COGNITIVE LOAD ON
RISK DECISION MAKING
Master thesis
August 22th, 2017
Abstract
The effect of a cognitive load on the precision of preferences in risk decision making is examined. In an experiment, participants were exposed to a cognitive load creating an interference with our reasoned thinking, which we will call system 2 thinking. This interference could make the decision making of an individual more automated and intuitive, this is called system 1 thinking. It is tested how a cognitive load interferes with this processes and consequently with the precision of preferences. Specifically, the influence on consistency, sureness and risk behavior in risk decision making is examined. Despite initial signals and minor support, the results show insignificant results. However, great support has been found to conclude that there is a positive effect of cognitive ability on consistency in preferences.
By:
Lennart van ’t Kruis Supervised by:
Acknowledgments
I am grateful for a number of persons that supported me in my study, thesis or life experiences. I wish to express my sincere gratitude to the following people / groups:
Dr. F. Bohn
Members of Corona Cinquintue Carlijn Cretier
Marjolein van Hardeveld Daniëlle van ’t Kruis
Jeffrey van ’t Kruis Leendert-Jan van ’t Kruis
Mary van ’t Kruis Manon Luinenburg Bettina Nyeste Dr. J. Qiu Merel Stemerdink Members of HJC UCIVI Yorick Wolff
“Take your time, think a lot Why, think of everything you’ve got
For you will still be here tomorrow, but your dreams may not From the moment I could talk I was ordered to listen Now there’s a way and I know that I have to go away
I know I have to go”
Stevens-Table of contents
1. Introduction...5
2. Theoretical background...7
2.1 Imprecise preferences...7
2.2 Prospect Theory of Kahneman and Tversky (1979)...9
2.3 The decision making processes under a cognitive load: dual process approach...10
2.4 Influence of a cognitive load on the dual process system...12
2.5 Neurological perspective...13
2.6 Applicability of a cognitive load on the dual process system in real life...14
2.7 Ability to correct behavior...15
2.8 Cognitive ability in decision making...15
2.9 Cognitive load and imprecise preferences in risk decision making...16
3. Hypotheses...18 4. Experimental design...21 4.1 Core experiment...21 4.2 Part I...22 Task C...22 Cognitive load...22 Task S...23 4.3 Part II...23
Overview decisions: Option to modify choices...23
Questionnaire...23
5. Analyzation of the experiment...24
5.1 Groups...24
5.2 Pay-offs...25
5.3 Participants...25
6. Methodology...26
6.01 Non-parametric models...26
6.02 Mann-Whitney U test & Levene’s test...26
6.03 Hypothesis 1...28
6.04 Hypothesis 2...29
6.05 Hypothesis 3...29
6.06 Wilcoxon signed-rank test...30
6.08 Kruskal-Wallis test & Dunn’s test...31
6.09 Jonckheere-Terpstra test...32
6.10 Hypothesis 5...32
7. Results...34
7.1 Hypothesis 1: The effect of a cognitive load on inconsistency...34
Inconsistency and time use revision...35
7.2 Hypothesis 2: The effect of a cognitive load on the sureness about decisions...35
Satisfaction rate and cognitive load...36
7.3 Hypothesis 3: The effect of a cognitive load on risk behavior...37
7.4 Hypothesis 4: The effect of a cognitive load on the adjustment rates...40
7.5 Hypothesis 5: Cognitive ability and inconsistency...41
Relation time used CRT and correct answers...42
7.6 Summary of results...43
8. Conclusion and discussion...46
9. Bibliography...50
1. Introduction
Within the economic field a lot of work is done about mapping the preferences of people. Economist are especially interested in risk decision making. Several findings show that the classical models of preferences are incorrect. The prospect theory of Kahneman and Tversky (1979) for example, illustrates that people do not calculate their decisions wisely by looking at their expected pay-offs, but rather look at the losses and gains that are involved with it. People are more sensitive for losses while making decisions under risk than to the gains. The authors show that humans are prone to errors in its economic choices.
Kahneman (2003), later brought new insights in explaining why humans do not behave rationally, by describing decision making as a dual process system. These ideas were not new, but Kahneman placed it in an economic perspective. The dual process theory states that decision making can be processed in two different ways: One that is more intuitive and emotional (system 1) and one that analyses the decisions in a mathematical way (system 2). The mental capacity requested by the system 2 process depletes our cognitive energy. Therefore, we have an automatic intuitive mechanism in our brain that tries to make the best decision without much effort.
A cognitive load can disturb the use of system 2. A cognitive load prevails if situations occur that require a lot of mental resources. This results in more exposure of behavior that is rather intuitive, which normally could be suppressed. It makes individuals less alert and more prone to mistakes (Kahneman, 2003; Stanovich and West 2000). This paper focuses on the effect a cognitive load could have on the dual process system by testing whether there is an effect of a cognitive load on the precision of individual preferences in risk decision making.
The following research question and hypotheses have been assessed:
Does a cognitive load make an individual more imprecise in its preferences for decisions under risk?
This paper especially looks at the effect of a cognitive load on the three following aspects which gives us indications on the precision of preferences:
o Inconsistency in decisions under risk; Hypothesis 1 o Sureness in decisions under risk; Hypothesis 2 o Risk behavior; Hypothesis 3
Inconsistency indicates imprecision since it reflects intransitivity in preferences i.e. no logical order in preferences between options. Sureness, is here interpreted as the declared degree of sureness in the participants’ own answers and indicates imprecision in preferences when low certainty prevails. Risk behavior, here interpreted as the willingness to take risks, indicates imprecision when the risk profile is affected. When the tendency to choose a risky or less risky option is affected after a cognitive load, it proves imprecision. In addition to the three indicators, it is also tested whether people are able to correct their initial answers to an answer that reflect their preferences better in hypothesis 4. Hypothesis 5 will test whether there is a relationship between inconsistency and cognitive ability.
An experiment has been conducted in which one group was treated with a cognitive load (cognitive loaded group) and one group was not treated (control group). By making multiple binary choices it could be tested whether there is a difference in consistency between the groups. These binary choices also reflected the risk profile of the participants (risk seeking vs. risk averse). The sureness of the participants is measured by the declared certainty in its answer on a ten-point scale rate. A cognitive reflection test examined the tendency of participants to respond automatically or reasoned, which will be interpreted as cognitive ability.
The responses of participants reflect their preferences in the given risk decisions. There should be no difference in preferences between the two groups if the cognitive load has no influence. This paper tests if there is a difference between these two groups, which would indicate a relation between cognitive load and the precision of preferences.
2. Theoretical background
This chapter discusses upon the available literature on preferences and risk decision making. It explains how decision making is bound to several features that hinder rational decision making. Specifically, precision of preferences and its departure from traditional axioms are discussed. Secondly, the prospect theory of Kahneman and Tversky (1979) is discussed. Thirdly, the dual decision process of system 1 and system 2 is studied, followed by a neurological perspective of this process.
