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Dynamics and Heuristics of Investment Decision Making
Under Time Constraints: an Eye-Tracking Experiment
on Online Stock Marketplaces
Master Thesis
by
Elvira Hobusch
4
Abstract
Rational deterministic normative models consider that the market agents are pos-
sessed with unlimited time and knowledge and discard the underlying cognitive pro-
cesses behind decision-making. Conversely, decision field theory implements a dy-
namic approach to decision processes under uncertainty, explaining systematic rela-
tions between variability of preferences and time constraints. Besides the theory
mentioned above, adaptive toolbox model further advances decision-making processes
by a composition of heuristics and adaptation to the environment structure. The hy-
potheses from these models are assessed in the eye tracking experiment which is
conducted using the information stimulus from three main stock marketplaces, e.g. the
Deutsche Börse, the London Stock Exchange, and the NASDAQ. The participants
made their decisions between buying or short selling stocks. The author examines the
dynamics of processing complex and excessive financial information provided by web-
based stock marketplaces in regards to a particular stock in the thesis. The experiment
investigates the dynamics of the participants’ attention to the particular information con-
tent in the decision-making process and identifies the heuristics behind the decision
process and how they are affected by time constraints. In this research, involving the
measure of attention, the author observed that participants did not rely on the
deliberative processing of information under time constraints but rather than on a col-
lection of simple heuristics. The results indicate that the content of the particular infor-
mation under the natural complexity of the provided financial information impacts the
decision-making process of participants under both time conditions.
Keywords: decision making, eye tracking, heuristics, stock marketplaces, time
constraints.
5
Table of Contents
Abstract ...................................................................................................................................... 4
Table of Contents ...................................................................................................................... 5
List of Abbreviations.................................................................................................................. 7
List of Figures ............................................................................................................................ 8
List of Tables.............................................................................................................................. 9
1 INTRODUCTION ................................................................................................................. 10
1.1 From Rational Models in Finance to the Study of Biases and Heuristics in
Behavioural Finance ........................................................................................................... 10
1.2 From static to dynamic decision: discovering the black box ................................... 12
1.3 Time constraints in decisions vs. time pressure ....................................................... 13
1.4 Eye-tracking perspective of research on decision-making ...................................... 14
1.5 Overall relevance of the topic and motivation of the research ................................ 15
1.6 The general and specific problems and the stated research questions ................ 17
1.7 The overview of the structure of the paper ................................................................ 18
2 LITERATURE REVIEW ....................................................................................................... 18
2.1 Eye-tracking research in economics and business .................................................. 19
2.1.1 Eye-tracking in consumer choice ........................................................................ 19
2.1.2 Eye tracking research in decision making under risk and uncertainty ........... 21
2.2 Financial and investment decisions under uncertainty and time pressure ................. 25
3 METHODOLOGY OF THE RESEARCH .......................................................................... 30
3.1 Methods and tools utilized in this area of research and justification of the adopted
methods ................................................................................................................................ 30
3.2 Description of possible and applied eye-tracking techniques, software, metrics
and tools ............................................................................................................................... 35
3.3 The design of the experiment...................................................................................... 37
3.3.1 Participants ............................................................................................................. 37
3.3.2 Eye tracking apparatus and measures ............................................................... 38
3.3.3 Stimuli ..................................................................................................................... 38
3.3.4 Procedure ............................................................................................................... 39
4 DESCRIPTION OF DATA ................................................................................................... 40
4.1 Detailed description of data collection, measures and recording ........................... 40
4.2 Definition of dependent variables ............................................................................... 44
4.3 Data procedure ............................................................................................................. 48
4.3.1 Cleaning and preparing data for R analysis ....................................................... 48
6
4.3.2 Descriptive statistics and regression................................................................... 50
4.3.3 Growth curve analysis........................................................................................... 50
5 RESULTS ............................................................................................................................. 52
5.4 Summary of the results ................................................................................................ 52
6 CONCLUSION ..................................................................................................................... 55
6.1 Overview of the research ............................................................................................. 55
6.2 Findings and limitations ............................................................................................... 58
6.3 Importance and further research questions .............................................................. 59
7 REFERENCE LIST .............................................................................................................. 60
ANNEX ..................................................................................................................................... 69
Appendix A ............................................................................................................................... 69
Appendix B ............................................................................................................................... 70
7
List of Abbreviations
aDDM Attention drift-diffusion model
AOI Areas of interests
arcsin Inverse sine function
ATB Adaptive toolbox model
b Billion
CPT Cumulative prospect theory
DCF Discounted cash flow
DDM Dividend discount model
DFT Decision field theory
EMH Efficient market hypothesis
EPS Earnings per share
EUH Expected utility hypothesis
Hz Herz
LCAM Leaky competing accumulator model
m Million
MDFT Multiattribute decision field theory
ms Millisecond
PCS Parallel constraint satisfaction model
PE Price/earnings ratio
PEG Price/earnings to growth ratio
SD Standard deviation
SEU Subjective expected utility
SMI SensoMotoric Instruments
EK ElringKlinger AG
Kr KRONES AG
3I III 3I GROUP PLC
FP FPO FIRST PROPERTY GROUP PLC
AD ADMA Biologics Inc.
