera (Sony, video camera) with an infrared-sensitive device with a frequency of 50 Hz. The resolution of the system as used in the experiment was one degree of visual angle which was related to the resolution of the infrared-sensitive plate inside the TV-camera. During the experiment the subject and the experimenter were seated in adjacent rooms. The subject was seated in an adjustable chair with the head fixed by means of a head-and-chm support in such a way that the eye camera (Sony, video camera) was focused on the right eye. In the experimenter room, two monitors displaying both the eye reflections and the stimulus scene enabled continuous control of the experiment. The Dezec 80, attached to the Debit 84, further reduced the eye position data according to predefined categories. Basically, X and Y coordinates of the eye positions were converted into instrument fixations. These data were sent to the PDP 11/23 which, for all 20 ms periods, registered the positions of the horizontal lines of the instruments and the eye positions in terms of which instrument was observed. The PDP 11/23 also registered the responses of the subjects. Design A within-subject design was used. Half of the subjects started with three sessions of the slow condition followed by three sessions of the fast condition. The other half had the reverse order. A Latin square determined four different arrangements of the rates of change over the rectangles. Each subject was presented with one arrangement over all sessions. In this way, each arrangement was presented to two subjects, who only differed with respect to the sequence of conditions in which they performed; i.e., fast-slow vs. slow-fast. Procedure The experiment started with presenting the subjects with written instructions. After reading the instructions, subjects were seated in such a way that their heads

38

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remained stable during each session by means of a head-and-chin support. After the eyecalibration, in which the subjects fixated several predefined dots on the screen (7 x 4 dot-matrix), the first session started. Subjects were informed about the different rates of change of the processes and about the positions of the rectangles. It was stressed that the resting point should be fixated as long as no need was felt for inspecting an instrument. In addition, subjects were instructed to detect a critical situation as soon as possible. The subjects were familiar with the bonus system in which they could earn additional money. A session started as soon as the complete display appeared on the screen. The measurement of eye as well as line positions started after one minute had elapsed. After another 15 minutes, the experimenter stopped the program for a five-minute break during which subjects received feedback about their performance. After the break, the second and the third session of the same condition were run. The proceedings in the second and third session were the same as in the first session. Following another ten-minute break, the first session of the other condition was carried out followed by the second and the third session of that condition. In between sessions there was always a minimal break of five minutes. 2.2. Results

Detection performance was roughly equal for the slow compared to the fast condition. In order to guarantee maximally practised sampling behavior, only the data of the last session of each condition were statistically analyzed for each subject separately. On average, the visual system samples less than three points in space per second (Moray, 1986). However, the variability of fixation durations, within and between subjects, is quite large. Therefore, only fixation durations of 200 ms and longer were included in the analyses. The intended object of the present experiment was to create two conditions in which at least the fast instruments (1.00 cm/s and 0.50 cm/s> were sampled more often than the slow instruments (0.20 cm/s and 0.17 cm/s). Indeed, the mean sampling interval, which is the time interval between two successive observations of an instrument, was 6956 ms for the fast instruments and 13113 ms for the slow instruments (F(1,7) = 5.33, p = 0.054). The mean sampling duration did not differ between the fast and the slow instruments (F(1,7) = 3.20, p = 0.117). The mean sampling duration was 662 ms. A two-way ANOVA with individual mean sampling intervals of the key instruments as cells and condition (slow vs. fast) and rate of change (0.33 cm/s vs. 0.25 cm/s) as main variables did not show significant effects (Condition: F(1,7) = 0.11; Rate of change: F( 1,7) = 1.41, p = 0.273; Condition X Rate of change: F(1,7) = 0.06). The mean sampling interval was 7827 ms. Although the experiment aimed to relate sampling interval to the independent variables, sampling duration data were also inspected. A similar two-way ANOVA

