LIL
MARIE-EVE lOBIDON
PERFORMANCE IN DYNAMIC DECISION-MAKING :
THE IMPACT OF DIFFERENT TYPES OF TEMPORAL UNCERTAINTY
Mémoire présenté
à la Faculté des études supérieures de !’Université Laval
pour l’obtention
du grade de maître en psychologie (M.Ps.)
École de psychologie
FACULTÉ DES SCIENCES SOCIALES UNIVERSITÉ LAVAL
NOVEMBRE 2001
RÉSUMÉ
Bien que certaines études se soient intéressées aux tâches dynamiques ou à différentes situations d’incertitude, aucune n’a porté particulièrement sur l’influence de différents types d’incertitude sur la prise de décision dynamique. Deux types d’incertitude sont comparés : Incertitude dans la connaissance (EU), soit la variabilité de !’information en lien avec une situation, et Incertitude dans les données (DU), soit la nature plus ou moins complète de cette information. L’objectif de la présente étude est d’établir l’existence empirique de ces types d’incertitude dans la sphère temporelle et d’évaluer leur impact sur la performance. La tâche dynamique utilisée est le jeu informatisé « Save the Whale » (Porter, 1991) dans lequel l’incertitude se situe dans l’occurrence des événements critiques. Les résultats montrent que les participants confrontés uniquement à EU obtiennent une
meilleure performance et que pour l'ensemble des variables et des conditions
expérimentales, la performance s’améliore avec la pratique indépendamment du niveau et du type d’incertitude. Ceci supporte l’existence empirique de différents types d’incertitude temporelle, EU et DU, ayant un impact distinct et additif sur la performance en prise de décision dynamique.
ABSTRACT
Although some studies have been concerned with dynamic tasks or different situations of uncertainty, none specifically addresses the issue of the influence of different types of uncertainty on dynamic decision-making. Two types of uncertainty are compared:
Knowledge Uncertainty (KU), the variability of the information about a situation, and Data Uncertainty (DU), the more or less completeness of that information. The purpose of the present study is to provide an empirical test of these types of uncertainty in the temporal domain and evaluate their impact on performance in dynamic decision-making. The computerized game “Save the Whale” (Porter, 1991) is selected as the dynamic task in which uncertainty is about the moment of occurrence of critical events. Results show that participants faced only with KU perform better and that for all variables and experimental conditions, performance increases with practice regardless of the level and the type of uncertainty. This provides an empirical support to the existence of two types of temporal uncertainty, KU and DU, which have a distinct and additive impact on performance in dynamic decision-making.
AVANT-PROPOS
Je tiens d’abord à remercier tout particulièrement mon directeur et mon codirecteur de mémoire, avec lesquels ce fut un immense plaisir de travailler. Merci au Dr Robert Rousseau pour sa confiance, sa patience, ses judicieux conseils, sa disponibilité et son support. Merci également au Dr Richard Breton pour son support, sa confiance et son enthousiasme contagieux. En vous, j’ai découvert deux scientifiques passionnés aux
qualités humaines exceptionnelles et vous m’avez permis de m’enrichir sans cesse au cours de ces dernières années. Je vous remercie de m’avoir ouvert les portes d’un champ de recherche fascinant et de m’avoir guidée et appuyée tout au long de la réalisation de ma maîtrise. Je ne dirai jamais assez à quel point j’ai été gâtée!
Merci à mes parents, Denise et André, qui m’ont transmis le désir et surtout le plaisir d’apprendre, ainsi qu’à mon frère Éric, pour être le grand frère que toute petite sœur souhaiterait avoir. Merci de votre présence, de votre amour et de votre encouragement. Mais par-dessus tout, merci de votre patience, particulièrement lors des mauvais jours.
Merci à mon meilleur ami Jonathan, un être extraordinaire, pour ton amitié indéfectible, ta générosité, ta compréhension et ton support constant. Merci pour toutes ces fois où tu as su quoi dire et où tu m’as évité de m’égarer. Merci aussi de m’avoir aidée à décrocher lorsque j’en avais besoin.
Merci à mes amis et surtout à ma famille du « 00 » : Isabelle, Julie, Lobna, Christian, François, Geneviève, Daniel, Bastien et Marie-Eve. Merci à vous tous pour tous les moments merveilleux que nous avons partagés. Un gros merci en particulier à Isabelle et Julie pour votre amitié et votre présence, qui m’ont souvent aidé à continuer lorsque je doutais. Merci à vous tous d’avoir été là, tant comme collègues que comme amis. Vous avez fait de ces années un souvenir impérissable et je vous en serai toujours
reconnaissante.
Merci à Andrée Gignac et Nicole Aubin pour être aussi merveilleuses. Merci pour votre aide si précieuse et votre bonne humeur rayonnante.
Enfin, merci à tous les participants qui ont accepté de prendre part à cette recherche et sans qui elle n’aurait pu être réalisée. Merci également au FCAR et au CRSNG pour leur appui financier au cours de ces deux dernières années, par !’intermédiaire des bourses aux études supérieures. Grâce à leur support, j’ai pu me concentrer entièrement sur mes études et mes recherches.
TABLE DES MATIÈRES
Résumé... 1
Abstract...2
AVANT-PROPOS... 3
Tabledesmatières...4
Tableslist...5
FIGURE captions... 6
Uncertainty... 9
Dynamic situation...11
Computer games... 14
Save the Whale... 16
Objectives and hypotheses... 18
Method...21 Participants... 21 Apparatus... 22 Procedure... 23 Results...25 Performance variables... 25 Control variables... 26 Questionnaires...28 Discussion...29 CONCLUSION générale... 33 references... 45 Appendixa...49 Appendix B...51 Appendixc...54
TABLES LIST
ANOVA and tests of simple main effects for the mean number of cycles spent in the second quadrant as a function of group and boards.
FIGURE CAPTIONS
Example of a trial for all experimental conditions, (a) A trial for the KU condition. Kayaks follow an irregular but constant pattern throughout boards, (b) A trial for the DU condition. Kayaks appear randomly according to a rectangular distribution of more or less four cycles around the original cycle (used in the KU condition), (c) A trial for the CU condition. A kayak can arrive at any moment between the preceding and following kayaks.
Mean total score as a function of group and boards (by groups of ten).
Mean number of harpooning as a function of group and boards (by groups of ten).
Mean number of crashed kayaks as a function of group and boards (by groups of ten).
Mean number of changes of direction as a function of group and boards (by groups of ten).
Mean number of cycles spent in the first quadrant as a function of group and boards (by groups often).