Am AMGN Company
8
List of Figures
Figure 5.1.1: Mean percentage fixations for each AOI per company 53
Figure 5.1.2: Mean percentage fixation across trials 53
Figure 5.1.3: Gaze effect per company under time conditions 55
Figure 5.1.4: Accuracy of the decision under time conditions 56
Figure 5.1.5: Cross proportion between decision and accuracy 57
Figure 5.2.1: Mean proportion score of the AOI depending on the decision
made
61
Figure 5.3.1: Looking at AOI stock and a decision to buy or short sell the stock
over time
63
Figure 5.3.2: Gazing at AOI stock in correlation with a decision to buy or short
sell the stock over time
64
Figure 5.3.3: Gazing at AOI stock in correlation with an accuracy of the deci-
sion over time.
65
Figure A.1: Example of the stimulus provided in the experiment 82
Figure A.2: Growth curve analysis of gazing over time at the AOIs 82
9
List of Tables
Table 5.1.1: Differences between gazing information (ms) and decision out-
come per company
54
Table 5.1.2: The changes in stock price and an investor’s decision 56
Table 5.1.3: Percentage change in fixation durations in a task, depending on
the accuracy of the decision
56
Table 5.2.1: The p-values of t-test and a fit to a simple linear model 58
Table 5.2.2: The Pr(Chi) values of fitting to a mixed-effect model 58
Table 5.2.3: The p-values of a paired t-test 59
Table 5.2.4: The p-values of fitting to a linear model 59
Table 5.2.5: The significant predictors in a mixed-effect model 60
Table 5.2.6: Mean proportion score of gazing at the AOIs depending on made
decisions
61
Table 5.2.7: Mean proportion score of gazing at the AOIs depending on accu-
racy of decisions made
62
Table B.1: Loss of eye tracking data per participant (%) 83
Table B.2: Summary statistic of raw data adjusted for the R software analysis 83
Table B.3: Summary statistics for the numerical variables 84
Table B.4: Example of descriptive data for each AOI of the AD stock 84
Table B.5: Example of descriptive statistics of aggregating data with three tar-
get conditions: a company, accuracy of decision and time condition
84
Table B.6: Examples of paired t-test between conditions with the predictor, pu-
pil diameter, for AOI.stock
84
Table B.7: Example of fitting the data to mixed-effects models for the AOIs 85
Table B.8: Example of growth curve analysis in R 86
10
1 INTRODUCTION
1.1 From Rational Models in Finance to the Study of Biases and Heuristics in Behavioural Finance Recent developments in economics, especially in behavioural economics, finance and
decision making, indicate the limitations of deterministic normative models in describ-
ing the behavioural and cognitive grounds and processes behind decision-making. Ne-
oclassical models in economics and finance usually assume that people are rational,
“equipped with unlimited time, knowledge, and computational might”; thus, they behave
as utility maximizers, and their behaviour is effectively coordinated via the invisible
hand of the price mechanism (Gigerenzer & Goldstein, 1996, p.650).
Traditional finance is based on the following main theories, models and principles: the
modern portfolio theory of Markowitz (1952), the arbitrage principles of Miller and
Modigliani (1958), the capital asset pricing model of Sharpe (1964), Lintner (1965) and
Black (1972), and the option-pricing model of Black, Scholes and Merton (1973)
(Kumar & Goyal, 2015). The models mentioned above hinge on the efficient market
hypothesis (EMH), which states that “in an efficient market, all the available information
is incorporated while estimating the prices of financial assets” and asserts that share
prices reveal all relevant information (Naveed et al., 2014, p.88). In addition, the ex-
pected utility hypothesis (EUH) of Daniel Bernoulli (1738) and von Neumann–
Morgenstern (1944) presumes that investors rationally evaluate all the alternatives by
their utility and the associated risk and subsequently make a balanced decision (Kumar
& Goyal, 2015). However, EMH’s and EUH’s assumptions that investors behave ra-
tionally in the financial market have proved to be inconsistent with irrational investor
behaviour (Naveed et al., 2014).