Furthermore, the paper deliberates on the applicability of a cognitive load in real life circumstances. After that the ability to correct initial answers is discussed. Followed by an examination of the influence of cognitive abilities on decision making. To complete, it is discussed how this cognitive load could possibly lead to imprecise preferences in risk decision making derived from the literature discussed. Based on the theoretical framework, hypotheses are drawn which will be tested in the experiment.
2.1 Imprecise preferences.
The ways how decisions are made,are widely discussed within economic sciences. The neoclassical view assumed people to make rational decisions, that try to reach maximum outcomes by calculating the expected pay-offs given the available information. This information is integrated in choices and the chances of specific outcomes and alternatives are calculated and decided upon. Preferences are consistent and could be expressed in a numeric value and the decision maker choses the alternative with the highest expected utility (Friedman & Savage, 1948; Von Neumann & Morgenstern, 1947; Keeney & Raiffa, 1993).
However, more recent economic research proves a wide range of phenomena that show the limitations of this homo economicus. This limitations are based on emotional behavior, in the sense that people do not always analyze their decisions but decide upon feelings (Loewenstein, Weber, Hsee & Welch, 2001). This creates a decision maker that systematically violates its own principles of behavior. Kahneman and Tversky (1979),
presented major violations of the expected utility theory in their research. They showed, with their prospect theory, that the value function is not linear but convex for losses and concave for gains with a steeper slope for losses. Besides that, small probabilities are overweighed and moderate to high probabilities underweighted.
Nowadays, economic research is more focused on behavior that departures from the traditional axioms. Behavioral economics, for example, provides theories of decision making under risk with a more realistic psychological view. This paper does not go in depth about the heuristics and biases that are involved with the violations of the expected utility theory, but does discuss some features of it. It merely focuses on how imprecision interferes with the neoclassical view and affects risk decision making.
Von Neumann and Morgenstern (1947), developed an utility theorem that proved to be of main importance of descriptive and normative decision theories like the expected utility theory (Tversky & Shafir, 2004). Short, this theory consisted of four axioms which could be applied in decision making. When these assumptions are met, the person will choose the option with the highest utility. Especially the axiom of transitivity is of importance for this paper. Transitivity describes the relationship and its preferences between available options. It assumes that people have clear preferences and have a complete order in which they prefer the options available. So when there are three options (x, y, z) and whenever x dominates option y and option y dominates option z, option x should also be preferred above option z. When transitivity does not prevail, it will be impossible to draw any conclusions on a
preference map with several options (Von Neumann & Morgenstern, 1947).
However, several authors proved the transitivity axiom to be violated in decision making. Besides situations where the available options are intrinsically intransitive, like the rock, paper, scissor game, intransitivity in preferences is also found in several situations where preferences really reflect contradictory outcomes. This is due to the fact that individuals are inconsistent in their choices. Even when the taste of individuals is held
constant, they appear to be inconsistent and change answers with repeated choices (Tversky & Shafir, 2004).
Preference reversals with regard to decisions under risk also prove intransitivity and therefore imprecise preferences. Preference reversals reflect a discrepancy between
(1971), participants had to value two different bets in money. It is expected that the higher the money value for a bet, the more likely the participant will choose for this specific bet when choosing between the two bets. However, this was not accurate, since it is shown that participants sometimes prefer the lower valued bet above the higher valued bet, which infringes with transitivity. So there is an inconsistency between the value people place on gambles and the choices they make. People’s judgements and preferences are therefore imprecise (Butler & Loomes, 2007). This imprecision for decision making is further
elaborated upon in the next section with support of the prospect theory of Kahneman and Tversky (1979).
2.2 Prospect Theory of Kahneman and Tversky (1979)
In order to provide a deeper insight of this theory, the literature review of Edwards (1996) is mainly used in this section.
The prospect theory, first initiated by Kahneman and Tversky (1979), is a well-known alternative for the widely accepted theory of expected utility of Von Neuman and
Morgenstern (1947). The expected utility theory was criticized for not reflecting individual decision making under risk precisely enough. It did not cover for vulnerability of decisions caused by framing and failed to explain why some people were more risk-seeking and others more risk-averse. The prospect theory tried to disentangle this caveats.
The prospect theory consists of two phases. Within the first phase (editing phase), an individual will go through four kind of mechanisms in the decision making process; coding, combination, segregation and cancellation. Within the second, the evaluation phase, the individual concludes and reflects upon the first phase and chooses the option that is valued the highest.
The prospect theory is often used as the framework in decision making processes in which individuals prove to show irrational behavior, especially in papers that show the effect of framing on certain decisions. This paper could increase the knowledge of the predictive powers of the prospect theory by examining a possible relation between a cognitive load and the precision of preferences. If preferences prove to be imprecise, this will mean that
make mistakes in analyzing the options and therefore have no complete and transitive preferences which is assumed in the prospect theory (Budescu & Weiss, 1987).
However, Tversky, does mention that in certain circumstances intransitivity can occur. This depends on the available alternatives and the difficulty of evaluation and judgement. The available information on complex multidimensional alternatives is difficult to utilize properly. Therefore, people simplify their decision making and try to make the best decision by rough calculation. Tversky concludes that this does not necessarily mean irrational behavior, since the intransitivity could be caused by the high costs of evaluating alternatives resulting in the individual preferring approximating the best decision to make. The essence of testing transitivity is therefore not whether it is violated or not, but if these violations can expose information about the decision process and approximation method used to establish preferences for risk decision making (Tversky & Shafir, 2004).
This paper will not discuss on whether intransitivity reflects irrationality or not. Nevertheless, the choice mechanism of approximation seems to be applicable in a substantial part of our real life decision making. Our brain sometimes has to make rough calculations in processing information (Kahneman, 2011). This paper can therefore find out whether people are imprecise in its preferences if they are confronted with a cognitive load. The binary choices the subjects faced in the eleven rounds of the experiment were not complex. Significant results would therefore have further implications than suggested by Tversky (1969). It would prove that individuals in certain situations that require a high level of cognitive effort are imprecise in its preferences.
2.3 The decision making processes under a cognitive load:
dual process approach
In order to understand the processes involved for decisions under risk and the effect of a cognitive load, one needs to understand the decision mechanisms of individuals. The focus within this paper is on the dual process mechanism. This theory is a widely accepted theory of the mind, which is especially ubiquitous in psychology (Barrett & Tugade, 2004). In this paper the terms used by Kahneman (2003) and Stanovich and West (2000) will be used,
(Kahneman, 2003). However, often different terms are used like the terms Heuristic
reasoning and Rule-based reasoning used by Ferreira, Garcia-Marques, Sherman and
Sherman (2006) which in my opinion sound more appropriate. The different terms that are used in other research barely differ in definition (Kahneman, 2003). In this paper the terms system 1 and system 2 are used, because of the wider acceptance in the economic field.
System 1 refers to the automatic intuitive process in which people’s cognitive use are merely formed from first impressions, impulsivity and emotions. The decisions are made fast, automatic, effortless, emotionally charged, associative and implicit, meaning that they are often governed by habits. Since it is an automatic process, it is hard to control this kind of behavior.