M. Donk /Acta Psychologica X6 (1994) 31-55

39

with the individual mean sampling durations of the key instruments as cells and condition and rate of change as variables showed no significant effects of the main variables (Condition: F(1,7) = 0.10; Rate of change: F(1,7) = 3.02, p = 0.126) nor of their interaction (F(1,7) = 0.00). The mean sampling duration was 679 ms. Neither sampling interval nor sampling duration of the key instruments was affected by the slow compared to the fast condition. In order to find out whether either speed context affected the strategy of sampling; i.e., whether sampling behavior was periodical or conditional, two other analyses were performed with the additional variable of process position. To obtain data at each process position, it is required that each instrument is observed by each subject at each process position. This did, particularly at the lower positions, not occur. In addition, measuring sampling performance as a function of Positions 15 to 20 (critical zone) would be useless; a detection of a critical situation generally resulted in a key press by means of which the line length immediately reduced to a random position in the non-critical zone. Therefore analyses were limited to Positions 5 to 14. To avoid empty cells, the mean reaction times were calculated separately for Positions 5 to 9 and Positions 10 to 14. An ANOVA performed on the individual mean sampling intervals of the key instruments with condition (slow vs. fast), rate of change (0.33 cm/s vs. 0.25 cm/s> and process position (Positions 5 to 9 vs. Positions 10 to 14) as main variables showed a significant main effect of process position (F(1,7) = 16.75, p = 0.0051. There was no significant effect of condition (F(1,7) = 0.15) nor of rate of change (F(1,7) = 0.54). The interactions were also not significant. The mean sampling interval decreased as a process came closer to the critical limit. Condition did not affect the sampling strategy of the subjects. A similar ANOVA on the individual mean sampling durations of the key instruments showed a marginally significant effect of position (F(1,7) = 5.03, p = 0.060). Neither condition nor rate of change had a significant effect on sampling duration (Condition: F(1,7) = 0.03; Rate of Change: F(1,7) = 0.57). The interactions were also not significant. Sampling duration increased as a process was closer to the critical limit. An ANOVA on the individual mean proportions of time spent on the resting point showed a marginally significant effect of condition (F(1,7) = 5.30, p = 0.055). On average, subjects spent 55% of the total monitoring time on the resting point in the fast condition and 69% in the slow condition. Obviously, monitoring the instruments in the slow condition was less demanding than in the fast condition. In order to test the hypotheses derived from Senders’ PSM and CSMs more specifically, additional analyses were performed on the sampling data of the other instruments in the slow and the fast condition. A MANOVA on the individual mean sampling intervals with rate of change (0.17 cm/s, 0.20 cm/s, 0.50 cm/s, 1.00 cm/s) and process position (Positions 5 to 9 vs. Positions 10 to 14) as main variables revealed a marginally significant effect of rate of change (Wilks’ lambda = 0.25814, F(3,5) = 4.79, p = 0.062) and a significant effect of process position (F(1,7) = 6.93, p = 0.034). The interaction was not significant at all. The mean sampling interval was larger for the slow than for the

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fast processes. In addition, the mean sampling interval decreased as a process approached the critical limit. A similar MANOVA on the individual mean sampling durations revealed no effect of rate of change (Wilks’ lambda = 0.57694, F(3,5) = 1.22, p = 0.393) but a significant main effect of process position (F(1,7) = 25.04, p = 0.002). The interaction was not significant. The mean sampling duration was larger close to the critical limit. With respect to transitions, an additional analysis compared the observed with the predicted proportions of transitions. In the case of independent sampling, the predicted proportion of transitions (p,,) from one instrument to the next can be estimated on the basis of the observed frequencies of sampling of each individual instrument; P uh

=

Na .- Nb 4 N, - Nt,’

-

in which N, is the number of fixations on instrument a, NJ, is the number of fixations on instrument b, N, is the total number of fixations. Predicted proportions of transitions were compared for each individual subject with the observed proportions of transitions for horizontal transitions (HT), vertical transitions (VT), diagonal transitions (DT) and transitions to and from the resting point (RT) (see Fig. 2). A Wilcoxon matched-pairs signed-ranks test (Siegel, 1956) showed that, in both conditions, the observed proportion of transitions to and from the resting point was significantly higher than predicted on the basis of independent sampling (Fast condition: T = 3, p < 0.05; Slow condition: T = 0, p < 0.01). Diagonal transitions occurred significantly less often than predicted (Fast condition: T = 0, p < 0.01; Slow condition: T = 0, p < 0.01). In addition, in the fast condition, the observed proportion of vertical transitions was significantly higher than the predicted proportion of vertical transitions (T = 1.5, p < 0.05) whereas the observed proportion of horizontal transitions did not differ significantly from the predicted proportion. In the slow condition, neither the proportion of horizontal transitions nor the proportion of vertical transitions differed significantly from the predicted proportions. Apparently, sampling behavior was strongly influenced by the presence of a resting point. Transitions from the resting point to an instrument and from an instrument to the resting point occurred more often than would be predicted on the basis of number of individual samples taken from the resting point and the individual instruments. 2.3. Discussion The main finding of the present experiment is that a fast or a slow speed context did not affect the sampling interval of the key instruments. In other words, whether two instruments are combined with two slow or two fast instruments, does not influence their rate of sampling. In this study, subjects did not sample multiple

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41

Slow Condition 0.8

Proportion

I

K

~diiBLL

~!

DT

VT

RT

Transitions m

observed

&:d

predicted

Fast Condition Proportion 0.8 0.7 I ______~ 0.6 1 0.5 0.4 0.3 0.2 0.1 0 HT

VT

DT

Transitions m

observed

Fig. 2. The mean observed and predicted vertical (VT), diagonal (DT) eye movements the slow and the fast condition.