Therefore, the idea of bounded rationality by Herbert A. Simon (1957) emphasizes the
need for behavioural consideration in economics and points out that human agents,
although “intending to make rational decisions,” they are still bound by their “limited
ability to process information” (Augier, 2001, p.331). Whereas these approaches pro-
duce simple and tractable models, they cannot fully capture uncertainties that affect
everyday decisions. Furthermore, based on their empirical studies Daniel Kahneman
and Amos Tversky developed prospect theory and later cumulative prospect theory,
which is an alternative to EUH in explaining decision making under uncertainty where
investor’s decision making is based on potential gains and losses rather than on final
outcomes. This phenomenon occurs because of the cognitive biases that affect the
judgement of these gains and losses (Kahneman & Tversky, 1979). Daniel Kahneman,
Amos Tversky and their followers demonstrate that investors “all harbour idiosyncratic
ideas” and that they tend to act on these thoughts, “regardless of the costs to their
11 economic welfare” (Curtis, 2004, p.21). Thereafter, the research in this area is contin-
ued in both directions: recognizing anomalies in the EMH that behavioural models fea-
sibly describe (De Bondt & Thaler, 1985) and identifying individual investor behaviours
that conflict with classical economic theories of rational behaviour (Odean, 1999).
However, during this half of the century not only were the models improved to reflect
the reality and nature of investors’ behaviour but also the market mechanisms have
become more complex and demanding more sophisticated deliberation and investiga-
tion instruments (Pop, Iorga & Pelau, 2013). Firstly, the process of deliberating the fu-
ture price of stock for investors is becoming more demanding and complicated. Nu-
merous factors both global and domestic might affect stock prices, and some of these
factors can reduce an expected future price promptly and drastically. Secondly, the
time available for decision making is shortened, considering that overall complexity has
increased. Therefore, under such time constraints, it is questionable to deliberate all
available information even with a known personal utility function, and a personal prob-
ability distribution as proposed by Leonard Savage (1954) in subjective expected utility
theory (SEU). Thirdly, under volatile conditions, it is not feasible for any decision maker
to reason “a reliable joint probability distribution of all prospect proceedings” (Naveed
et al., 2014). And approximation of probability distributions leads to an uncertainty of
probability distributions concerning the prospect events. Previous researchers indicate
that the processing of uncertainty highly hinges on the situation and context
(Preuschoff, Mohr & Hsu, 2013). Therefore, the decision makers are dubious to define
a distinct utility function and as a result to maximize approximated utility function. Con-
sidering all the complexities mentioned above, constraints, and human cognitive limita-
tions as well as biased behaviour, perhaps these matters can lead to further profound
research to reconcile the decision-making process and deliberate possible variations of
satisfying outcomes.
Before moving to the methodological development of decision-making concepts, it is
necessary to clarify that the author applies the same definition of uncertainty in this re-
search as stated by Bland and Schaefer (2012) which separates meaning of uncertain-
ty into three main forms: expected uncertainty (including risk), unexpected uncertainty
and volatility. The investment decision maker addresses all three forms of the uncer-
tainty to some degree. This work is concerned mostly with decisions involving uncer-
tainty when a decision maker must deliberate possible multiple outcomes for which the
probabilities can be partially calculated or completely unknown due to lack of
knowledge, experience and time (Huettel et al., 2006).
12
1.2 From static to dynamic decision: discovering the black box
The author introduced the behavioural aspect to decision making in economics and
finance. Now it is time to glance at why the dynamic of decision-making is more ap-
pealing to study rather than a decision outcome. Therefore, it should be noted that the
same development pathway from deterministic static normative models to stochastic
dynamic descriptive models in decision making in economics and finance can be
traced from a methodological point of view. This approach is another look at the im-
portance of the topic of study. The extensions and modifications of EUH, for example
von Neumann-Morgenstern’s utility theorem (1944), multi-attribute utility analysis
proposed by W. Edwards (1954), SEU model of L. Savage (1954) culminated by
cumulative prospect theory (CPT) of Kahnemann and Tversky (1992) and the transfer-
of-attention exchange model of M. Birnbaum (1997), speculate that various “integration
of payoff and probability of outcomes” drive the individuals’ choice (Fiedler & Glöckner,
2012). CPT proposes that gains and losses are the carriers of value, “not final assets
and the value of each outcome is multiplied by a decision weight, not by an additive
probability” (Tversky & Kahneman, 1992, p.299). However, the models mentioned
above predict choices as outcomes and do not discuss the processes underlying the
decision making (Glöckner & Witteman, 2009). In the following literature Payne, John-
son, Schulte-Mecklenbeck and others state the significance of considering the underly-
ing processes in studies (Payne et al., 1988; Johnson et al., 2008; Franco-Watkins &
Johnson, 2011; Schulte-Mecklenbeck et al., 2011).