The process of system 2 is the opposite. Here decisions are made slowly, serial with effort and more control. The decisions can be monitored better and are therefore governed by rules. The mental activity is higher and therefore requires more cognitive capacity. The actions are explicitly taken and monitored by reasoned thought (Kahneman, 2003;
Kahneman 2011).
Consequently, decision making under risk can be processed in two different ways: One that is more intuitive and emotional and one that really analyses the decision that has to be made in a mathematical way. As Slovic, Peters, Finucane and MacGregor (2015) mention, people might not analyze every decision under risk, as is assumed in several studies. It is not the case that every individual tries to gather all information that is available and takes into account this information during every decision they make. However, unclarity still exists in the literature about the extent of the role automatic decision making plays in decisions involving risks.
The mental capacity requested by the system 2 process will deplete cognitive energy. Consequently, people have this system 1, automatic intuitive mechanism, in their brain that tries to make the best decision without too much effort. There is no room for doubt. In most of these situations, only one option comes to mind. Most of the time system 1 is sufficient at what it does, however it is vulnerable for biases and has little understanding of logic and statistics. Only system 2 can follow rules and compare objects on several attributes (Kahneman, 2011). The next section elaborates on how this dual process system can be interfered by cognitive load and its possible consequence: imprecision in preferences.
2.4 Influence of a cognitive load on the dual process system
As stated above, the cognitive energy capacity of our brain is depletable. The use of system 2 reasoning therefore costs quite some energy. System 1 therefore helps out, by making decisions automatically. Most of the time, this involves tasks that are not of major importance and that do not require a lot of thinking. However, system 1 can also have its influence when fulfilling multiple tasks at the same time. As discussed in the next section, the brain has to split its cognitive resources and prioritize, leading to system 1 interferences. This means that when there are multiple tasks to fulfill that request too much mental activity, this interferes with our system 2 processing. In this case, system 1 will prevail for some tasks, which therefore will be responded to automatically.
A cognitive load occurs when situations require a lot of cognitive energy, this could influence the dual process system. In other words, a cognitive load could possibly interfere with reasoned decision making and result in individuals responding more automatically (Kahneman, 2003). An example of interference with decision making that could influence the outcome of the decision made is framing, where the formulation of the task given influences the decision made. A frame can influence the automated decision making of system 1. A decision mostly entails multiple aspects. The extent to which system 1 can have its influence on the outcome depends on the characteristics of the decision presented. A math equation for example, cannot be solved without proper computations (Kahneman, 2003).
A cognitive load can possibly disturb the use of system 2; it would make individuals less alert. This results in an increased rate of errors and more exposure of behavior that is rather intuitive, which normally could be suppressed i.e. it makes the occurrence of imprecise preferences more likely. System 2 will protect the task with the highest priority and system 1 will take over the tasks that are less important (Kahneman, 2011). The next section gives insight on how the brain works when exposed to a cognitive load and explains how this could lead to imprecise preferences.
2.5 Neurological perspective
The effect of a cognitive load on our actions can be ascribed to the functioning of our brain. The cognitive capacity of an individual has limits and depletes. The neurological explanation for its existence can be found in the frontal cortex which is primarily devoted to the
processing of our actions (Tanji & Hoshi, 2008). This paper does not provide deep insights of the anatomical background of it, but provides the essence of how it influences our decision making.
The lateral prefrontal cortex (LPFC) is viewed as playing an essential role for our volitional behavior1. The LPFC is intensely connected with multiple networks in our brain, allowing the collection and integration of information. The prefrontal cortex (PFC) regulates this information flow and therefore provides a resource for adaptive control of information. The primary functional role is not to store information but to control behavior. It selects responses, guides behavioral sets and mediates the effects of interference in the working memory. It therefore plays a crucial role in coding and filtering information that is important to behavior in the specific environment in a retrospective and prospective manner. It has a large role in preparing or planning actions, especially in optimizing decision-making
strategies (Tanji & Hoshi, 2008).
Tanji and Hoshi (2008), also state that if the PFC dysfunctions, individuals will fail to achieve behavioral goals when exposed to a situation that requires cognitive control, such as multi-tasking. So it is hard for them to effectively deal with complex behavioral demands. Even if the PFC is not dysfunctional, the capacity of cognitive information processing is limited. Watanabe and Funahashi (2014), state that flows of information can conflict or interfere when someone is performing two tasks at the same time. The resources in our brain are finite, therefore there is a limited amount of information one can process at a time. The information available could exceed the amount someone is able to process. The
activation of overlapping activities in the LPFC when performing two tasks at the same time prove that a capacity load affects our behavior and decreases the performance of tasks. This multiple tasks interference is present in the LPFC and results in an increase of time needed to
1 The lateral prefrontal cortex (LPFC), is essential for the following behavioral factors: Information processing: Selection and retrieval, retention and monitoring, transformation, manipulation, synthesis and generation; attentional and cognitive-set regulation; integrative action planning; judgment, interference and speculation; language processing; other aspects of cognitive behavior (Tanji and Hoshi, 2008, pp. 38, table 1)
fulfill a task and an increase in the total errors made in decision making. However, there is still a lot unknown about the effect of multiple tasks inferences (Watanabe & Funahashi, 2014).
A cognitive load is seen as a good method to create this situation in an experiment. It deteriorates our decision making, since two tasks have to be processed at the same time and cognitive resources have to be split (Brünken, Steinbacher, Plass & Leutner, 2002; Kahneman, 2011). The next section discusses how the influence of a cognitive load on the dual process system plays a role in our everyday life.
2.6 Applicability of a cognitive load on the dual process system in real life
What follows is how the literature discussed above relates to real life situations. Several perspectives on how the decision making processes work have been discussed. They all relate to each other and show that individuals do not act rationally, respond emotionally, are intransitive and make mistake. Besides that, the dual process mechanism of system 1 and system 2 is explained and a neurological perspective is given.
It is important not to underestimate the extent in which our brain is loaded in our daily life. In our daily life there are a lot of things that distract us from doing our tasks. This influences our cognitive resource distribution and therefore our decisions. A multiple task situation forces individuals to split attention and therefore distracts from the tasks they are doing. The distraction influences for example our driving, our educational absorptiveness and how we do our work. The stronger the distraction, the more careless mistakes we make (Lavie, 2010).
Besides performing two tasks at the same time, also stressful life events interfere with our cognitive capacity and therefore competes for demanded resources with other tasks leading to more task errors. The more individuals are prone to stress, the more their working memory suffers. The practical implementation is that the effects of stressful events on the decision making process are equivalent to performing a secondary task (Klein & Boals, 2001). If results prove to be significant, this could entail a wide applicability on our daily life decision
1.1 Ability to correct behavior
The intuitive judgements of system 1 can be corrected by the monitoring ability of system 2. In that case, an individual that makes an error could revise its initial response and correct by the reasoned system 2 mechanism that brings extra considerations to bear. Of course to correct a decision, the mistake of the intuitive judgment should also be detected by the system 2 mechanism. This corrective behavior depends on the awareness of a present bias and the accessibility to competing alternatives (Kahneman, 2003).