Li:::j predicted

proportions of transitions separate for horizontal (HT). and eye movements to and from the resting point CRT) in

instruments with a common time base as suggested by Van Delft (1987). Van Delft (1987) used a manual observing response as indication for sampling. As compared to visual sampling, manual observing responses might be more under strategic

42

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control and therefore more liable to a fixed sequential order. For instance subjects could develop a constant rhythm of button presses. A similar rhythm in the structure of eye movements might not occur due to more automatic elicitation and more external control of eye movements. A second finding was that sampling was roughly in accordance with the information generation rates of the instruments in that fast instruments were more often sampled than slow instruments. In addition, subjects tended to sample the instruments so as to estimate when a critical event occurred; i.e., sampling interval decreased when an instrument approached the critical limit. This finding is in accordance with the Conditional Sampling Models of Senders (1983). In the case of periodic sampling, the sampling interval had to be independent of the process positions. The mean sampling duration deviated from the predictions of either model of Senders. Sampling duration increased as a process approached its critical limit. Senders’ PSM predicts the sampling duration to be constant and independent of the last observed process position of an instrument. The CSMs predict sampling duration to remain constant or to increase as the time since the last observation increases. However, the present results show that the mean sampling duration increases with decreasing sampling interval; i.e., the mean sampling interval decreases when a process approaches the critical limit while the mean sampling duration increases. Apparently, subjects ‘waited’ longer; i.e., fixated longer, when a process was close to the critical limit in order to be able to confirm an occurring critical situation. A third main finding concerns the relative low proportion of transitions between diagonally arranged instruments. Such an arrangement-dependent sampling pattern is neither predicted by Van Delft (1987) nor by Senders (1983). Apparently, instrument arrangement does have an effect on sampling in that diagonal transitions occurred less often than predicted on the basis of the individual instrument sampling frequencies. In addition, sampling behavior was strongly influenced by the presence of a resting point. Generally, sampling appeared to occur more often over the resting point than expected on the basis of independent sampling. In conclusion, sampling one instrument seems to be independent of the dynamics of the other instruments in the array. Furthermore, sampling intervals seem to be grossly related to the information generation rates of the individual instruments, and the mean sampling interval decreased when a process approached the critical limit. This is rather well in accordance with the CSMs of Senders (1983). Sampling duration tended to increase when a signal approached the critical limit. This does not fit either model of Senders. More important, however, is the finding that monitoring behavior in the present experiment is not independent of the instrument arrangement. This, obviously, contradicts normative modelling. Independent sampling decisions should result in a sampling pattern which is roughly predictable on the basis of the number of observations on each individual instrument and thus be unrelated to instrument arrangement. The availability of a resting point pervasively affected the sampling pattern. The second experiment investigates whether arrangement-dependent sampling also occurs when no resting point is available.

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3. Experiment

43

2

In the second experiment, there was no resting point to investigate further to what extent the observed proportions of transitions between various independent instruments deviate from the predictions of the independent sampling hypothesis. In the first experiment, the resting point was implemented so as to assure that the monitoring task would be totally demanding and sampling would not occur for the sake of pastime. However, Hannen (1987) and Van Delft (1987) have shown that whether or not subjects are fully occupied by a monitoring task, does not affect the relative amount of time devoted to each instrument in an array. Thus, sampling behavior did not appear to be qualitatively different for a condition in which subjects were free to choose how often to take a sample from a condition in which subjects were forced to sample in a more economical way (by a restriction in the maximal number of samples allowed). In an analogous manner, omitting the resting point may not qualitatively change sampling behavior. It may, however, be expected that the omission of the resting point results in higher sampling rates and longer fixation durations. In order to be able to test the predictions derived from Senders’ PSM and CSMs more accurately, six instruments were presented instead of four. By using six instruments, six different rates of change could be used. In addition, subjects could not only make horizontal, vertical, and diagonal eye movements but also eye movements from one instrument to a non-adjacent instrument. In the second experiment, transition probabilities could no longer be affected by a resting point. Therefore, it is expected that the relative distribution of transitions should be more in accordance with the assumptions of the normative models. 3.1. Method Subjects Four males and two females between 18 and 30 years of age participated in a 1.5hour experiment. All subjects reported having normal visual acuity and having no previous experience with experiments of this kind. All subjects were paid for participation (DMlO,- per hour plus a bonus which depended on performance). Stimuli The full display consisted of six pseudo-randomly moving processes in the form of six lines in six rectangles (see Fig. 3) which were continuously visible in any of three sessions of 15 minutes each. The display was similar to the display in Experiment 1 except that the resting point was substituted by two additional instruments. The rectangles had a horizontal separation of 11 cm (2.7” of visual angle) and a vertical separation of 62 cm (15.1’ of visual angle). The dynamic properties of the instruments were the same as in Experiment 1 although their mean rates of change differed. The mean rates of change of the processes within a display were 1.00 cm/s, 0.50 cm/s, 0.25 cm/s, 0.125 cm/s, 0.0625 cm/s, and 0.03125 cm/s. The

M. Donk /Acta Psychologicu 86 (1994) 31-55

44

J Fig. 3. The display as presented

arrangement subjects.