In this paper, the author focuses on simple heuristic models, i.e. the adaptive toolbox
model (ATB) by Gerd Gigerenzer (2001) and evidence accumulation models, i.e. deci-
sion field theory (DFT) of Jerome Busemeyer and James Townsend (1993) to explain
the results of the eye-tracking experiment. Simple heuristics models hypothesize that
individuals adapt their decisions to the situations by using simple shortcuts, optimal but
sufficient only for the immediate goals, and do not integrate all pieces of information.
Simon’s idea of “satisficing” heuristics in decision making introduces the importance of
order in which alternatives are evaluated. Because of the limitations of the human mind
and the structure of the environments in which the mind operates, individuals “must
use approximate methods to handle most tasks" (Simon, 1990, p. 6). Brandstätter
claims that priority heuristic or fast and frugal heuristic is based on a simple lexico-
graphic rule for decisions, and this heuristic better predicts the outcome between
gambles than the other ones (Brandstätter et al., 2006). Adaptive toolbox model ex-
tends the simplifying of the heuristics approach to “ecological rationality, frugality, ro-
bustness and building blocks of heuristics” where “domain specific heuristics” applies
to the decision under certain conditions and limitations (Gigerenzer, 2001, p.139).
13 On the other hand, evidence accumulation models such as DFT of Busemeyer and
Townsend (1993), the leaky competing accumulator model of Usher and McClelland
(2001) and the parallel constraint satisfaction model for risky choice of Glöckner (2008)
assume that individuals integrate information quickly, efficiently and sequentially “until
enough evidence has been accumulated to pass a decision threshold” (Hausmann,
2008, p.229). DFT considers “the variability of preferences and the systematic relation-
ship between preferences and deliberation time” (Busemeyer & Townsend, 1993,
p.455). The deliberation process includes not only an accumulation of information but
also an amount of attention allocated over time. In value based decisions, attention
fluctuates over attributed dimensions at each step in the accumulation process with the
differences in attributed values on the attended dimensions accumulated at each step.
Thus, dynamic models describe the decision-making process as influenced by uncer-
tain environments such as cognitive limitations, past experiences, expectations, prefer-
ences, emotional state, memory and time constraints. Therefore, “given that economic
actions are exerted by biological organisms embedded within their environment”, it is a
scientific responsibility to take into account the behavioural aspect of decision making
(Giordano, 2012, p.45).
1.3 Time constraints in decisions vs. time pressure
Hitherto, the author explains the choice of the topic by referring to the previous studies.
However, the decision-making area of research in economics and finance is very di-
verse. It is necessary to limit the study to a specific aspect. As known many decisions
in economics and finance are made under time constraints. Furthermore, payoffs in
many cases directly depend on the speed of decision making, for example when buy-
ing and selling stocks (Kocher & Sutter, 2006). Time constraints limit available re-
sources and deliberation of information which results in information overload. There-
fore, time constraints not only interfere with the decision-making processes but can al-
so lead to a less objective and more intuitive than a rational decision. Adopting some
heuristics, or mental shortcuts, individuals deliver applicable decisions under time con-
straints with limited logical decision-making deliberations.
Considering the points mentioned above, the author concludes that time constraints
are the main limitations in decision making that intensify the cognitive and tangible
drawbacks. Therefore, this research examines the decision-making process under time
constrained conditions as a significant part of decision making in applied economics
and finance. Additionally, the author separates time constraints from time pressure.
Even though the terms "time constraints" and "time pressure" are used interchangeably
in most of the previous literature, Ariely and Zakay (2001) indicate that “time con-
straints” “often is used as internally or externally imposed deadlines” (Ordóñez, Benson
14 III & Pittarello, 2016, p.520). Whereas “time pressure” mostly indicates “the subjective
feeling of having less time than is required (or perceived to be required)”. Therefore,
the author of this thesis agrees with Ariely and Zakay that there is a denotative differ-
ence between “time constraints” and “time pressure” and does not examine any emo-
tional aspect of time limitations, although both terminologies are considered for the re-
view in the literature part of this paper.
1.4 Eye-tracking perspective of research on decision-making
Now it is comprehensible why the study of dynamics and heuristics of the decision-
making process under time constraints is motivating to perform. However, the author
additionally commits to addressing the decision for the use of eye tracking techniques
for the research. Acknowledged, as early as 1596, Du Laurens, a sixteen-century
French anatomist and medical scientist, “referred to eyes as windows of the mind” (van
Gompel et al., 2007, p.3). Next, starting in 1924, the eye-tracking research in business,
in the field of marketing, was conducted by Nixon. Currently, over the last twenty years,
eye-tracking studies in economics have drastically increased. Assuming that the visual
system interacts with attention, cognition and behaviour (Yarbus, 1967, Rayner, 1998,
2009; Liversedge & Findlay, 2000), experimental economics tests the validity of eco-
nomic theories and endeavours to explain market mechanisms.