However, there are weaknesses in the corrective operations of system 2. People are rather reluctant to reconsider the initial answer of system 1. Despite the cognitive abilities, it seems that individuals are not keen to use it the whole time and take pleasure with a
plausible judgment that came in our mind, resulting in a higher rate of errors. This corrective ability of system 2 can be weakened by a cognitive load (Kahneman & Frederick, 2002).This implies that system 1 can result in judgment mistakes and system 2 might fail to recognize or change it to the correct outcome, although it could. Within this research it is tested if indeed participants are reluctant to correct their initial answers. This corrective capability also depends on the intellectual capacity of the specific intellectual. (Kahneman & Frederick, 2002). The corrective operations of system 2 tend to be more present for people with a higher intelligence (Kahneman, 2003). The following section discusses how intelligence affects the dual decision process system.
1.2 Cognitive ability in decision making
Intelligence, here interpreted as cognitive ability, has major influence on the dual decision process of individuals. The choices made are often more consistent and close to the expected value with an increase in intelligence (Cokely & Kelley, 2009). Both system 1 and 2 are subject to intelligence. The automatic rules that system 1 follows are more logical and applicable for the specific situation. For system 2, higher intelligent individuals have a better corrective performance for intuitive responses that are not optimal, have better skills in responding to a multiple task situation and have better statistical thinking (Kahneman & Frederick, 2002; Kahneman, 2003).
The processing capacity is larger with a higher level of intelligence. Intelligent individuals can recall more numbers when needed to remember. It is easier for intelligent people to change perspective, regulate themselves and be flexible, which is beneficial in decision making (Barrett & Tugade, 2004). The regulation of thought is better managed by more intelligent individuals which makes them less prone to distraction and impulsive errors (Kane & Engle, 2003). Within this paper, it is tested whether a higher level of intelligence indeed leads to less imprecise preferences. The next section ends the theoretical background by concluding how a cognitive load can affect our preferences in risk decision making derived from the literature discussed above.
1.3 Cognitive load and imprecise preferences in risk decision making
The two cognitive processes of system 1 and 2 have been discussed extensively. With system 1 being our automatic intuitive and effortless behavior and system 2 our reasoned effortful thinking that requires cognitive energy. This cognitive energy is depletable, people therefore use system 1 for more routine decision making. However, also system 2 activities can be interfered by system 1 in the case of performing two tasks at the same time or stressful events.
A cognitive load can create this situation and make the LPFC split its brain activity for two different tasks. It results in an information load that could exceed the amount that someone is able to efficiently process. This will affect our behavior and decrease the
performance of tasks as cognitive resources have to be split. When this occurs individuals will think more uncontrolled and automatic (system 1).
System 1 activities can result in errors in decision making. These mistakes can be corrected by system 2 monitoring. However, this corrective ability is often not used by people. Therefore, our decision making can still be imprecise and contain flaws. Being imprecise in preferences depends on how people perceive and evaluate risks. It is expected that people mainly use their system 2 mechanism in making decisions under risk. A cognitive load can possibly interfere with this risk decision making, since it could lead to an influence
In the next section hypotheses are stated. An experiment has been conducted in which participants had to make decisions under risk. Groups were split in two, with one being exposed to a cognitive load. It is checked whether one group is more or less imprecise in its decisions. By using three indicators of imprecision we test whether there is a difference between the cognitive loaded group and the control group. In addition, it tests whether the corrective mechanism is present and if there is an influence of cognitive ability on
2. Hypotheses
The discussion above highlights that a cognitive load can affect our decision making and create imprecision in individuals’ preferences. It could affect our dual process system and lead to more intuitive responses. It is, however, still questionable to what extent this is the case for decisions that involve risks. If indeed a cognitive load would influence risk decision making, this will lead to individuals making mistakes and therefore giving answers that are imprecise with its true preferences.
This paper tests the effect of a cognitive load on the precision of preferences by conducting an experiment and examining whether responses of the group exposed to a cognitive load deviates significantly from the control group. Inconsistency, risk behavior and sureness are seen as three indicators for imprecise preferences. Based on the previous discussions, five different hypotheses have been drawn, which are tested with the experiment introduced in the following section.
Inconsistency
Firstly, inconsistent answers indicate imprecise preferences. When a participant prefers the certain amount of money at value X it should also prefer the certain amount to X+1. If this is not the case, the participant prefers a lower amount of money, which is intransitive and most likely does not reflect his real preferences. It is expected that a cognitive load will increase the use of system 1 use and therefore leads to more inconsistent answers.
H0= People that are exposed to a cognitive load are equally consistent in risk decision making.
H1= People that are exposed to a cognitive load are unequally consistent in risk decision making. 1 1 1 1 1
Sureness
The second indicator of imprecision is the sureness people have about their own decisions. If the cognitive loaded group is more unsure about its decisions compared to the control group it reflects that decisions are made in less certainty and preferences are affected. Since participants exposed to a cognitive load have to fulfill an extra task it is expected that they will have more difficulty in making the binary choice and therefore use more system 1 thinking resulting in more unsureness about their answers.
H0= There is no effect of the exposure of a cognitive load on the sureness of people H1= People that are exposed with a cognitive load tend to be more unsure about their decisions
Risk behavior
The last indicator of precision in preferences is risk behavior. This is interpreted as the willingness to take risks. Under a cognitive load, individuals can take more or less risks than they actually prefer to take, indicating imprecise preferences. This is the case when the average risk profile of the control group significantly differs from the cognitive loaded group. Even when it is acknowledged that risk preferences deviate among participants, the average risk behavior of participants should not differ between groups if there is no influence of an exposure of a cognitive load.
H0= There is no influence of the exposure of a cognitive load on the amount of risk people are willing to take
H1= The exposure of a cognitive load influences the amount of risk people are willing to take. 2 1 1 1 1 3 1 1 1 1
Adjustment rates
It is also tested whether there is a difference between the control group and the cognitive loaded group concerning the adjustments made. This will give more insight about the corrective ability of system 2 reasoning to adapt initial answers that are not completely in accordance with the true preferences of individuals. It is expected that the participants that were in the cognitive loaded group initially make decisions not in accordance with its true preferences and recognize the faults in their initial answers after viewing the overview and correct more compared to the control group.
H0= There is no effect of the exposure of a cognitive load on the adjustment rates of decisions under risk.
H1= There is a positive effect of the exposure of a cognitive load on the adjustment rates of decisions under risk.
Cognitive ability and inconsistency
In addition to that, considering the literature discussed, there seems to be a negative interaction effect of the cognitive ability of the participant on the rate of inconsistency. Individuals that have better cognitive abilities could possibly make better use of system 1 and 2 and therefore make less mistakes.