Mean number of cycles spent in the second quadrant as a function of group and boards (by groups of ten).
Mean number of cycles spent in the third quadrant as a function of group and boards (by groups of ten).
Figure 1, Figure 2. Figure 3, Figure 4, Figure 5, Figure 6. Figure 7, Figure 8,
Figure 9. Mean number of cycles spent in the fourth quadrant as a function of group and boards (by groups of ten).
Figure 10. Mean number of cycles spent in the center as a function of group and boards (by groups of ten).
INTRODUCTION GÉNÉRALE
La prise de décision est omniprésente dans la vie quotidienne et toutes les décisions impliquent un niveau d’incertitude plus ou moins élevé. En effet, il est rare que l’ensemble des options possibles ainsi que toutes leurs caractéristiques soient connues et clairement définies. Afin d’assister les personnes dans leur processus décisionnel, des systèmes d’aide à la décision sont développés. Ces systèmes visent à supporter l’humain dans l’exécution de prises de décision complexes impliquant une multitude de sources d’information, ces sources présentant un niveau d’incertitude plus ou moins élevé. Ainsi, !’utilisateur du système, qui se garde toujours la responsabilité de la décision finale, se voit de plus en plus confronté à des situations complexes et incertaines et subit une pression temporelle accrue. La composante temporelle étant critique dans ces situations, l’étude de l’incertitude
temporelle et de ses impacts sur la performance s’avère particulièrement pertinente.
La présente étude s’intéresse aux effets de l’incertitude temporelle sur la prise de décision dans le cadre d’une situation dynamique complexe. La prise de décision est envisagée ici non pas de façon traditionnelle en tant que résolution d’un dilemme entre plusieurs options, mais plutôt en termes de contrôle d’un procédé ou d’un système. Ainsi, tel que le propose Brehmer (1990) la prise de décision dynamique est considérée comme le processus permettant d’atteindre le contrôle d’un système afin de parvenir à un objectif précis.
Jusqu’à maintenant, peu d’études se sont intéressées à l’impact de différents types d’incertitude sur l’action. L’intérêt de cette question réside notamment dans le fait que les contraintes temporelles sont omniprésentes en prise de décision et que les stratégies utilisées pour diminuer efficacement le niveau d’incertitude devraient différer en fonction du type et du degré d’incertitude rencontrés dans une situation donnée.
Performance in dynamic decision-making : the impact of different types of temporal uncertainty
Uncertainty
There are many well documented cognitive factors that have been proved to exert an important influence on decision-making, among others, time pressure, mental workload, available attentional resources, and working memory limitations (Cook & Woods, 1994; Reason, 1990; Wickens, Gordon, & Liu, 1998). However, while playing a significant role, uncertainty in decision-making has received less attention in previous work in psychology. Uncertainty is intrinsically linked to decision-making. That is, as pointed out by Achrol (1988), without the necessity to make a decision, there is no reason to be uncertain. Uncertainty is a concept that has been mostly studied under a formalist viewpoint or in regard of the degree of tolerance to it, and even if several definitions have been proposed over the years, no consensus has been reached yet. Levis and Athans (1988) give a global definition of uncertainty, which they define as the difference between information needed to solve a problem or a situation, and the information available at the time the decision has to be made.
While it is possible to give a general definition of uncertainty, it appears, when one attempts to define it more specifically, that it is a complex concept with various aspects. For example, Correa da Silva et al. (Correa da Silva, Robertson, & Hesketh, 1994) propose three particular aspects of uncertainty, which embrace this concept in a relatively
exhaustive manner. The first aspect, vagueness, refers to the degree to which a non
categorical statement is true. The second aspect, statistics, concerns the probability that an element or a group of elements that belong to a domain is being selected. Finally, the third aspect is the degree of belief, which corresponds to the truth subjectively attached to each statement. For his part, Ralston (1988) points out four types of uncertainty commonly linked to a field of expertise: (a) uncertain knowledge (often, the expert has only a heuristic knowledge of the domain of expertise); (b) uncertain data (it is impossible to obtain precise
data); (c) incomplete information (data may be precise but it is not possible to obtain all the information required to make a decision); (d) randomness (some domains include inherent random properties).
Furthermore, Rastegary and Landy (Gifford, Bobbit, & Slocum, 1979; Rastegary & Landy, 1993) propose two interdependent categories of uncertainty: (a) the variability of a situation; (b) the character of the information related to that situation. The first category refers to the degree to which the situation is changing and to the possibility to predict the different consequences related to those changes, while the second category refers to the more of less completeness of the information that one possesses to make a decision regarding that situation. It is important to note that Gifford and his colleagues (Gifford et al., 1979) originally presented this distinction as applying to definitions of uncertainty rather than to the concept of uncertainty itself; that is, a given definition being either classified in the first or second category depending on the approach it supports. However, this differentiation is here considered as being applied to the categorization of uncertainty itself (and of its components) instead of to the categorization of its definitions. Uncertainty may exist at different levels (individual, group, organization, environment, etc.) and the degree of uncertainty at one level influences the degree of uncertainty at the others. A given level contains several sources of uncertainty (for example, complexity and novelty), and sources at one level may influence the degree of uncertainty at another level of the system.
All types or aspects of uncertainty proposed by these authors can be categorized into two general types of uncertainty, based on the distinction made by Rastegary and Landy (1993), that are labeled knowledge uncertainty and data uncertainty. Knowledge
uncertainty refers to the variability of a situation, which corresponds to the degree of change and irregularity of the situation and the possibility to anticipate the related
consequences; it can be reduced by a recurrent exposure to the situation. Data uncertainty refers to the nature of the information linked to that situation, which corresponds to the
vague and uncertain aspect of the data, and allows only a probabilistic knowledge of a situation despite repetitive exposure.