The eye movements in response to visual stimuli reveal the individual experience of
the world (Horsley et al., 2014). The eye-tracking technology is a research tool used to
measure visual attention. Attention allows individuals to monitor objects, subjects, or
areas of visual space and extract information from them to use for reporting or storage.
Moreover, considering that 83% of the information used in cognitive processing is
obtained visually, eye tracking measurement provides contextually relevant data that
can be analysed to advance models of decision making (Wästlund et al. 2010). The
recent research in neuroeconomics confirms that both saliency (key attentional mech-
anism) and value influence the final decision. To be precise, saliency affects fixation
locations and durations, which are predictors of choices (Towal, Mormann and Koch, 2013).
The following examples of the correlations between eye tracking measurements and
cognitive processing experimentally have been established: there is a close link
between fixations and comprehension (Rayner, 1998); an attentional shift to the target
location guides saccades (Kowler, Anderson, Dosher, & Blaser, 1995); the shifts in
attention are usually reflected in the fixations (Corbetta et al., 1998); pupil dilation
responses indicate emotion, arousal, or cognitive load (Wang, 2011). However, previ-
ously Yarbus in 1967 experimentally proved that the role of vision is much more com-
plex. On one hand, the analysis of eye-tracking data affirms the importance of the task
15 in determining where participants look. On the other hand, the particular fixations do
not disclose what the observer “really” thought while looking at these locations. There-
fore, “a given cognitive event might reliably lead to a particular fixation, the fixation it-
self does not uniquely specify the cognitive event” (Hayhoe, 2004, p.268).
Understanding the relationship between eye-tracking data and cognitive processes be-
hind them can help to comprehend how human economic behaviour can be affected by
the informational content, attention and emotional state. Recently, as eye tracking
technology has become more affordable and accessible to academics. It has become
more preferred to conduct an experiment with eye tracking application in behavioural
areas of economics and finance (Gould & Zolna, 2010).
Because this research comprises the information stimuli from the online stock market-
places, the web introduces new opportunities and challenges for an eye tracking re-
search. Scholars have utilized eye-tracking mostly for analysis of online human-
computer interactions and web searches, although it can be a very promising field of
research in the future because of increasing interest and usage of the internet in many
areas of human performance. Even though some techniques have been developed to
quantify, compare and aggregate eye movements linked to these online environments,
there are indeed some complications related to the usage of eye tracking in online con-
texts, for example, due to dynamic content. However, some experimental results
demonstrate its value and demand for further research (Granka, Feusner & Lorigo, 2008).
1.5 Overall relevance of the topic and motivation of the research
Previously the author designates the importance of studying the behavioural aspect of
the decision-making process under time constrained conditions and with eye tracking
techniques to comprehend the cognitive process of decisions in economics and finance
that lead to a specific investment decision. Additionally to the demands mentioned
above, it should be considered that the online share trading is “no longer restricted to
the expert brokers.” A vast and diverse population of investors with varying abilities,
knowledge and experience is making their investment decision every single day in the
markets (Richardson, Gregor and Heaney, 2012, p.523). Decision making in this con-
text can be suboptimal and risky. Thus, first of all, the research in this area is crucial to
understand the investors’ behaviour and decision-making processes behind their deci-
sions and consequently facilitate the investors to make better investment decisions in
the extremely complex and complicated financial markets (Naveed et al., 2014). Sec-
ond, the stock offering companies from all around the world strive to make improve-
ments in data representation available on their websites. The results of the research
are a first attempt to demonstrate what kind of information and data are more attentive
16 in investment decisions under time constraints. This paper focuses on financial infor-
mation provided by the online stock marketplaces to make a decision (buy or short sell
the stock) under time constraints. The author measures decisions of participants with
the SMI eye-tracker.
Hitherto scholars focused on creating an experimental design of alternatives that limit
and simplify all other possible influences in the decision-making process except one
aspect to be analysed and fitted to the model such as value, probabilities, etc. The ex-
perimental economists typically have designed “an artificial or hypothetical content,
which makes searching for information irrelevant” (Gigerenzer, 2001 p. 119). However,
the decision-making process always faces a complexity in natural settings. Therefore,
in this experiment the stimuli of the experiment are not created artificially, or manipu-
lated, they are actual representations of information from the websites themselves, and
participants make their decisions by deliberating actual information presented in online
stock marketplaces with a similar layout but without advertising windows. The author
restricts the experiment to the exactly defined areas of interests (AOI) to test the spe-
cific hypotheses, understanding the possible complications and indistinctness. The ex-
periment simplifies the analysis of the decision-making process by putting aside the
matter of comparison between stocks. Most important in this thesis is the deliberation
process of obtaining information about the performance of only one particular stock in
order to make a decision to buy or short-sell it. Considering this particular setting, the
author concentrates on the examination of attention to the specific kind of information
which influences the decision1.