H0= There is no relationship between the cognitive ability of people and being inconsistent
H1= There is a negative relationship between the cognitive ability of people and being inconsistent 5 1 1 1 1 4 3 1 1 1 1
3. Experimental design
The following is a detailed description of the experiment2. All information regarding the set-up of the experiment is provided here. It also explains how specific tasks were structured and how the cognitive load is implemented. First the experiment is briefly described, followed by a detailed explanation of the different aspects within the experiment. For screenshots of the experiment see Appendix 13.
4.1 Core experiment
The experimental setup consists of two parts. Part one contains two tasks with both eleven rounds: Task C and task S. For every screen there was a limited amount of time in which the participant had to answer or fulfill the task. Each of the rounds started with task C in which the participants had to make a choice between two options. Option A was always the same and consists of a lottery. Option B offered a sure payment which differed each round
randomly between €4,- and €14,-. The treated, group was shown a six-digit numbers before task C, this to create a cognitive load. After making the binary choice, the participant had to recall the numbers. Subsequently, in task S, the participants were asked to indicate their sureness about the choice they made in the specific round on a slider scale.
In part two, the participants were shown an overview of their decisions made for tasks C and task S in sequential order (€4,- to €14,-) . They had to confirm or modify their choices if wanted. A questionnaire followed consisting of a cognitive reflection test (CRT) and some demographic questions. The experiment ended with showing the experimental pay-off for the participant. For the complete experiment see Appendix 1. The following section elaborates more on every component of the experiment
2 The experiment is conducted by dr. F. Bohn and dr. J. Qiu. The property right of the data used for the analyzation is theirs.
3 If this document is opened on a computer, both appendices and figures are linked to the relevant appendix or figure and can be clicked on.
4.2 Part I
Task C
For task C the participants had to make the binary choice between option A and option B in a total of eleven rounds. Option A consisted of participating in a lottery with the following chances: 50% of winning 3 euro, 20% of winning 7 euro and 30% of winning 17 euro. Option B consisted of a sure amount of money which randomly differed between 4 euro and 14 euro each round.
In each of the rounds the participant got a different sure payment so that every number from 4 to 14 came by once. Without making any mistakes, the participant should be consistent in its own answers. Meaning that there should be a switching point from option A to option B if the eleven rounds are put in the right order from 4 euro to 14 euro. If for example the lottery is preferred to the alternative of 8 euro then the lottery should also be preferred for the alternative of 7 euro. If this is not the case the participant is inconsistent.
The expected pay-off of the lottery is 8 euro. Meaning that a risk neutral person would be indifferent between the lottery and a sure amount of 8 euro. If, for example, the switching point to choose the sure pay-off is at 6 euro, it can be concluded that the
participant is risk averse. Task C is used to test hypothesis 1, 3 and 5.
Cognitive load
For every round in task C, the participant had to remember a six-digit number. Before tasks C started the participants were shown a randomly created six-digit number. However, since the numbers are created randomly, it cannot be ensured that the numbers do not follow a pattern or that numbers are repeated within a code. After making the binary choice of task C the participant had to recall the number. The participants were randomly assigned of being in the treated- or in the control group. The attempt to hold in mind the six-digit code creates the cognitive load that could initiate the individual to respond more intuitively (Gilbert, 1989; Kahneman, 2011).
Task S
After recalling the number at a specific round of task C, participants were shown the choice they made and had to indicate their sureness by moving a ten-point slider scale. Completely left being completely sure that they preferred the lottery (option A) over the sure pay-off (option B); completely right being completely sure of preferring option B over option A; The middle being unsure. Task S is used to test hypothesis 2 and 4.
4.3 Part II
Overview decisions: Option to modify choices
After the participant finished all eleven rounds, the participants were shown a complete overview of the decisions they made for task C and task S. First they were asked to rate the satisfaction of their choices on a four-point scale. After that they could modify the choices they made and adapt if wanted. The choices they made were shown on a sequential order with the sure amount of 4 euro being on the top of the overview and 14 euro at the bottom. This way, the participant would get a good impression of the decisions they made. This would therefore be a good opportunity to correct for any inconsistencies or mistakes made.
Questionnaire
When participants were done revising their initial answers, a questionnaire followed. Starting with a Cognitive Reflection Test (CRT). This reflects if the participant’s answers are intuitive or reasoned. In other words, it tests the system 1 and 2 use of the participant. The test
consisted of 7 items. The CRT has been proved an efficient test to measure the tendency in answering intuitively wrong. These questions mostly need more cognitive reflection in order to be answered correctly. The test is a potent predictor of the cognitive abilities of subjects (Toplak, West, Stanovich, 2011; Frederick, 2005). The CRT is used in order to know whether more reflective participants tend to make more consistent decisions. After the CRT the participants had to fill in their age, gender and field of study. Then the experiment ended and participants was told their pay-off. The CRT is used to test hypothesis 5.
4. Analyzation of the experiment
5.1 GroupsAs stated before, the participants were randomly placed in two groups: One that was exposed with a cognitive load and one control group without cognitive load. Besides that, the participants had the opportunity to revise their initial answers and modify them if
wanted. This gives us the following group division in order to answer the hypotheses (Figure 1).
Before revision (part I) After revision (part II) Cognitive loaded group
(51 participants) CL 1 CL 2
Control group
(60 participants) NL 1 NL 2
1. Figure – Experiment group division
The effect of a cognitive load on the outcomes of task C and task S can be measured by comparing the treated group with the control group. This way the following comparisons can be made (Figure 2).
Compare to…
Hypothesis 1: Inconsistency rates
NL1 CL1
NL2 CL2
Hypothesis 2: Sureness (slider scale scores)
NL 1 CL 1
NL 2 CL 2
Hypothesis 3: Risk profiles ( switching point binary choices)
NL 1 CL 1
NL 2 CL 2
Hypothesis 4: Adjustment rates (slider scale scores)
NL 1 NL 2
CL 1 CL 2
Hypothesis 5: Inconsistency rates and CRT score
2. Figure – Comparisons hypotheses 5.2 Pay-offs
To incentivize the participants, pay-offs were granted for fulfilling the two parts of the experiment. For task C the participants were granted with the outcome of one of the rounds which was randomly selected by a computer. This way the participant was deciding upon its own pay-off when fulfilling task C. The participant received 40 cents for every round of the choices made in task S. The computer randomly selected if they received the pay-off for task C and S in part I or task C and S after revision. The ones that were in the cognitive load group received 40 cents if they were able to perfectly memorize the six-digit number. This way the participants were motivated to use their cognitive capacity. The average payment was €16,60. Monetary incentives are deemed critical for theory testing in order to have responses that are consistent with the theory that is being tested (Croson, 2002).
5.3 Participants
In total there were 116 participants, of which 60 were in the control group and 56 in the cognitive loaded group. In the first session of the experiment (out of 2) something went wrong with measuring the age, field of study and gender of the participant. However, for the second session, the average participant is 21,8 years of age and 25 out of 59 people were female. The summary regarding the participants of the second session can be seen in Appendix 2.