Dynamic situation
Uncertainty has been the subject of an extensive body of work with static tasks like risk evaluation or probabilistic decision-making. For example, Barkan, Zohar and Erev (1998) conduct an experiment to study probabilistic decision-making under uncertainty, in which participants are presented with a signal detection task. They have to decide whether or not a white square presented on the screen was high or low, according to the hint they are given prior to the beginning of the experiment about the probabilistic nature of the square. Participants earn points based on their decision (a penalty was attributed for a Miss) and on the payoff matrix used. Six payoff conditions are tested, three being gain matrices and three others loss matrices, and participants are not aware of the matrix employed. Results show that initially, participants tend to make riskier decisions and that they adopt safer behaviors with experience. Also, with a lower probability of penalty, the learning process is impaired because decisions become riskier. According to the authors, these results suggest that a little amount of quantitative information can exert a significant influence on risk taking behavior in uncertain situation as well as on the rapidity of the adaptive and learning process
While static decision-making refers to a situation in which decisions are independent from each other, dynamic decision-making is of more complex nature. A dynamic situation is a situation in which the decision made and the action achieved by someone at a time t have an effect on what happens in that situation at a time t+J. Edwards (1962) identifies three criteria that define dynamic decision-making: (a) to reach the objective requires a succession of decisions, and each decision can only be understood in the context of the other decisions related to the situation; (b) decisions are not independent, previous decisions conditioning subsequent decisions; (c) the state of the situation changes, both autonomously and as a result of decision maker’s actions. Brehmer (1992) adds a fourth
criterion to those of Edwards: for the situation to be qualified as dynamic, decisions must be made in real time. Brehmer (1992) concludes that dynamic decisions take place within a given moment and context. Therefore, a dynamic situation can be qualified as complex, fluid and continuous, since it takes place in real time (Porter, 1991). According to Porter, this kind of situation contrasts with traditional tasks used to study decision-making in psychology, like anagram solving, in which each response is discrete and unlinked with previous or subsequent responses or events. In fact, traditional tasks are based more on the trial-error principle, because the correct answer is known and determined in advance by experimenters.
According to Dörner (1991), a complex and uncertain situation is defined as a dynamic situation of which one does not hold complete knowledge and which exerts a time pressure because of its continuously changing nature. Such a situation is also too complex to be totally understood and the goal of the actions is often not clearly explicit and not detailed. Dörner (1991) stresses that the use of computerized simulations of real dynamic systems is ideal to study human behavior faced with uncertainty and complexity, because it offers a diagnostic tool allowing the identification of action-related errors (goal elaboration,
gathering and analyzing data, actions planning, etc.) as well as of strengths and weaknesses of a person who has to deal with a particular situation.
In order to study the process of achieving control over a complex system and to evaluate the impact of different variables in dynamic situations, researchers have developed and used a methodology based on the use of computerized simulations of a dynamic system (e.g. Brehmer & Allard, 1990; Dörner, Kreuzig, Reither, & Stäudel, 1983; Dörner, Stäudel, & Strohschneider, 1988, reported in Brehmer & Dörner, 1993). Such a simulation, called “microworld”, combines the prominent characteristics of the system, without including details. It is a simplification of a system, from which the complexity requiring a specific expertise is withdrawn. Thus, the original system that is represented is easily recognizable, but no expertise or particular knowledge is required to take part in the experiment, training being maximally reduced. All microworlds share three principal
characteristics; that is, they are complex, dynamic and opaque (Brehmer & Dörner, 1993). Micro worlds are complex because of the fact that they imply multiple goals, decisions and courses of action, constraining someone to continually make choices between various alternatives. They are dynamic in the way that they evolve in real time both autonomously and as the consequence of someone’s actions. Hence, the person has to deal with several time scales simultaneously, which is why microworlds are intrinsically stressful. Finally, microworlds are opaque, which means that some of the system’s characteristics are not observable and must be inferred.
Different system’s aspects or variables have been studied over the years using dynamic situations in general or microworlds in particular. For example, in a series of experiments using a forest fire fighting simulation (Brehmer, Lovborg, & Winman, 1992), it has been demonstrated that if they have the opportunity, participants faced with a task they cannot perform optimally will find a way to complete the task in a reasonable manner (that is, costs might be higher than previously expected). Precisely, in these experiments, participants manage to successfully accomplish the task without having to consider a critical element, that is, time constant.
Kerstholt (1995) conducts a study in which participants have to monitor the fitness level of a simulated athlete and to administrate a treatment whenever the fitness level decreases significantly, suggesting a physiological problem. To evaluate the effect of time pressure and false alarms, Kerstholt manipulates the pace at which the fitness level declines and the a priori probability of false alarms (a false alarm happens when no real problem sustains a lower fitness level and is followed by a spontaneous recovery). According to Kerstholt, when faced with an uncertain situation, people generally wait before taking action in order to appraise how the situation evolves through time. Under time pressure however, the optimal strategy would be to react immediately after the onset of the disturbing event, even if it increases the risk of unneeded intervention. The results show that participants do not use this optimal strategy under time pressure, but rather make judgement-based decisions, gathering more information before applying an action. Also, when time pressured,
participants adjust the number of interventions according to the a priori false alarm
probability rather than on the time constraint. Another interesting result is that participants tend to be risk averse: they try to prevent an athlete’s collapse by taking action before the critical point in time; that is, when participants intervene, there is still time to verify the possibility of false alarm and to gather more information on the exact nature of the problem. As Kerstholt points out, these results suggest that strategies adopted in dynamic situation may not be as adaptive as what was previously demonstrated in static tasks (Kerstholt, 1995).
Carreras, Valax and Cellier (1999) assess how people reduce the temporal complexity of a dynamic system to achieve control over it. They use a microworld simulating a water purification plant, in which participants have to manage the different steps and operations underlying the purification process. Results show that regardless of the degree of
complexity encountered, participants reduce temporal complexity over time by organizing their actions based on temporal occurrences and regularities. According to the authors, these results suggest that participants construct a mental representation of the temporal structure of the dynamic situation, in order to achieve control over it.
Computer games
Computer games, which can be considered as a type of micro worlds, are dynamic situations that have been used for many years in experimental researches (e.g. Foss, Fabiani, Mané, & Donchin, 1989; Logie, Baddeley, Mané, Donchin, & Sheptak, 1989; Porter, 1991; Toda, 1962). The use of such games is interesting because of its advantages compared to traditional laboratory tasks. Video games represent a complex reality similar to those we encounter in real life, with multifaceted situations and complex problem solving. Moreover, according to Malone (1980), most games are intrinsically motivating because of three main characteristics: challenge, fantasy and curiosity. For Porter (1991), the game situation implies also a considerable motivational component, which often brings participants to entirely concentrate on the game and to forget the laboratory context, which
can, at the same time, increase the ecological validity of the results. However, as stressed by Donchin (1995), researchers must developed their own experimental games since with commercial games, it is not possible to control and manipulate game’s parameters.