This master’s thesis incorporates some of the techniques of eye-tracking analysis pub-
lished in the research of Susann Fiedler and Andreas Glöckner (2012) such as a
measure of attention and pupil dilation. However, the author of this thesis additionally
applies a few other experimental and behavioural economics’ methods in decision-
making processes by designing and conducting an own experiment on investment de-
cision making under time constraints. The experimental data is collected and examined
by using the eye tracking SMI software: Experiment Center and BeGaze and R statistical
software.
The main purpose of this master’s thesis is to investigate what kind of financial infor-
mation from online stock marketplaces, i.e. the Deutsche Börse, the London Stock Ex-
change and the NASDAQ, is more attentive for investors to make a decision under
time constraints and what heuristics the participants apply in their decision-making pro-
cess. Generally speaking, this master’s thesis examines the decision process by which
1 In most experiments, the provided options are a set of two alternatives. This experiment has one op-tion - an information block and two alternative choices - buy or short-sell.
17 “investors” process visual information to predict the future expected value of financial
assets and thus to invest accordingly (Duclos, 2015).
1.6 The general and specific problems and the stated research questions
The general idea of this research is an analysis of investment decision-making pro-
cesses under time constraints. Social challenges, learning and experience, cultural
background and time constraints influence the decision. Assuming the first three im-
pacts are being equal, the author measures only how time constraints affect the decision-
making process.
The following main questions are investigated in this paper: What type of information is
more attentive in making decisions under time constraints? What heuristics do
participants apply to make a decision under time constraints? The research measures
the attention and pupil dilation of the participants under time constraints and compares
the following main areas of interest (AOI): stock price summary or stock quotes, chart,
information about the company and ratios. The behaviour and experimental models of
the decision-making process such as adaptive toolbox (ATB) and decision field theory
(DFT) are tested on experimental data whether they can predict the choices made. The
thesis focuses on the main idea from ATB, i.e. domain depending or adaptive collection
of heuristics. DFT considers an accumulation of information, the amount of attention
and the time of deliberation that influences the decision-making process (Busemeyer &
Townsend, 1993). Therefore, as stated by researchers, “only the most prominent di-
mension tends to be processed, and the first alternative should be chosen more fre-
quently” under time constraints (Busemeyer & Townsend, 1993, p. 455). However,
with longer deliberation time, because additional information is considered, “the second
alternative should be chosen more frequently” (Busemeyer & Townsend, 1993, p. 455).
Consequently, the following hypotheses are formulated to test the attention to the con-
tent of the provided information that influences the decision under time constraints:
1. The fixation durations are stable over time and tasks.
2. The gaze cascade mechanism supports the decision (attentional bias).
3. Visual information such as graphs and charts impact the decision.
Additionally, following hypotheses based on ATB and DFT verifies the decision-making
process under time constraints:
1. The most prominent dimension tends to be processed the most and the first
(assumed that it is the summary of the stock price information).
2. The longest alternative should be chosen more frequently because of longer
deliberation time (i.e. the option to buy a stock).
18
3. Changing to simple heuristics decreases the accuracy of the decision or under
time constraints the accuracy of decision decreases.
1.7 The overview of the structure of the paper
The subsequent parts of the thesis are organized as follows. The second part of the
thesis presents the literature review of the previously published studies of investment
and financial decisions under time constraints employing different methods including
eye-tracking experiments. The third part defines the methodological framework for the
paper and explains the relevance of the adopted methods such as adaptive toolbox
and decision field theory and techniques such as eye tracking, statistical software R;
both of which are utilized to collect and analyse the experimental data. The following
fourth part provides the description of the experiment, the definitions, explanations and
reasoning behind the chosen variables, also detailed data collection conditions. The
fifth part introduces the interpretation of the results according to the stated hypotheses
in regards to the information content and heuristics employed in the decision-making
process and provides critical assessments of the findings. Finally, the research paper
concludes with the summary, importance of the research in the area of behavioural fi-
nance and description of limitations that the author has faced during the process of this
research and possible further extensions of the work.
2 LITERATURE REVIEW
In this paper, the literature review considers not only the studies of investment deci-
sions under time constraints using eye-tracking but also the publications in the area of
investment and financial decisions under time pressure and uncertainty using other
methods of behavioural and experimental economics. The author decides on this
approach for two reasons. First, to overview the extension of previous studies in this
area and the usage of different applications and methods. Second, to demonstrate that
this research is unique in applying eye tracking techniques to examine the decision-
making process of obtaining information from online stock marketplaces under time
constraints to make a decision to buy or short-sell the stock. Therefore, the author em-
ploys the following structure for the review of publications:
(1) publications in economics, finance and business that employ eye-tracking tech-
niques under time pressure and constraints, including:
(a) consumer economic decisions as a purchase choice,
(b) decision making under uncertainty (including risk, determined as uncertainty
with certain probabilities) and time pressure/constraints;
19 (2) decision making in economics and finance under uncertainty and time pres-
sure/constraints.