of these

Experimental

task

rates of change

to the subjects.

over the six rectangles

was varied

between

The task of the subjects was to monitor the six instruments with regard to entering the critical zone. If a process entered the critical zone, the subject was required to press a button in order to get the line back to the non-critical zone. As in Experiment 1, much care was taken that fixation of an instrument excluded the possibility of detecting any of the other processes to enter its critical zone. Thus, fixation of an instrument was necessary to watch an instrument. Subjects could earn extra money for minimizing the time a process was in a critical zone. Independent variables were rate of change (1.00 cm/s, 0.50 cm/s, 0.25 cm/s, 0.125 cm/s, 0.0625 cm/s, and 0.03125 cm/s) and position of the processes (Position 1 to 14; only the non-critical zone>. Dependent variables were sampling interval and sampling duration. In addition, the proportions of transitions were registered separately for horizontal, vertical and diagonal eye movements and for ‘jumps’ (eye movements from one instrument to a non-adjacent instrument). Apparatus See experiment

1.

Design

A complete within-subject design was used. For each subject, the assignment of the rates of change to the rectangles was determined by a Latin square design resulting in six different arrangements. Each subject received one arrangement during three sessions. Procedure

Subjects first read the written instructions. After the eye calibration, the first session started. The first session took about 16 minutes and was equal to the two subsequent sessions except that the experimenter clarified eventual remaining problems. Prior to the start of a session the experimenter emphasized the impor-

M. Donk /Acta Psychologica 86 (1994) 31-55

45

tqnce of detection when a process entered the critical zone. Furthermore, subjects were informed about the rates of change of the processes as well as about the distribution of the rates of change over the rectangles. After each session, subjects had a short break during which they received feedback about their performance. 3.2. Results Detection performance was roughly equal for all rates of change in the display. Only eye fixations of 200 ms and longer were included. Analyses were performed on the third session only in order to guarantee maximally practised sampling behavior. Fig. 4 shows the mean sampling intervals as a function of rate of change. Except for the highest rate of change, the data suggest a decrease in sampling interval as the rate of change increases, which was substantiated by a repeated measurement MANOVA on the individual mean sampling intervals, with rate of change as a variable (Wilks’ lambda = 0.00062, F(5,l) = 323.73, p = 0.042). A similar repeated measurement MANOVA on the individual mean sampling durations showed no significant effect of rate of change (Wilks’ lambda = 0.01628, F(5,l) = 12.08, p = 0.215). The mean sampling duration was 934 ms. As in Experiment 1, additional analyses were carried out to find out whether subjects’ sampling strategy was more in accordance with Senders’ PSM or CSMs. Due to the process dynamics, the processes rarely entered the first positions. In addition, various data points were missing for intermediate positions. To avoid empty cells, a MANOVA was performed on the individual mean sampling intervals with two levels of process position in the non-critical zone (Positions 5 to 9 vs. Positions 10 to 14) and six levels of rate of change (0.03125 cm/s, 0.0625 cm/s,

Sampling 16 ,mpp ~

Interval

(s)

I 14 1 :‘, i

12

‘1,

10

’

I

2t o

~~.I_

0

___I

0.1

_~__I

-__1

0.2

0.3

Rate Fig. 4. Mean sampling

A_-L_

~1

~~

0.4

0.5

0.6

of Change interval

-L--.1

0.7

0.8

0.9

(cm/s)

as a function

of rate of change.

~

1

J

46

M. Dank /Acta

Psychologiccr 86 (3994) 31-55

Proportion 0.6 r- ~~~~

DT

VT

JT

Transitions m

observed

Fig. 5. The mean observed and predicted vertical (VT), diagonal (DT) eye movements

proportions and jumps

?,!

predicted

of transitions (JT).

separate

for horizontal

(HT).

0.25 cm/s, 0.50 cm/s, 1.00 cm/s). There was a significant main effect of rate of change (Wilks’ lambda = 0.00055, F(5,l) = 364.77, p = 0.040) and a significant main effect of process position (F(1,5) = 26.32, p = 0.004). The interaction was not significant. The mean sampling interval decreased with increasing rate of change and with increasing process position. A similar MANOVA on the individual mean sampling durations revealed a significant main effect of position tF(1,5) = 12.03, p = 0.018). The other main effect as well as the interaction were not significant. The mean sampling duration was larger close to the critical limit. An analysis on the transition data was carried out to compare observed and predicted proportions of eye movement transitions on the basis of the hypothesis that instruments are independently sampled. Observed proportions of transitions were compared separately for each subject with predicted proportions of transitions for horizontal transitions (HT), vertical transitions (VT), diagonal transitions (DT) and ‘jumps’ (JT = transition between non-adjacent instruments) (see Fig. 5). A Wilcoxon matched-pairs signed-rank test proved the proportions of horizontal transitions to be significantly higher than the predicted proportions (T = 0, p < 0.05) whereas diagonal transitions and jumps occurred significantly less often than predicted on the basis of independent sampling CDT: T = 0, p < 0.05; JT: T = 0, p < 0.05). The observed and predicted proportions of vertical transitions did not differ significantly from each other (T = 2.5, p > 0.05). 0.125 cm/s,