Two good examples of such methodology are the Fungus-Eater game, developed by Toda (1962) and the Space Fortress game, developed in the early 1980’s and used in a number of studies since its creation. The Fungus-Eater (Toda, 1962) is a game in which a robot is sent to a planet to dig uranium. In order to have the strength to mine, the robot eats fungi that grow on the soil of that hypothetical planet. Thus, the participant must manage robot’s resources to make sure the robot has always enough energy to mine uranium and to feed itself. Toda considers this game as a microcosm; that is, as a “problem consisting of a wide variety of mutually dependent subproblems” (Toda, 1962, p. 166). The Fungus-Eater game is then a dynamic complex task that requires the execution of simultaneous activities to be completed successfully.
The Space Fortress game was mainly used as the research tool of a project called Learning Strategies Program that took place in seven different universities spread in four
countries, from 1983 to 1986 (Donchin, Fabiani, & Sanders, 1989). In this game, the participant controls a spaceship that aims to destroy a space fortress, while avoiding being damaged either by projectiles fired from the fortress or by foe mines that appear on the screen. Mines can also be friend, and their exact nature (friend or foe) is indicated by a predetermined letter. The effect of different independent variables can be evaluated with this game, like time pressure, resource management, skills acquisition or memory load. The general purpose of the program is to assess the degree to which it is possible to improve skill acquisition by supervising the process of practice. Results obtained from studies conducted with a control group (Foss et al., 1989) show that performance
systematically increases with practice and that strategies and control behaviors adopted are determined not by instructions given to the participant, but by the scoring rules specified; that is, participants try to maximize their score rather than to respond to a specific
non negligible influence of individual differences with the use of a video game in experimental work, such differences being attributable in part to the degree of previous exposure to video games (Donchin, 1995; Foss et al., 1989).
Save the Whale
In order to study cognitive processes like decision-making in a more real, complex and dynamic situation than the commonly used static laboratory tasks, Porter (1991) developed the game “Save the Whale”. That computerized game provides the opportunity to study simultaneously several variables, amongst others uncertainty, and to record many
performance indexes without requiring more resources. Thus, the recorded measures are more representative of the complex reality of decision-making. Complexity arises both from the presence of uncertainty and from several events that happen simultaneously. As for the dynamic aspect, it corresponds to the fact that action takes place in time in a continuous way. As a result, the current state of a situation, and consequently possible course of actions, are delimited in part by the decision maker’s previous actions. The correct response is therefore determined a posteriori rather than a priori, based on
performance indexes that allow the comparison between the appropriate response patterns with those which lead to a poor performance.
The dynamic task used in the present study is the computerized game “Save the Whale”, adapted from Porter (1991). Originally, the game included two distinct tasks in the course of which the participant must move the whale on the screen (an ocean with icebergs) according priority to one of two objectives, either eat plankton or escape kayaks that try to harpoon the whale. The plankton task consists in the pursuit of a green plankton chunk that progresses according to a probabilistic trajectory, from the middle of the screen to the right, going first toward the bottom of the screen and then coming back up. When it reaches the right border of the screen, the plankton disappears and then reappears at the left border, to resume its path. Although the general trail is repeated, the precise sequence of plankton’s movements is variable and generated by a complex random-walk type
algorithm. As indicated by Porter, the uncertain moves of the plankton solicit the player’s attentional resources and require quick reactions. Thus, this task is simple but uncertain, and it relies more on the motor skills than on cognitive planning; it is a simple motor pursuit task.
In the second task, the kayak task, kayaks that enter from any of the four borders of the screen at various moments chase the whale. From the moment that a kayak appears on the screen, it follows only one rule: moving toward the whale, either vertically, horizontally or diagonally. Kayaks disappear from the screen after one of two events; that is, either if a kayak crashes into an iceberg or harpoons the whale. The whale must therefore force kayaks to crash on an iceberg in order to avoid being harpooned. This task is considered complex but predictable, and the participant has to elaborate certain strategies to eliminate kayaks. Porter (1991) stresses that the execution of the kayak task would not involve attentional resources, and that verbal reports on the accomplishment of the task are generally vague and inconsistent.
In an experiment with this game, Porter (1991) studies the impact of a concurrent memory load on the performance at both the kayak and plankton tasks. It is observed that an increased concurrent memory load has no effect on the performance at the kayak task while interfering significantly with that of the plankton task. In addition, while verbal reports of participants, notably about strategies used, are consistent with performance in the plankton task, there is a lack of correspondence in the kayak task. According to Porter (1991), these results suggest that the two tasks are processed differently, and that the plankton task requires attentional resources while the kayak task does not requires such resources.
The main interest in using Porter’s game is the possibility it allows to manipulate uncertainty variables within a complex controlled dynamic task, which at this time has only been done a few times. In fact, as stressed by Brehmer (1992), it is possible, on one hand, to study dynamic decision-making in real settings, but the complexity of the systems
encountered complicates the analyses and makes more difficult the elaboration of models and theory. On the other hand, laboratory tasks are often artificial and not representative of dynamic situations of which the course is both autonomous and influenced by the person’s actions, while taking place in real time (which often is not the case with traditional
laboratory tasks).
The resort to computerized dynamic tasks, like the microworlds developed and used by Brehmer and Dörner and their colleagues (e.g. Brehmer & Allard, 1990; Dörner, Kreuzig, Reither, & Stäudel, 1983; Dörner, Stäudel, & Strohschneider, 1988, reported in Brehmer & Dörner, 1993) thus constitutes a judicious choice for the study of uncertainty, since this paradigm represents a complement to field researches by preserving their opaque (that is, all system’s characteristics are not automatically and simultaneously revealed to the participant, allowing him or her to elaborate hypotheses and possible courses of actions), dynamic and complex aspects, while enabling a better control than usually authorized by laboratory methods. In particular, the choice of the game “Save the Whale” relies on the fact that it is a simple task that requires little training and allows the manipulation of different variables without interference from the environment.
Objectives and hypotheses
The present research aim is to study the effect of different types of temporal uncertainty on decision-making in the context of complex dynamic tasks and this, in order to improve the understanding of human behavior in this kind of situation. Temporal uncertainty is of main interest because of the intrinsic nature of dynamic situations. Indeed, because a dynamic situation takes place in real time, the temporal constraint is omnipresent and has to be dealt with efficiently. Also, this interrogation appears particularly pertinent, because the strategies one has to apply to decrease uncertainty efficiently will differ according to the type or degree of uncertainty encountered in a situation.