The publications are chronologically organized where it makes sense to review the de-
velopment of the ideas in certain areas of the research.
2.1 Eye-tracking research in economics and business
The analysis of eye movement has a long tradition dating back to the end of the 19th
century in several scientific disciplines. However, in economics and business, eye
tracking techniques have been used mostly in marketing over the last few decades, in
the analysis of consumer choices recently, in brand and product management occa-
sionally, and in the other areas of economics and finance very rarely. Such positioning
can be explained not only by expensive eye tracking equipment and complex eye-
tracking data analysis but also by the complexity of the financial information. The fol-
lowing publications apply eye-tracking to the research in business and marketing, for
example, Pieters and Warlop (1999) analyse eye movement data during the brand
choice, Pieters, Warlop and Wedel (2002) and Pieters and Wedel (2004) the attention
to advertisements. Feiereisen, Wong and Broderick (2008) apply eye-tracking to test
the role of visual attention in the context of product innovations. Zülch and Stowasser
(1999) discuss eye-tracking in the context of quality management in production (Zülch
and Stowasser, 2001). Successful applications of eye-tracking are also found in ac-
counting (Hunton & McEwen, 1997). However, as mentioned by Koller et al. (2012), the
previous studies that employed eye tracking were limited to certain topics, especially
“to facilitate our understanding of methodological issues” in economics and business.
Yang and Wang (2015) published a more recent review of using eye tracking applica-
tions in business research. They indicate the same lack of sufficient studies using eye
tracking in business disciplines and, as stated before, publications encompass mostly
the fields of marketing, electronic commerce, advertising and consumer behaviour.
In this review, the author focuses on publications that measure decisions under time
pressure and constraints in economics and finance using an eye tracker. Therefore,
publications in a field of marketing are not considered. However, a consumer economic
choice under time pressure can be regarded as a purchasing decision that involves
financial and economic factors, and therefore is taken into account.
2.1.1 Eye-tracking in consumer choice
One of the first eye-tracking studies in consumer choice under time pressure is
provided by Reutskaja and her colleagues in 2011. They analyse a subjects’ choice
between different numbers of items under time pressure using eye tracking to screen
20 the search process of the consumers. The scientists observe that subjects optimize
their search very well within the set of multiple items, which they saw on the screen,
even if the initial search process was random in value. With an increasing number of
alternatives, the subjects are “shortening the duration of their fixations”, but it had only
“a small impact on the quality of the choices” (Reutskaja, 2011). Additionally, subjects
of the experiment (or consumers) tend to have choice biases because of their attention
on certain focal regions of the display which lead them to choose more fixated items.
Reutskaja analyses internet consumers’ decisions, i.e. the effects of information
presentation on the consumers’ thoughtful choice. She observes that the table format
of information is strengthened while the map (or graph) weakened deliberateness of
the consumers’ value choice and lead to emotional choices vs. careful rational deci-
sions. The effect of presentation (or display) is mentioned by Huang and Kuo (2011).
Their research is one of the first attempts to investigate the joint effects of presentation
and decision orientation on careful consideration of the internet domain.
One year later Krajbich with his colleagues examines the validity of the attentional drift-
diffusion modelling on purchasing decisions. They further develop the drift-diffusion
model and tested it in an eye-tracking experiment (Krajbich & Rangel, 2011). The re-
sults indicate that the model provides a reasonably accurate quantitative description of
the relationship between choice, reaction time and visual fixations in this purchasing
decision. According to the experiment, “fixations to prices are shorter and less varia-
ble”; however, “the results suggest that they are also integrated noisily over time” in the
choice (Krajbich et al., 2012).
The same study with Krajbich and Rangel (2011) evaluates binary value choice in
comparison with trinary value choice. The results support the idea that the same com-
putational processes are taking place in simple binary vs. trinary value-based choices
and that the decision process is guided by visual attention in the conducted experi-
ment. Additionally, Krajbich and Rangel show that “the fixation process is not fully in-
dependent from the valuation process” and understanding how the fixation process
takes value into account can be the reasoning for further research in this area (Krajbich
& Rangel, 2011).