The subject pool that is selected consists of students in the field of Economics, Business, Natural science, Social science and Art Humanities. The selection that is made is therefore not completely accurate to measure inconsistency in general behavior. However, the treatment effect is expected to be homogenous and therefore to be the same across the entire population. When the treatment effect is heterogenous, the consequence of this selection could be that students score better at the CRT and make more reasoned decisions. The effect of a cognitive load could therefore be mitigated. However, Druckman and Kam (2009), found that the use of students do not necessarily create problems for causal
inferences. The treatment effect is expected to be homogenous and therefore to be the same across the entire population.
5. Methodology
In this section, the used methods to answer the specific hypotheses are clarified. Inspiration for the methods that are used and its applications are built on the statistics book by Field (2013).
6.01 Non-parametric models
Since this research deals with ranked data, non-parametric methods are used to answer the hypotheses. A non-parametric test entails a distribution free test which entails fewer
assumptions. This is especially useful for ordinal outcomes since it is hard to analyze these outcomes with major assumptions, such as having a normal distribution. The use of the t-test can be invalid when the data is not normally distributed, especially for small sample sizes. The disadvantage of having fewer assumptions however, is that the outcomes of non-parametric tests are often less powerful and therefore, it is harder to reject the null hypothesis when the alternative is true (Scott & Mazhindu, 2014).
6.02 Mann-Whitney U test & Levene’s test
For hypothesis 1, 2 and 3, the Wilcoxon-Mann-Whitney U test (later: Mann-Whitney U test) is used. According to Bürkner, Doebler and Holling (2017), the Mann-Whitney U test is one of most widely used non-parametric method. This test checks whether the average ranks differ between two groups based on a sum of the ranks in each group. The alternative hypothesis of this test implies that the measured data of one group is significantly different from the other group. It is to test whether the distribution of the two groups differs or not and find stochastic dominance. By assessing the distribution, it measures the difference in all locations. If a significant result would be found, stochastic dominance prevails.
Stochastic dominance, can be interpreted that there is a bigger chance that a randomly chosen value from one group exceeds a randomly chosen value from the other group. If a random variable (i) of the distribution function of the control group (X) and (j) as
the random variable of the distribution of the treated group (Y), it could mean that P(i > j) > 0.5, and therefore X > Y (Mann & Whitney, 1947).
Rejecting the null hypothesis could still imply that the means or medians are the same but that the values are significantly different for moments. The Mann-Whitney U test can, in that case, only be significant when extreme unequal variance between the
distribution of the groups occurs. However, if distributions are equal the Mann-Whitney U test can be used to know if the medians are identical (Nussbaum, 2015). Thus differences in shape and spread as well as differences in medians can be detected by the Mann-Whitney U test. Keeping things more simple, it tests whether two groups differ or not. Differences in medians are not the most important (Hart, 2001).
The core of this paper is to look whether both groups differ. Whether it is merely the median or the distribution that makes group differ is not the most important. But still, in order to get more insight in the distributional differences, this paper also tests for
homogeneity of variance by using Levene’s test. So it does not simply reports a P-value but also reports the variance.Important to note, is that the data is rank based. Hence, the Levene’s test only reports the variances in ranks.
The non-parametric Levene’s test is a good test to examine variance differences if data is skewed, which is highly likely to be the case. When the test proves to be significant the distribution is deemed unequal. However, if the test proves to be insignificant, it does not mean that an equal distribution can be concluded. There seems to be no test that could prove equality of distributions between two groups. Consequently, differences between medians can never be concluded for sure, but the distribution shapes and Levene’s test could provide raw indications. Even if the Mann-Whitney U test proves to be insignificant, Levene’s test will still be ran since it could provide extra information concerning the data.
Most non-parametric tests involve ranked data. At least the tests that are used in this paper are all based on ranked data. With the Mann-Whitney U test the data of the two groups are ranked together in one group. After that the group is separated again and the ranks are summed per group (control group and treated group). There are three assumptions of the Mann-Whitney U test that have to be met. The first one is that the independent variable should be continuous or ordinal. Secondly, there should be independence between
the groups should be random in order to avoid sampling errors (Nachar, 2008) . All three assumptions are met for all hypotheses, so the Mann-Whitney U test can be used with confidence.
6.03 Hypothesis 1
H0= People that are exposed to a cognitive load are equally consistent in risk decision making.
H1= People that are exposed to a cognitive load are unequally consistent in risk decision making.
The Mann-Whitney U test is used to look at ordinal ranked data. When using this one can look if there is a difference between the treated group and the control group. It is expected that the cognitive load leads to more inconsistency in the binary choices of the participants since the cognitive load could interfere with rational behavior in having clear preferences. Levene’s test is also conducted in order to figure out if there is inequality in distribution.
The output of task C (binary choices), is used. The inconsistency rate for every participant is measured and ranked. The measurement to rank the inconsistency rate for a given subject, depends on the moment the subject starts to be inconsistent till the switching point to consistent answers. For illustration, four examples are given in Appendix 3. It
appears that no literature is available that tested this before. One problem of measuring inconsistency by this means, is the magnitude of inconsistency. It is not taken into account when a participant makes multiple inconsistent choices within the measured inconsistency frame. However, it is assumed that this does not have to interfere with the essence of the hypothesis stated, since the used measure is still reflecting whether the subject is
inconsistent in its answers within a specific range.
The time that the subjects needed to revise their answers is also measured. This could provide us with extra information about whether the corrective mechanism of system 2 reasoning is quick or slow. It is expected that within the group of participants, that were inconsistent in part I of the experiment, took more time in revising them than the consistent participants. This would mean that the corrective mechanism of system 2 requires time to revise answers and change outcomes when needed. However, physically changing answers
1
1 1 1 1
itself also takes time. It is not possible to correct for this, so carefulness should be taken into account when interpreting this result.
6.04 Hypothesis 2
H0= There is no effect of the exposure of a cognitive load on the sureness of people H1= People that are exposed with a cognitive load tend to be more unsure about their decisions
To test the second hypothesis the Mann-Whitney U test is used. The data of the slider scale scores (Task S) both before and after revision are used for this hypothesis. One disadvantage is that the Mann-Whitney U test has to be done for all eleven rounds of the task S scores apart. When a test turns out to be positive, it could mean that the groups differ for the specific round. So it is not possible to combine all rounds and see if they differ on the whole. The advantage is that there is more information about differences in sureness on the specific rounds. If Levene’s test has significant result, it implies a difference in the distribution
between both groups. When insignificant, it means that the variances are not unequal which could indicate that the median values differ.
As an extra test for this hypothesis the same Mann-Whitney U test is done for the four-point scale rate for satisfaction between both groups. The satisfaction rate is presumed as an indicator for sureness of the answers individuals gave. If the cognitive loaded group appears to have a significantly lower satisfaction rate, this reflects lower sureness.