The task through which uncertainty is manipulated is the game “Save the Whale” (adapted from Porter, 1991). The predictable character of the kayak task is manipulated in order to study the influence of different types and degrees of uncertainty. Thus, by
modifying the temporal pattern of kayaks entrance (by making it more or less uncertain) it is possible to evaluate the effect of uncertainty on decision-making and to determine if participants are capable of anticipating the events. It is important to note that the spatial pattern of events, that is, the sequence of points from where kayaks arrive on the screen is invariable throughout the game; from one board to another, kayaks always arrive from the same fives points of entry, which are the same for all three groups. Hence, since the spatial aspect is maintained constant, temporal uncertainty is isolated.
From Javaux (1994) and Grosjean and Terrier (1999), temporal awareness can be
defined as the mental representation that one develops about the temporal characteristics of a situation; that is, the evolution of events in a recent past, the present and a near future. Temporal uncertainty is therefore the lack of knowledge about the temporal structure of events, leading to an incomplete or vague representation. Similarly, the spatial awareness is the representation developed about the characteristics of a situation in the physical space, like the exact place where an event will take place in the environment. Consequently, spatial uncertainty is the vagueness or incompleteness of that representation.
As previously noted, the two types of uncertainty studied here are based on the
distinction presented by Rastegary and Tandy (1993) and originally established by Gifford and his colleagues (Gifford et al., 1979). Three different conditions, illustrated in Figure 1, are evaluated within the scope of the current research. The uncertainty is linked to the complexity of the temporal pattern of events. Low uncertainty would be the case when the occurrence follows regular isochronic pattern. Rhythmic patterns would be the
intermediate and arbitrary patterns in which occurrence follows no rule other than the sequence of fixed intervals bearing no relation to each other would provide the highest level of uncertainty. Consequently, the first condition, Knowledge Uncertainty (KU) refers to Rastegary and Tandy’s first type of uncertainty, which is the variability of a given
situation. Participants of this group are faced with a complex pattern of kayak arrivals, which is repeated for each board. Precisely, these events are the moments and places determining kayaks appearance on the screen. Therefore, the occurrence of the events themselves is certain and always happens at the same moment from one board to another, but the nature of the pattern of events is uncertain because of its complexity. In that kind of situation, uncertainty can be reduced with expertise, since there is an increase of the
statistical knowledge of the environment and consequently, of the sequence of events.
The second experimental condition, Data Uncertainty (DU) refers to the second type of uncertainty presented by Rastegary and Landy (1993), that is, the more or less complete nature of the information available for the person to make a decision in regard of the
situation, which is included in addition to the first type of uncertainty. In this condition, not only the sequence of events is complex, but the moment of occurrence itself is uncertain, since it happens within a temporal window centered on the moments of the original sequence. Thus, the moment of occurrence of a kayak can be seen as a random variable with a rectangular distribution of which the mean corresponds to the moments of kayaks appearance in the pattern used in the first condition. In this condition, the pattern becomes approximate.
The third condition, Control Uncertainty (CU) implies also the two types of
uncertainty, but to a greater degree than the second condition. A new irregular pattern is defined at each board, delimited only by the spatial sequence of events that remains constant. Temporal information is reduced to the minimum, which means that the
succession of kayak arrivals (that is, Kayak 1 always arrives first, followed by Kayak 2 and so on) is the only certain information available to the participant from board to board, which makes impossible the use of strategies based on the development of the knowledge of a recurrent temporal pattern. Temporal information is then limited to temporal order information. Interval information (between events) is not maintained, leading to
Two types of measures are recorded. First, the behavior of the whale, that is the participant’s actions, is evaluated through continuous performance measures recorded by the software, such as the total score accumulated for each board or the number of cycles spent in each quadrant of the screen. Thus, it is possible to observe if the player improves his or her performance (and consequently his or her mastery of the uncertainty) through the repetition of boards. The second measure is a questionnaire presented to participants after the second experimental session. It is a means to obtain information from them on the strategies they used, their capacity to anticipate the events and on the degree of uncertainty experienced during the experimentation (Appendix A).
It is possible to elaborate different hypotheses regarding the expected results. Thus, participants in the KU condition should be able to reduce uncertainty through the improvement of their statistical knowledge of the environment, developed by practice. Indeed, from board to board, participants of this group should be capable to infer the pattern of the sequence of events, leading to an increase in performance (as indicated by the total score) due to the fact that actions are based on anticipation of the events rather than only to reaction to their occurrence. Because of the vague and uncertain aspect of the moment of occurrence of the events from one sequence to the next, learning should be lesser in the DU and CU conditions than in the KU condition. A difference between the second and third conditions is also expected, since the possibility to reduce uncertainty is even more diminished in the latest, the temporal window of occurrence of each events being random.
METHOD
Participants
Fifty-seven participants, 33 women and 24 men whose age varied from 18 to 58 years, the mean being 24,23 years (sd.=l,53 years) take part in this study. Participants are mainly undergraduate and graduate students of Université Laval who give a written consent of
their participation (Appendix B). Participation is on a voluntary basis and each participant receives a 10S monetary compensation.
Participants are equally and randomly divided into three experimental groups
approximately matched in regard of age and gender. Therefore, each group includes eleven women and eight men and the average age is respectively 23,42 (sd=8,58 years), 25,05 (sd=6,09 years) and 24,21 years (sd=5,81 years) for the KU, DU and CU groups.
Apparatus
This experiment is run on a PC with a VGA 13 inches color screen and a keyboard. The experimentation takes place in an isolated experimental room to maximally reduce external distractions, and each participant is evaluated individually. Participants are seated at about 50 centimeters from the screen. The dynamic task used is the computerized game “Save the Whale”, adapted from Porter (1991). In this game, the whale represents the participant. It evolves in a blue ocean in which are dispersed static white icebergs. Movements are
accomplished with the cursor keys, four arrows displayed on the keyboard, the whale moving in the direction indicated by the arrow on the depressed key. The whale keeps moving in the same direction as the last key pressed, until an other key press changes the direction of the movement. The whale can move toward the top, bottom, left and right to the rhythm of one movement each 500 ms, but it cannot go beyond the limits of the screen neither move diagonally. If the whale runs across an iceberg, this one disappears. Kayaks appear from five different origins on the four sides of the screen, according to a
predetermined and experimentally controlled sequence. For the purpose of measurement and data interpretation, the screen is divided into five distinct areas: four quadrant, counted clockwise from the upper left corner of the screen, and the center section of the screen (see Appendix C for an illustration of the game and of the quadrants).
At the end of the second session, participants fill a custom questionnaire designed to gather various information like the uncertainty perceived during the game, the capacity to
anticipate events and the strategies used to play. Also, since the exact goal of the research cannot be revealed prior to the experimentation, participants sign a second consent form to allow or deny the use of their data. They do so after having received complete information about the objectives of the study.