3.3. Discussion There was a relatively high number of transitions between horizontally arranged instruments and a relatively low number of transitions between diagonally and

M. Donk /Ada

Psychologica 86 (1994) 31-S

47

npn-adjacently arranged instruments. This result is at odds with Senders’ claim of external control on the basis of process dynamics. A perceptual heuristic seems to be utilized in which scanning occurs preferentially by means of horizontal and to a lesser extent vertical eye movements. Subjects apparently monitored the array of instruments according to a simplifying rule. Another result of importance concerns the finding that, again, sampling behavior appeared to be rather well in accordance with the information generation rates of the individual instruments. Sampling generally increased with increasing rate of change. In addition, the mean sampling interval decreased as an instrument approached the critical limit. Both of these findings fit quite well with the predictions of the CSMs of Senders (1983). However, two marginal notes have to be made. First, the mean sampling intervals of the relatively fast processes (0.25 cm/s, 0.50 cm/s, and 1.00 cm/s) appear to be less dependent on the information generation rates of the instruments. It seems that subjects utilized a fixed rate of sampling when the rate of change exceeded a certain maximal value. A second point to be made concerns the sampling duration. Sampling duration was longer close to the critical limit than far from the critical limit. As in Experiment 1, subjects seemed to wait; i.e., fixate longer for noticing a process exceeding the critical limit. Obviously, this is neither in accordance with the PSM nor with the CSMs of Senders. At this point, the question arises whether sampling behavior is ultimately determined by individual process dynamics as assumed by Senders (1983) or by relative instrument arrangement. The present experiment suggests that sampling behavior is a function of both. This might appear to be true under some conditions, however, it seems to be logical to assume that in conflict situations; i.e., situations in which the process dynamics require one and the instrument arrangement another pattern of sampling, either the influence of process dynamics or the influence of instrument arrangement is dominant. When subjects mainly sample according to a rule which depends on the process dynamics, then instrument arrangement may only influence sampling behavior when the dynamics of the various instruments do not allow for a decision as to which instrument has to be sampled first. On the other hand, when subjects primarily sample according to a rule which depends on the instrument arrangement, then sampling behavior may under some circumstances be unrelated to the individual instrument dynamics. The next experiment aimed to find out whether one or the other rule plays a dominant role in the determination of sampling behavior.

4. Experiment

3

The present experiment was designed to find out whether sampling determined by a heuristic of avoiding diagonal transitions or by an optimal as proposed by Senders (1983) in which sampling behavior depends individual information generation rates of the instruments.

is more strategy on the

4x

M. Dank /Acta

Psychologicu

X6 (1994) 31-55

Twelve subjects performed a simple supervisory task in which two fast and two slow instruments were monitored. In one condition, the instruments were arranged in such a way that the relatively fast instruments were on one and the relatively slow instruments on another diagonal of an imaginary square (diagonal arrangement condition). In the other condition, the fast instruments and the slow instruments were horizontally arranged; i.e., the fast instruments in the upper corners of an imaginary square and the slow instruments in the lower corners or the other way around (horizontal arrangement condition). The present set-up was chosen to create a conflict situation in the diagonal arrangement condition. Sampling by avoiding diagonal transitions results in either strong oversampling of at least one slow instrument and/or strong undersampling of at least one fast instrument as compared to sampling behavior in the horizontal arrangement condition. On the other hand, sampling according to an optimal model leads to an increasing number of diagonal transitions at the cost of horizontal and vertical transitions in the diagonal arrangement condition in comparison to the horizontal arrangement condition. In this third experiment an attempt was made to match more accurately the dynamic properties of the instruments with the dynamic characteristics of the instruments described by Senders (1983). Senders’ models apply to random bandwidth-limited Gaussian signals. In addition, the task of the subject is supposed to be a tolerance band monitoring task in which a to-be-monitored process moves between two extreme values that cover a range which is larger than the tolerance band. The subjects’ task is then to note when a process exceeds its explicitly indicated tolerance band. In Experiments 1 and 2, the task of the subjects was indeed a task in which they had to note when a process exceeded a critical limit. However, subjects could affect the state of either signal by pushing a button when a critical situation occurred which resulted in the immediate return of the line to a random position in the non-critical area. Obviously, this was done to prevent the signals from remaining in the critical area for too long a period of time. Once noticed, a critical situation would not be demanding anymore when the signal would remain in the critical area. In the present experiment, subjects were presented with a tolerance band monitoring task in which the instruments could not be affected by the subjects. Their task was now mainly to note when a critical situation occurred. Thus, instrument values changed independently of the actions; i.e., button presses, of subjects. Three different rates of change combinations were used so as to investigate whether varying demands would affect the pattern of sampling. The three different rates of change combinations were assigned to three different groups of four subjects each. Although the absolute rate of change of the instruments differed between groups. all groups basically performed the same supervisory task in which two fast and two slow instruments were monitored. Sampling intervals and sampling durations for the individual instruments as well as the number of transitions were measured in either condition.