6.05 Hypothesis 3
H0= There is no influence of the exposure of a cognitive load on the amount of risk people are willing to take
H1= The exposure of a cognitive load influences the amount of risk people are willing to take.
Again a Mann-Whitney U test is used in order to know if the risk profile of the treated group
3 2
group both before and after revision.In order to do this, consistency has to be assumed. Inconsistent answers are therefore not included in the test. The moment when the
participant makes the switch to the certain option is recorded. This number reflects the total risky decisions that were made before the switch. This gives a kind of ranked view of risk preferences, with €8,- being the risk neutral option, since the expected pay-off is the same for both options at this point. If the participants switched at round 5 and 6 ( €8,- and €9,- respectively), they were considered risk neutral. Risk choices that deviated from this point were measured in the total rounds it departed from the risk neutral option, with positive values being risk seeking and negative being risk averse. Besides that, Levene’ test is been conducted in order to give insight about the distributional differences.
6.06 Wilcoxon signed-rank test
When one compares two sets of choices that come from the same participants, i.e. matched samples, the Wilcoxon signed-rank test has to be used. This is the case for hypothesis 4. Just like the Mann-Whitney U test, the test is based on the differences between two sets of scores that are compared. These differences are calculated and ranked just like the Mann-Whitney U test.
The major difference between the two, is that the Mann-Whitney U test assumes independence between both groups and the Wilcoxon signed-rank test involves matched pairs. So the two groups, that are compared, are the same, since the treated group is being compared with the treated group (before and after revision). Similarly, for the control group. Regarding the interpretation of the results, it also has the same explanation as the Mann-Whitney U test. So no there is no distributional assumption, but if the distributions of both groups are similar, the results indicate a difference in median.
The technical difference between the two tests is that the calculation of differences is paired. Meaning that the difference of the two scores of the same participant is calculated (Task S before revision – Task S after revision) and ranked. After that, ranks are separated in positive and negative ranks, totals are summed and give us results.
6.07 Hypothesis 4
H0= There is no effect of the exposure of a cognitive load on the adjustment rates of decisions under risk.
H1= There is a positive effect of the exposure of a cognitive load on the adjustment rates of decisions under risk.
A comparison between the ranks of the slider scale tasks (task S) is needed in order to examine a possible difference between the scores of the participants before revision with the scores after the revision. These scores are compared for both the control group and the treated group. The null hypothesis states that the sureness levels do not change significantly after revision for both groups. The alternative hypothesis expects a positive effect of a cognitive load on the adjustment rates. This entails that the cognitive loaded group should show significant results while the control group does not. The differences between paired scores are calculated and ranked. If the difference is zero, i.e. ties, these scores are excluded from the data. If the Wilcoxon signed-rank test of the specific group is found to be significant it indicates a difference between the scores.
6.08 Kruskal-Wallis test & Dunn’s test
For hypothesis 5, the Kruskal-Wallis test is conducted. This test is used in order to check whether multiple independent groups come from different populations. In this case the Kruskal-Wallis test is conducted to show whether there is a relation between cognitive ability, that is measured by the cognitive reflection test, and inconsistent answers. The participants are grouped in the number of answers they had wrong. This test is also very similar to the Mann-Whitney U test. All pairs of groups are being compared on a Mann-Whitney U test method. The only difference is that the Kruskal-Wallis test corrects for familywise error rate that can result in type 1 error. When performing multiple tests, the chance of rejecting the null hypothesis wrongly is higher than the significance rate. The Kruskal-Wallis test corrects for this hazard.
To give a detailed view on the outcomes of the pairwise comparisons of the Kruskal-Wallis test, Dunn’s test is conducted. The test gives the raw p-values of every pairwise comparison made. So it is also checked how certain groups relate to each other.
6.09 Jonckheere-Terpstra test
In addition, the Jonckheere-Terpstra test is also conducted for hypothesis five. This tests whether there is an ordered pattern of the medians of the groups compared. In essence, it is similar to the Kruskal-Wallis test. However, the Jonckheere-Terpstra incorporates an order in the groups. In other words, the Kruskal-Wallis test provides all possible pairwise comparisons and looks whether multiple independent groups come from different populations. The Jonckheere-Terpstra reports the probability for a descending or ascending trend. The Jonckheere-Terpstra test therefore seems to be somewhat more appropriate for the hypothesis, since the inconsistency is expected to increase when the cognitive ability decreases.
6.10 Hypothesis 5
H0= There is no relationship between the cognitive ability of people and being inconsistent
H1= There is a negative relationship between the cognitive ability of people and being inconsistent
A Kruskal-Wallis test is conducted in order to test this possible relationship. However, the number of observations is not very high, splitting them in seven groups would decrease the trustworthiness. The Mann-Whitney U test is therefore also conducted. In this case the total participants are grouped in two. One group consisting of participants having four or more right answers and one group having less than four right answers. Since the total of questions are uneven, the observations are also split from three right answers on. Though, splitting the participants in two rather than seven also makes the test less precise.
5
1 1 1 1
Therefore, the Jonckheere-Terpstra test is done in order to see whether there is a trend between the total right answers of the CRT and inconsistency rates. All three tests give insight on the relation, however, since a trend is expected, the Jonckheere-Terpstra seems to be the best suit. Since there is a very low amount of inconsistent answers after revision, the tests is only conducted for the inconsistency rates before revision. It tests whether
individuals with lower CRT scores, are more inconsistent. The CRT scores of participants are grouped by the total answers they got right.
Besides that, the Jonckheere-Terpstra test is also used to know whether participants that spend more time in answering the questions had more right answers, despite being in the cognitive loaded group or not. The time that the participants needed in order to fulfil the tasks is recorded. It is expected that the more time participant used in order to answer the CRT questions, the less answers they got wrong. This would mean that there will be a lot of groups with low observations. Therefore, caution has to be taken with interpreting the results. To be sure the Mann-Whitney U test is also performed. These tests are run in order to provide more information about time consummation and system 2 use. If the time used has a positive effect on the amount of right answers it could mean that system 2 reasoning is more in play when using more time in fulfilling tasks.
6. Results
7.1 Hypothesis 1: The effect of a cognitive load on inconsistency4 H0= People that are exposed to a cognitive load are equally consistent in risk decision making.
H1= People that are exposed to a cognitive load are unequally consistent in risk decision making.
The Mann-Whitney U test is ran to see whether there is a difference in consistency between the control group and the group exposed with a cognitive load by remembering a six-digit number. As can be seen in figure 3 below, there is quite some difference between both groups. The cognitive loaded group appears to be more inconsistent than the control group. Despite this, the test shows no significant result. The P-value indicating that the two groups differ is 0.2766 (see Appendix 4.1).
Levene’s test also proves to be insignificant with a P-value of 0.92, so inequality in distribution cannot be concluded. However, since there is a low total of participants being inconsistent it is hard to conclude anything with the Levene test. Similarly, not much can be said about the distribution by looking at the graph.