Procedure
The experimentation includes two experimental sessions, with a total duration of approximately 60 minutes, during which the participant completes a certain number of boards (each board corresponding to one trial). The task consists of accumulating points by bringing red kayaks to crash on icebergs (each crashed kayak is worth 100 points) or by eating plankton (one bite is worth 10 points), while avoiding being harpooned by kayaks, each harpooning leading to a loss of 100 points. At the end of each board, the total score collects during the trial is displayed on the screen.
In this game, the participant completes a series of boards. A board includes a certain number of cycles, each one having a predetermined fixed duration according to the
objectives of the study. At each cycle, the plankton, the kayaks and the whale execute one move. Thus, the duration of cycles establishes the speed at which the game progresses. Conditions concerning the point value assigned to the various events (eating plankton, whale being harpooned, kayak crashing into an iceberg) are fixed for a board and the computer registers performance measures for each board. The moment (the cycle) when a kayak will appear on one of the side of the screen, as well as its position, are
preprogrammed. In this study, the spatio-temporal sequence of a series of kayak appearance within a board is called a “pattern”.
Kayaks occurrence constitutes the events that happen in the environment, and they appear according to a predetermined spatial-temporal sequence within each board.
Precisely, for the KU condition, kayaks arrive at cycles 5, 19, 26, 31, 45, 49, 63, 70, 74 and 88. For the DU condition, each cycle of the first condition is substituted by an interval of
plus or minus four cycles, of which the median is the original cycle. For example, the kayak arriving at the fifth cycle in the KU condition arrives between the first and the ninth cycle in the DU condition, the exact cycle being uncertain from one board to the next. Concerning the CU condition, the temporal interval of kayak’s arrival is delimited only by spatial sequence: for example, the Kayak 3 can appear at any cycle between the arrival of the Kayaks 2 and 4.
If kayaks are vertically or horizontally aligned with the whale, they move directly toward it at the rhythm of one space every 500 ms. If they are not aligned with the whale, kayaks then move diagonally toward it. There can be zero to five kayaks present
simultaneously on the screen. A kayak disappears from the screen when it crashes or when it harpoons the whale. If five kayaks are present on a cycle when a new one should enter the game, it simply does not appear and thus the total number of kayaks occurring in that board is reduced by one.
Each board includes 100 cycles of 500 ms each and is then 50 seconds long. For each session, participants completed 30 experimental boards in addition of a practice board, at the beginning of the session, in order to familiarize with the task and the manipulation of the keys. General instructions are given verbally to the participant and specific task related instructions, both for practice trial and experimental trials, are displayed on the screen at the beginning of the session.
At the beginning of the first session, the researcher gives general instructions about the game, its rules and the mode of control with the cursor keys to the participant, who signs a consent form in which it is specified that the exact goal of the study cannot be revealed. At the end of the second session, the researcher presents the exact goal to the participant who then signs a second consent form by which they either agreed or not to the use of the data gathered through their participation.
RESULTS
Analyzed data are draw from measures recorded by the software, which represents various performance and control variables. The data were gathered during 60 experimental trials, 30 trials per session, for 57 participants.
Analysis of variance (ANOVAs) were completed according to a split-plot factorial design (SP-p.q) (Kirk, 1995) to verify the presence of significant differences between means for the total score, the number of direction changes of the whale, the number of harpooning, the amount of crashed kayaks and the number of cycles spent in the four quadrant and in the center of the screen, as a function of groups and boards (the board variable represents the division of all 60 boards in groups of ten). For all statistical procedures, an alpha level of .05 was used.
Performance variables
Results obtained from the ANO VA performed for the total score show a significant difference between the three groups, F(2, 54) = 3.86, p < .05. Therefore, participants in the KU condition obtained a mean total score higher than those in the DU and CU conditions. Furthermore, as displayed in the Figure 2, total scores obtained by the participants
increased significantly throughout the boards, for all three conditions (F(5, 270) = 109.17, P < .0001). Interaction between group and boards was not significant (F(10, 270) = 1.21, p = .29).
Regarding the number of harpooning, both group and board effects appeared
significant. Therefore, participants in the KU condition were harpooned significantly less often than the participants in the DU and CU conditions (F(2, 54) = 3.21, p < .05). The number of harpooning decreased significantly throughout the boards for participants in the
three groups (F(5, 270) = 103.34, g < .0001), as shown in Figure 3. Interaction between group and boards was not significant (F(10, 270) = 1.31, g = .22).
Figure 4 displays the number of crashed kayaks according to groups and boards. Both group and board effects were significant. Hence, participants in the KU condition brought significantly a higher number of kayaks to crash compared to those in the DU and CU conditions (F(2, 54) = 4.59, g < 05). In addition, for each group, the number of crashed kayaks increased significantly throughout the boards (F(5, 270) = 109.85, g < .0001). Interaction between group and boards was not significant (F(10, 270) = 1.01, g = .43).
Control variables
The main control variable evaluated in the current study was the number of direction changes of the whale, as a function of practice, which are shown in Figure 5. Only the board effect was significant (F(5, 270) = 7.36, g < .0001). It appears that participants in all three groups made more direction changes throughout the boards. However, no difference between groups appeared, all participants making about the same number of changes of direction during the game (F(2, 54) = 1.38, g = .26). Interaction between group and boards was not significant (F<1).
The number of cycles spent in the four quadrants and in the center of the screen was also analyzed. In regard of the first quadrant, neither the group effect (F<1) and the interaction (F(10, 270) = 1.36, g = .20) were significant, but as can be seen on Figure 6, participants in all groups spent more cycles in the first quadrant as practice progressed
(F(5, 270) = 5.79, g <.0001).
Regarding the number of cycles spent in the second quadrant, no significant differences was obtained between groups (F(2, 54) = 1.82, g = .17), but the board effect was
all groups spent significantly less cycles in the second quadrant throughout the boards. The interaction between group and board effects being significant (1(10, 270) = 2.30, p < 0.05), tests of simple main effects were conducted (Table 1). With a Dunn’s procedure, a
significant difference was obtained between groups of boards for the DU group only (F(5, 270) = 16.83, p < 0.0001), but not for the KU and CU groups. Also, there was a significant difference between groups for the first group of boards (representing the first ten boards) (F(2, 270) = 16.49, p < 0.0001), while there was no difference for the other groups of boards. Thus, for the first ten boards, participants in the DU group spent more cycles in the second quadrant than those in the KU and CU groups, but the three groups were equivalent for all the other groups of boards.