M. Donk /Acta Psychologica 86 (1994) 31-55

49

4.1. Method Subjects Two female and ten male right-handed students participated in one three-hour session. The subjects were 21 to 31 years old and reported having normal vision. Pay varied between 30 and 35 DM and depended partly on performance. Apparatus and stimuli The instruments were generated by a program on a Motorola MVME 133 system with a graphic card on a high resolution color screen (Aschenbrenner; 38 cm x 29 cm, visual angle: 28.2” x 22.2”) 71 cm in front of the subject. The instruments were equally sized (8.5 X 8.5 cm, visual angle: 6.8”) and spaced horizontally and vertically 7 cm (5.6” of visual angle) apart from each other (see Fig. 6). They were red against a black background which had been proved to be most appropriate to avoid eye strain. In order to read its value, an instrument needed central fixation. The outer ranges of the instruments were marked by lines indicating the critical areas. Subjects were instructed to press a button whenever any pointer exceeded the critical boundary. The pointer of each instrument moved continuously along a 90” of arc area according to a sequence of pseudo-random end positions. The 90” area was divided in two outer ranges of 18” (critical areas) and a middle range of 54” (non-critical area). The rate of change of the pointers was variable between some predefined minimum and maximum value. The position of the pointer could not be affected by the subjects. One display always consisted of two equally fast and two equally slow

Fig. 6. The display as shown to the subjects

50

M. Donk /Actu Psychologica 86 (1994) 31-55

instruments. Instruments with the same rate of change were either horizontally arranged (the two fast instruments in the upper two positions and the two slow instruments in the lower two positions or the other way around) or diagonally arranged (one fast instrument in the right upper position and the other one in the left lower position, one slow instrument in the left upper position and the other one in the right lower position or the other way around). The method for measuring eye positions was the same as in Experiment 1 and 2. The Motorola system received on-line eye movement data and registered these data in terms of instrument fixations. As in Experiment 1 and 2, subjects could earn extra money by minimizing the time an instrument was unnoticed in a critical area. Design In a within-subject design, each subject monitored four instruments, arranged in a square, from which two instruments changed fast and two instruments changed slowly. There were two horizontal arrangement conditions and two diagonal arrangement conditions. Each subject performed in all four conditions. The sequence of presentation of these four conditions was determined by a Latin square. Twelve subjects were randomly assigned to three groups of four subjects each. The groups differed in that the absolute rates of change were different. In one group the rate of change of the fast instruments was between 6.25” of arc/s and 1.79” of arc/s and the rate of change of the slow instruments was between 0.74” of arc/s and 0.57” of arc/s (Group 1). In the second group the rate of change of the fast instruments was between 6.25” of arc/s and 1.79” of arc/s and the rate of change of the slow instruments was between 0.45” of arc/s and 0.39” of arc/s (Group 2). Finally, in the third group the rate of change varied for the fast instruments between 6.25” of arc/s and 4.17” of arc/s and for the slow instruments between 0.52” of arc/s and 0.50” of arc/s (Group 3). Procedure After instruction and an appropriate eye calibration, the first session started. It took about 25 minutes and was, except for the arrangement of the instruments, equal to the three following sessions. Each session consisted of a five-minute practice part and a subsequent 16-minute experimental part. The arrangement of the instruments was always the same in both parts of one session. Prior to the start of a session, the experimenter emphasized the importance of detecting when a process entered the critical zone. Furthermore, subjects were informed about the rates of change of the processes, the distribution of these rates over the display and the bonus system for earning extra money. Loading the stimulus generating program took about a minute. Subjects were instructed to start monitoring as soon as the display appeared. After five minutes of practice, the program was restarted and subjects were subsequently required to monitor the same arrangement for 16 minutes. Between sessions subjects had a six-minute break during which they received feedback about their performance.