For the comparison between both groups after revision we can conclude that most participants changed their initial answers to a more consistent outcome. The graph already indicates that no significant difference should be expected. Nevertheless, the test is still done. Using Levene’s test would however tell us nothing because of the extremely low inconsistent responses and is therefore not included. As expected after viewing the graph, with a P-value of 0.6716 no significant result is found, so the null hypothesis cannot be rejected.
` To conclude, there seems to be no difference between the treated group and the control group. In other words, The null hypothesis is not rejected and a cognitive load is considered to have no effect on consistency in risk decision making.
4 See appendix 4.1 for output
1
1 1 1 1
3. Figure – The difference between the control group and cognitive load group regarding their inconsistency before revision.
Inconsistency and time use revision
Also was expected that within the group of participants, that were inconsistent in part I of the experiment, took more time in revising them than did the consistent participants. Conclusion is that there appears to be a trend, but caution should be taken in stating that inconsistent participants take more time in revising the answers. Especially since physically changing answers itself also takes time and the trend could be attributed to this instead of concluding that system 2 corrective behavior takes time to revise correctly.
7.2 Hypothesis 2: The effect of a cognitive load on the sureness about decisions5
H0= There is no effect of the exposure of a cognitive load on the sureness of people H1= People that are exposed with a cognitive load tend to be more unsure about their decisions
For the second hypothesis, the Mann-Whitney U test is used for every round the participant had to rate their sureness about their decision of the specific round on a slider scale. This
2 1 1 1 1 51 3 4 2 42 7 2 4 1 0 1 0 2 0 3 0 4 0 5 0 0 1 2 3 5 6 0 1 2 3 5 6
Control group Cognitive load group
fr eq ue nc y Rate of inconsistency
hypothesis tests whether there is a difference between the cognitive loaded group and the control group before and after revision.
Figure 4, below illustrates the mean scores of all slider score rates per round, with round one offering the option of the certain amount of €4,- and round eleven offering the option of €14,- . To repeat, the 10 point slider scale was constructed in an order from, completely sure choosing the lottery (0), to being unsure (50), to being completely sure to choose the certain amount of money (100).
The graph illustrates that the cognitive loaded group is more unsure in every round before and after revision. The mean values clearly show that the cognitive loaded group tend to be more near 50 for every round (50 being unsure). This can especially be seen at the first and last round. The expected value of both choices is equal at round five, where the
expected value is €8,- . Besides the figure, the table in appendix 4.2 shows more clearly that for every round where the certain option is lower or higher than €8,-, the cognitive loaded group has a mean score that is more towards being unsure.
Nevertheless, the results show that only for one round a significant result is found (round 3 before revision). Despite the first observations, the tests prove insignificance for almost all rounds, both before and after revision. To conclude, the null hypothesis cannot be rejected, i.e. the values of the treated group do not differ from the control group.
Satisfaction rate and cognitive load
For the four-point scale rate between the treated group and the control group no significant result is found. Looking at the graph in appendix 4.2, it can already be concluded that both groups barely deviate from each other. Nevertheless, a Mann-Whitney U test is ran and indeed, the P-value of 0.5708 shows that it is far beyond the significance level.
4. Figure – Slider scale scores both groups before and after revision6
6 Vertical axis: Mean rate of sureness, horizontal rate: The specific round of Task S, chronically ordered, with round one offering the option of the certain amount of €4,- and round eleven offering the option of €14,-
1 2 3 4 5 6 7 8 9 1 0 1 1 0 10 20 30 40 50 60 70 80 90 100
decision certainty
S u re n e ss r a te7.3 Hypothesis 3: The effect of a cognitive load on risk behavior7 H0= There is no influence of the exposure of a cognitive load on the amount of risk people are willing to take
H1= The exposure of a cognitive load influences the amount of risk people are willing to take.
To see whether there is a difference in risk behavior between both groups, the Mann-Whitney U test is used. As stated in the methodology, inconsistent answers are dropped in this analysis. Consequently, the total number of subjects are less for the cognitive loaded group. The graph below reflects how risk profiles of participants are divided. Zero means that the switching point is equal to the point where the expected value of the binary choices were the same (round 5 and 6; for more information: See methodology). Positive numbers reflect risk seeking behavior and negative numbers reflect risk aversion. The higher the deviation from zero, the higher the magnitude.
Figure 5 indicates that most people were risk neutral. However, the cognitive loaded group deviates more from the risk neutral option. This is especially the case before revision, 21 out of 42 observations, i.e. 50% of the treated group deviated. For the control group 17 out of 51 observations, i.e. 33%, deviated. Contrary to our expectations, the deviations of the cognitive loaded group, just as the control group, tend to show more risk averse than risk seeking behavior. Even more than the control group (percentage risk averse control group: 29%; percentage risk averse treated group: 40%).
The risk profiles after revision show no remarkable differences between both groups (see figure 6). The total observations increased, because less participants were excluded due to the decrease of total inconsistent answers. For the control group, 39% deviated from the risk neutral option, of which 32% was risk averse. The treated group showed 48% deviation from the risk neutral option, of which 37% was risk averse.
Levene’s test proves to be insignificant, indicating that none of the distributions are significantly unequal. The results of the Mann-Whitney U test show that there is no
7 See appendix 4.3 for output
3
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difference between both groups, before and after revision. The p-value before revision is 0.5115, and 0.7361 after revision (appendix 4.3). Therefore, the null hypothesis cannot be rejected, i.e. There is no significant result indicating an effect of a cognitive load on the willingness to take risks.
5. Figure – The difference between the control group and cognitive load group regarding their risk profile before revision. A negative value reflects
a risk averse choice, a positive value risk seeking.
1 1 2 11 34 1 1 2 3 12 21 4 0 1 0 2 0 3 0 4 0 -4 -3 -2 -1 0 2 6 -4 -3 -2 -1 0 2 6
Control group Cognitive load group
fr e q ue nc y
Measured risk profile
15 35 15 28 2 0 3 0 4 0
Control group Cognitive load group
fr
eq
ue
nc
6. Figure – The difference between the control group and cognitive load group regarding their risk profile after revision.
7.4 Hypothesis 4: The effect of a cognitive load on the adjustment rates8
H0= There is no effect of the exposure of a cognitive load on the adjustment rates of decisions under risk.
H1= There is a positive effect of the exposure of a cognitive load on the adjustment rates of decisions under risk.
The Wilcoxon signed-rank test is ran for every round in which the participant had to rate their sureness about their decision. By looking at the graph that was shown before (figure 4), it appears that most participants became more sure about their decisions when seeing the overview of their decisions and changed their initial answer, since most of the means deviate more from 50 after revision. This can also be seen in the table of appendix 4.4.
The outcomes of Levene’s test all prove non-significance, indicating that none of the distributions are significantly unequal. Again, this does not mean that equal distributions, can be concluded although it is not ruled out.
The Wilcoxon signed-rank test proves to be significant for the first three rounds of the group that was exposed with a cognitive load. Besides that, round nine till eleven appear to
8 See appendix 4.4 for output