For the third quadrant, no significant differences appeared (F<1 for the group effect and the interaction and F(5, 270) = 1.90, p = .095 for the board effect)(Figure 8).
Although, for the fourth quadrant, the results were not significant for group and board effects (respectively F(2, 54) = 2.91, p = .06 and F(5, 270) = 1.84, p = .11) nor the interaction (F<1), a marginal effect was observed for the group effect. Therefore, as displayed in Figure 9, the participants in the KU condition tended to spend less cycles in the fourth quadrant than participants in the DU and CU conditions.
Regarding the number of cycles spent in the center of the screen, neither the group effect nor the interaction were significant (F<1). However, as illustrated in Figure 10, a significant difference was obtained for the board effect (F(5, 270) = 9.05, p < .0001), which means that participants in all groups spent more cycles in the center of the screen throughout the boards.
Questionnaires
When asked if they were able to anticipate events or if they mostly reacted to them, the majority of participants in the KU group answered that after a few boards, they noticed the pattern was always the same and that they were able to anticipate the events. However, answers of participants in the DU and CU conditions were more varied. Participants in the DU group tended to respond that they reacted to events during the first session and that they were able to anticipate during the second session, but some also responded that they mostly reacted to events and others that they were able to get an overview of the pattern but that it was difficult to anticipate. Finally, most participants in the CU condition answered they were not or barely able to anticipate events and that they generally reacted to events throughout the two sessions.
When asked to which degree they experienced uncertainty during the game, about all participants in the KU condition answered that they perceived uncertainty only at the beginning of the game and that after a few boards, it disappeared. For the DU and CU conditions, participant’s answers were more heterogeneous. Hence, participants in the DU group were divided between experiencing uncertainty at the beginning or during the first session but not the second, at an average level throughout the two sessions or until a good strategy was found. Concerning the CU condition, some participants experienced
fluctuating uncertainty during both sessions (some points at a low degree and some others at a high degree), some experienced a relatively constant degree of uncertainty throughout the game, either low, average or high, and finally, some participants answered that they felt a high degree of uncertainty during the first session, which decreased to a lower level in the second session.
When asked about the strategies they used to complete the game, most of the
participants in the KU group ignored the plankton and used the cluster of icebergs in the first quadrant to force kayaks to run aground. Participants in the DU and CU conditions also reported using these strategies, but it was less commonly used than in the KU
condition. Strategies reported by participants in the DU group also included staying in the third or forth quadrant, or in the middle of the screen and controlling the whale’s
movements to get kayaks to crash. In addition to all strategies already mentioned,
participants in the CU condition also reported using strategies like forcing kayaks to crash away from the whale, positioning the whale in precise and strategic places, and moving the whale very fast to slow down kayaks. Therefore, strategies reported by participants in the DU and CU conditions were more varied and vague than those reported by participants in the KU condition.
DISCUSSION
Few studies have examined the influence of different types of uncertainty on dynamic decision-making. Although some have been concerned with dynamic tasks or different situations of uncertainty, none specifically address the issue of the types of uncertainty. The present research aim is to study the effect of different types of uncertainty on decision- making in the context of complex dynamic tasks. Three conditions of uncertainty are compared: knowledge uncertainty, data uncertainty and a control condition. Generally, results indicate that temporal uncertainty has little effect on performance, while affecting efficiency and control behaviors. Significant differences appear between the three groups for all performance variables, participants of the KU group showing a better performance than those of the DU and CU groups, and participants of the KU group also tend to obtain different results on some of the control variables, particularly regarding the number of cycles spent in the fourth quadrant.
Results show that participants of the KU group get significantly more kayaks to crash and are harpooned significantly less often than participants of the DU and CU groups, leading to a significantly higher mean total score, while participants of the DU and CU groups show an poorer performance. The presence of significant differences between groups for all performance variables support the distinction made by Rastegary and Tandy (1993) between knowledge and data uncertainty and it indicates that these types of
uncertainty have a distinct and additive impact on the performance in a dynamic complex task. However, thé increase of performance is similar for all three conditions and that it is seemingly attributable to a practice effect. Thus, these results suggest that temporal uncertainty has no effect on the learning rate. This may be explained by the fact that the spatial pattern was kept constant, and since this is mainly a visual-spatial game, the spatial component probably plays a significant role in achieving control over the system.
Regarding the control variables, it appears that the control that participants exert over the system increases with practice effect, that is, from one board to another. However, for all variables, there is no significant difference between groups, and a marginal effect is denoted for the fourth quadrant, where participants of the KU group tend to spend less cycles in that quadrant than participants of the DU and CU groups. Given the lack of icebergs, the fourth quadrant is not a strategic place to stand, and participants of the KU group tend to be able to acquire that knowledge faster while it takes more time for those of the DU and CU group. The significant interaction obtained for the second quadrant
indicates that participants of the DU group spend more cycles in that quadrant during the first ten boards than participants of the KU and CU groups, while for all the other boards, there is no significant difference between groups. It is noteworthy that as for the fourth quadrant, the second quadrant is not a strategic one since there are only a few icebergs and also because it is the only quadrant with two points of entry for kayaks. The results for this quadrant suggest that participants of the DU group take more time than those of the KU and CU groups to gain that knowledge.
The data gathered through questionnaires suggests that the type and the degree of temporal uncertainty influence the verbal reports of participants. That is, answers became more vague and variable with increased uncertainty. Hence, it appears that performance is little affected when participants are faced with greater uncertainty, while the verbal report they made of the situation shows greater alterations. These observations are similar to those of Porter’s (1991) regarding the lack of consistence between performance and verbal reports in the kayak task.
On one hand, the control over the system increases with practice, but no significant difference appears between all three groups. However, the KU group tend to show early signs of adjustment of their actions compared to the other two groups. On the other hand, performance also increases with practice and in addition, participants of the KU group show a significantly better performance than participants of the DU and CU groups. Hence, types of temporal uncertainty do not seem to affect significantly the capacity to achieve control over the system, while performance is affected. Furthermore, results also demonstrate that both types of uncertainty do not influence the rate of learning and more specifically, data uncertainty does not impair learning but generates an overall decrement in performance level independent of practice level.
Briefly, the present study provides empirical support to the differential effect of different types of temporal uncertainty on performance. Knowledge uncertainty and data uncertainty appear to have a distinct and additive impact on decision-making and on strategy’s development in dynamic situation, even though another variable, like spatial information, may also play a critical role in performance and control achievement in dynamic complex tasks.