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51

4.2. Results The description of the results will be limited to the experimental parts of the sessions. The first minute of each experimental part was excluded from analysis. In addition, fixation durations below 200 ms were excluded from the analysis, since they are considered to play no role in sampling (Moray, 1986). Detection performance was practically equal for the slow and the fast instruments. To test whether the sampling interval of either the slow or the fast instruments changed under the diagonal as compared to the horizontal arrangement condition, an ANOVA was carried out on the individual mean sampling intervals with rate of change (fast vs. slow), condition (horizontal arrangement vs. diagonal arrangement) and the grouping factor (Group 1 vs. Group 2 vs. Group 3) as variables. There was a significant main effect of rate of change (F(1,9) = 7.48, p < 0.05). All other main effects were not significant, but the interaction between arrangement and rate of change was also significant (F(1,9) = 4.83, p < 0.05). A subsequent Newman-Keuls Test revealed a significant difference in the mean sampling interval of the fast compared to the slow instruments under horizontal arrangement conditions (Slow-Fast = 811.75 ms, Di = 669.89 at p = 0.05), and a non-significant difference in the mean sampling interval of the fast compared to the slow instruments under diagonal arrangement conditions (Slow-Fast = 366.33

Sampling 4400

- -~

3200

‘p

Interval

(ms)

1 fast

slow Rate of Change ~Fig. 7. Mean sampling horizontal arrangement

horizontal

-

diagonal

interval for the fast and the slow instruments conditions.

under

diagonal

arrangement

and

M. Donk /Acta Psychologica 86 (1994) 31-55

52

ms, Di = 669.89 at p = 0.05). Another Newman-Keuls Test showed the difference in the mean sampling interval of the fast instruments under diagonal compared to horizontal arrangement conditions also to be significant (Diagonal-Horizontal =

Horizontal Condition Proportion o.6l--

~

~~

1

0.5

0.4 ,v-

0.3

-

0.2, 0.1

0 r Ii

VT

HT

DT

Transitions m

observed

k8@ predicted

O.’ ,~ 0 Lm~p VT

HT

DT

Transitions m

observed

k%$! predicted

Fig. 8. The mean observed and predicted proportions of transitions separate for horizontal (HT), vertical (VT) and diagonal CDT) eye movements under diagonal and horizontal arrangement conditions.

M. Donk /Acta Psychologica 86 (1994) 31-55

53

226.67 ms, Di = 224.21 at p = 0.05). The difference between the mean sampling interval for the slow instruments under diagonal compared to horizontal arrangement conditions was not significant (Horizontal-Diagonal = 218.75 ms, Di = 224.21 at p = 0.05). Obviously, the sampling intervals for the fast instruments were strongly influenced by the arrangement in that there was a significantly larger interval when going from the horizontal to the diagonal arrangement. Furthermore, there was a significant difference between slow and fast instruments in the horizontal arrangement condition. Under diagonal arrangement conditions this difference was not significant (see Fig. 7). A similar ANOVA on the individual mean sampling durations did not show any significant effects. The mean sampling duration was 829 ms. An additional analysis was carried out to compare observed and predicted proportions of transitions on the basis of the hypothesis that the displays are independently sampled. For each subject, the predicted proportion of transitions was separately calculated for horizontal (HT), vertical (VT) and diagonal (DT) transitions within each condition and compared with the observed proportion of transitions (see Fig. 8). A Wilcoxon matched-pairs signed-rank test revealed that both under horizontal and diagonal arrangement conditions, the observed proportions of horizontal transitions were significantly larger than predicted on the basis of independent sampling (Horizontal arrangement condition: T = 0, p < 0.01; Diagonal arrangement condition: T = 0, p < 0.01). The observed proportion of diagonal transitions was, under both conditions, lower than predicted (Horizontal arrangement condition: T = 0, p < 0.01; Diagonal arrangement condition: T = 3, p < 0.01). The observed proportion of vertical transitions did in neither condition differ significantly from the predicted proportion of vertical transitions. To investigate whether the difference values between observed and predicted proportions of horizontal, vertical and diagonal transitions were influenced by arrangement, three subsequent Wilcoxon-tests were carried out. They revealed a smaller difference in the diagonal condition compared to the horizontal condition for horizontal transitions (T = 0, p < 0.01) and diagonal transitions (T= 5, p < 0.01). However, even under diagonal arrangement conditions, the proportion of horizontal transitions was still significantly higher and the proportion of diagonal transitions still significantly lower than predicted on the basis of independent sampling. The difference between observed and predicted proportions of vertical transitions did not differ between both conditions CT = 25.5, p > 0.05).

5. General discussion The results are at odds with the predictions of the normative models (Senders, 1983; Sheridan, 1970). Although the relative amount of diagonal transitions increased at the cost of the horizontal transitions under the diagonal arrangement conditions, there are still significantly more horizontal and less diagonal transitions

hf. Dunk /Actu Psychologica 86 (19941 31-55

54

than predicted on the basis of independent sampling. Furthermore, the difference in mean sampling interval of the slow compared to the fast instruments tended to disappear in the diagonal arrangement conditions, suggesting indeed that subjects sample preferably by means of horizontal transitions. This result is not predicted by the normative models, in which sampling behavior is supposed to depend only on the information generation rates of the individual instruments, and also not by Van Delft (1987) who claims that the rate of sampling depends on speed context. In fact, speed context did not change between the horizontal arrangement and the diagonal arrangement. There were no group effects of absolute rate of change. This implies that at least within the limits of the present variations of rate of change, no differences in sampling pattern could be detected. In fact, independent of the absolute rates of change, each group showed the same pattern of results. So far, modelling human monitoring and control behavior has been largely dominated by normative mathematical approaches. The present study does not only show that human monitoring behavior substantially deviates from the optimal but also that monitoring is affected by factors that are not accounted for by the normative models. Research on decision making has shown that there are many fairly simple, logical reasons for systematic departures from optimal behavior (Wickens, 1984). Generally, humans employ heuristics (simplifying rules) to decrease demands on attention and on working memory. The use of heuristics induces systematic biases in performance (Wickens, 1984). A horizontal sampling strategy is such a bias. While independent sampling puts a high demand on processing capacity, the avoidance of diagonal sampling is simple and probably much less demanding (see also Van Delft, 1987). Horizontal eye movements are much more common in our daily activities than diagonal eye movements are. Many tasks like reading and driving may even profit from a habitual tendency of the eyes to move from the left to the right and the other way around. On the other hand, while monitoring, a sampling strategy with an aversion from diagonal and a high priority for horizontal eye movements may unavoidably lead to an increase in control errors. For example, monitoring a fast instrument might suffer substantially when horizontally arranged with a relatively slowly changing instrument. Under such conditions, it might be expected that a horizontal sampling strategy leads to strong ‘oversampling’ of the slow and strong ‘undersampling’ of the fast instrument. On the basis of the present experiments, it might be claimed that, provided that multiple instruments are adjacently arranged in a square, monitoring an array of multiple instruments is biased in such a way that at each moment in time: Pd
in which pd represents the of a vertical transition, and behavior may still be mainly individual instruments in dictated by the information

probability of a diagonal transition, p, the probability p,, the probability of a horizontal transition. Sampling determined by the information generation rates of the the array. However, when the sampling intervals, as generation rates of the instruments, are in conflict with

M. Donk /Acta Psychologica 86 (1994) 31-55

55

the transition bias, observers tend to sample less in accordance with the information generation rates of the individual instruments. Obviously, this rule cannot simply be applied to monitoring tasks involving more than four instruments. Furthermore, it is not clear whether other arrangements, like circular or triangular arrangements, have the same pervasive influence on sampling as rectangular arrangements have. Future research still needs to find out to what extent and under what circumstances arrangement-dependent sampling occurs. However, taking into account the great consistency of the present findings, it seems appropriate to no longer accept the assumption of arrangement-independent sampling. Human-machine system design may certainly be disadvantaged when models are utilized which are based on such a rather untenable assumption. In conclusion, the active role of the operator has been underestimated by the normative models. New models should include heuristics and strategies. Future system design may profit more from such models than from the traditional engineering models which might well have little connection to human behavior.

References Fitts, P.M., R.E. Jones and J.L. Milton, 1950. Eye movements of aircraft pilots during instrument landing approaches. Aeronautical Engineering Review 9, 1-5. Hannen, P., 1987. Systematik in der Reihefolge der Beobachtungen mehrerer unabhangiger binarer Stochasten. Master Thesis, RWTH Aachen. Hogarth, R.M., 1980. Judgement and choice. New York: Wiley. Kvilseth, T.O., 1978. Human and Bayesian information processing during probabilistic inference tasks. IEEE Transactions on Systems, Man and Cybernetics SMC-8, 224-229. Moray, N., 1986. ‘Monitoring behavior and supervisory control’. In: K.R. Boff, L. Kaufman and J.P. Thomas (Eds.), Handbook of perception and human performance, Vol. II: Cognitive processing and performance (pp. 40, I-40, 51). New York: Wiley. Senders, J.W., 1955. ‘Man’s capacity to use information from complex displays’. In: H. Quastler (Ed.), Information theory in psychology. Glencoe, CT: Free Press. Senders, J.W., 1964. The human operator as a monitor and controller of multidegree of freedom systems, IEEE Transactions on Human Factors in Electronics HFE-5, 1-6. Senders, J.W., 1983. Visual scanning processes. Tilburg: University of Tilburg Press. Shannon, C.E., 1948. A mathematical theory of Communication. Bell Systems Technical Journal 27, 379-423. Sheridan, T.B., 1970. On how often the supervisor should sample. IEEE Transactions on Systems, Science and Cybernetics SSC-6, 140-145. Siegel, S., 1956. Nonparametric statistics for the behavioral sciences. New York: MC Graw-Hill. Stein, W. and P.H. Wewerinke, 1983. Human display monitoring and failure detection: Control theoretic models and experiments. Automatica 19, 711-718. Van Delft, J.H., 1987. The development of a response sequence: A new description of human sampling behavior with multiple independent sources of information. Proceedings of the Human Factors Society, 31st Annual Meeting. pp. 151-155. Wickens, CD.. 1984. Engineering psychology and human performance. Columbus, OH: A Bell and Howell Company. Young, L.R., and D. Sheena, 1975. Survey of eye movement recording methods. Behavior Research Methods and Instrumentation 7, 397-429.