There are some methodological limits to the present study. It is possible that the impact of temporal uncertainty was limited by the pace of the game, which was relatively slow. As a consequence of the lack of temporal pressure, participants had time to adjust their
behavior and to use spatial information to increase their performance. Furthermore, data gathered through the software were recorded for each board. It would have been more accurate and of particular interest to have access to data for each cycle in addition to board information. Finally, the use of an open-questions questionnaire may have lead to a greater variability in answers, particularly for the second question about the degree of uncertainty experienced during the game, which was more vague. In this case, participants were asked about uncertainty in general since there was no mention of temporal uncertainty in the question. It is then possible that some participants gave a more global answer while others answered considering only temporal uncertainty.
There have been few studies on the impact of uncertainty on dynamic decision-making, and none specifically addresses the issue of empirical support of different types of
uncertainty in dynamic complex situations. The present study provides empirical evidence to the existence of two types of temporal uncertainty, that is knowledge uncertainty and data uncertainty, which have a distinct and additive impact on performance and decision- making in dynamic complex situations. It has also been demonstrated that verbal reports of the degree of uncertainty experienced and of the strategies used are not consistent with objective measures of performance. Consequently, the development of training programs and decision support systems must take into account the effect that different types of uncertainty may have on performance and on the attempts to achieve control over a system as well as the fact that decision makers may not be able to give an accurate report of their efforts to deal with a complex and uncertain situation.
CONCLUSION GÉNÉRALE
L’objectif de la présente étude est d’évaluer les effets de différents types d’incertitude temporelle sur la prise de décision dans une tâche dynamique complexe, la prise de décision étant ici envisagée en termes de contrôle. Deux types d’incertitude temporelle sont étudiés, basés sur la distinction établie par Rastegary et Landy (1993) : l’incertitude dans la connaissance, qui réfère à la variabilité de !’information liée à une situation, et l’incertitude dans les données, qui réfère à la nature plus ou moins complète de cette
information. Le jeu informatisé « Save the Whale », adapté de Porter (1991), est utilisé afin de comparer l’effet de ces deux types d’incertitude et différentes mesures de performance et de contrôle sont enregistrées.
Les résultats démontrent que les participants du groupe KU présentent une performance significativement supérieure à celle des participants des groupes DU et CU et ils tendent également à présenter des comportements de contrôle plus efficaces. Par ailleurs, il apparaît que le rapport verbal que les participants font en regard du niveau d’incertitude ressenti et des stratégies utilisées n’est pas consistant avec les mesures objectives
enregistrées. De façon générale, les résultats appuient l’existence empirique de deux types d’incertitude temporelle ayant un impact distinct et additif sur la prise de décision en situation dynamique.
La présente recherche étant la première à s’intéresser à la distinction empirique entre différents types d’incertitude, il serait particulièrement intéressant de poursuivre dans cette direction en tentant de démontrer l’existence empirique de différents types d’incertitude non seulement dans la sphère temporelle, mais également dans d’autres sphères comme la sphère spatiale. Des recherches pourraient aussi être entreprises afin d’affiner la
Table 1
Source df SS MS F
Between blocks
Group 2 427.30 213.65 182
Blocks within Group 54 6344.26 117.49 Within blocks
Boards (by groups of ten)
5 1947.10 389.42 !036***
Group X Board 10 863.29 86.33 2.30*
a) Group for boardl 2 883.55 441.77 16.49***
b) Group for boardl 2 134.42 67.21 2.51·
c) Group for boards 2 53.08 26.54 0 99
d) Group for board4 2 64.42 32.21 1.20
e) Group for boards 2 46.62 23.31 0.87
f) Group for boardó 2 108.49 54.24 2.02
c) Board for KU 5 275.38 55.08 2.06
d) Board for DU 5 2255.17 451.03 16.83***
e) Board for CU 5 288.99 57.80 2 16
Board x blocks within 270 10 150.71 37.60 Group
Note. The board variable represents the boards by groups often; that is Boardl represents the first ten boards, then Board2 the next ten boards and so on.
i i
I
H---:—I--- l· ---1---Kayak 1 —:—1---Kayak 2 --- 1---Kayak 3 ±4 ±4 ±4 T * f * 1 1 Kayak 1 1 Kayak 2 1 Kayak 3 V --- 1— u ---1--- --- !---Kayak 3 Kayak 1 Kayak 2 Figure 1ר 700 600 500 400 300 -200 -KU -a-DU -100 --200 -Boards Figure 2 Mea n tota l sc o re
+-KU «—DU +-CU --- 1---2 3 4 ך 6 5 00 ן 4 3 - 2 ή 1 -0 Boards Figure 3 M ea n n u m b er
o
f
h ar p o o n in ;+-KU «—DU +-CU 6 4 5 1 3 I 1 2 ך 8 ך 7.5 1 י 6.5 -j
H
5·H5 i
-י 4.5 -4 3.5 3 y 2.5 -2.4 Boards Figure 4 M ea n number o f cr as h ed k ay ak s־#—KU fl-DU *-CU --- 1 6 Γ 5 --- [---3 4 --- 1---1 2 40 39 - 38 - 37 - 36 - 35 - 34 - 33 - 32 - 31 - 30 - 29 - 28 - 27 - 26-Boards Figure 5 M ea n n u m b er o f ch an g es o f d ir ec ti o n
־·־—KU 58־—DU ■A— CU Boards Figure 6 Mea n n u m b er o f cy cl es in Q 1
KU «—DU *— cu Boards Figure 7 M ea n n u m b er o f cy cles in Q 2
«—KU -*—DU Boards Figure 8 M ea n n u m b er o f cycles in Q 3
*-KU *—DU *-CU Boards Figure 9 M ea n n u m b er o f cy cl es in Q 4
*-KU «—DU 1 2 3 4 5 6 Boards ך 60 ־ 55 ־ 50 45 -j 40 -־ 35 -30 ־ 25 -20 Figure 10 M ea n n u m b er o f cycles in c en te r
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« Sauvez la baleine »
Tout au long du jeu, avez-vous été en mesure d’anticiper les événements et de planifier vos actions, ou vos actions étaient-elles plutôt en réaction face aux événements qui
survenaient? Y a-t-il eu une différence entre la première et la seconde séance?
A quel degré avez-vous ressenti de l’incertitude au cours du jeu?
Quelle(s) stratégie(s) avez-vous employée(s) tout au long du jeu afin de parvenir à bien faire la tâche demandée? (De façon générale, comment vous y êtes-vous pris pour effectuer la tâche?)