Previous studies were mostly focused on visual attention during consumer choice deci-
sions. The following paper by Lee (2013) investigates how a retail brand’s name affects
consumers' decision-making quality in the online shopping environment and how a
brand’s name influences on decision making. Lee (2013) demonstrates that branding
improves consumers' decision-making processes and enhances the quality of their de-
cisions by reducing cognitive effort and appealing emotionally through heuristic choices
to consumers. In addition, branding can increase trust towards products. Furthermore,
21 branding leads consumers to think positively about the quality of their decisions
(Lee, 2013).
The connection between visual attention and consumer behaviour, mentioned above,
has numerous implications in terms of understanding consumer purchasing decisions.
Therefore, in their introduction to eye tracking technology and methodology, Khacha-
tryan and Rihn (2014) explain how successfully eye-tracking technology can be used in
exploring the relationship between visual attention and consumer behaviour in con-
sumers’ decision making (Khachatryan & Rihn, 2014).
The influence of time pressure to the decision in connection with visual attention is the
topic of the next publication in this area. Meißner et.al (2015) recently publish their eye-
tracking study, which reveals decision processes in conjoint choices. This research
points out that combined choices take less time and are more accurate with practice.
Thus, greater speed and reliability of the decisions are a result of two simplification
processes: alternative focus gradually shifts attention towards options that represent
promising choices, while attribute focus directs attention to important attributes that are
most likely to alter or confirm a decision. Meißner with his colleagues detects a small
but consistent focus on positive aspects of the item chosen and negative aspects of the
items not chosen regarding biases. In conclusion, they point out that overall, the
conjoint choice is revealed to be a process that is largely formed by goal-driven values
that respondents bring to the task, one that is relatively free of distorted effects from
the task layout or random exposures (Meißner et. al, 2015).
As a result, publications in the area of consumer value-choice under time pressure
provide very important conclusions: (1) consumers optimize their choice strategies
under time pressure; (2) a presentation or a display of information influences the
decision; (3) a consumer decision is a subject to common cognitive biases; (4) the
decision process is guided by visual attention and (5) the same computational
processes are taking place in simple binary and trinary value-based choices (this is a
matter of the discussion in different articles).
2.1.2 Eye tracking research in decision making under risk and uncertainty
The next set of publications in economics and finance focus on decisions under risk
and uncertainty using eye tracking. Arieli, Ben-Ami and Rubinstein (2009) apply eye
tracking techniques to examine decision makers’ motivations and procedures in choice
problems between lotteries. In a simple choice between lotteries, the decision is based
on a comparison of prizes and probabilities rather than on calculation of expected utili-
ty. In motivation games, participants who selfishly behaved nevertheless take into con-
sideration the size of the payment compared to the other less selfish person. However,
22 overall participants are not motivated solely by selfishness in their decisions under un-
certainty (Amos, Yaniv & Rubinstein, 2009). Another experiment with lotteries conduct-
ed by Arieli, Ben-Ami and Rubinstein (2011) reinforces the same outcome: decision
makers often compared prizes and probabilities separately and this is particularly true
when the multiplication of sums and probabilities is laborious to compute.
Shavit et al. (2010) compare the performance of individual assets vs. portfolio in the
decision-making process. Using an eye tracker they conclude that investors spend
more time looking at the performances of an individual asset than at the performance
of the overall aggregated portfolio. Investors look at the net value change more than
the assets’ final value. Moreover, investors gaze at the change of the monetary value
longer than at change in percentages. Specifically, participants observe longer the val-
ue change of gaining assets than at the value change of losing assets leading to loss
aversion.
The following year, Glöckner and Herbold (2011), conducted the eye tracking
experiment of two gambles with two non-negative outcomes each in order to
investigate how the decision-making process, i.e. choices, decision times, and
information search fit with the hypotheses derived from cumulative prospect theory,
decision field theory, priority heuristic and parallel constraint satisfaction models. They
discover that individuals use compensatory strategies in their decisions. Even if their
choices are consistent with the predictions of cumulative prospect theory, decision pro-
cess measures testify that individuals do not consider the calculations of weighted
sums (Glöckner & Herbold, 2011).
The subsequent publication is based on the analysis of eye-tracking results of the pre-
vious research as well as the original one, where Fiedler and Glöckner (2012) describe
the underlying cognitive processes of risky choices by measuring attention and pupil
dilation and if they are consistent with existing models of decision theories. According
to the observation, the participants’ attention to an outcome of a gamble increased with
its probability and its value and that attention shifted toward the subsequently favoured
gamble after about two-thirds of the decision process, indicating gaze cascade effect.
Additionally, pupil dilation increased during the decision-making process and increased
with the mean expected value.
The debate over whether making a risky choice is based on a weighting and adding
process has a long history and is still unresolved. Su et al. (2013) address this question
in their research using eye tracking in single-play and multiple-play conditions. The re-
sults show that participants might use a weighting and adding process to make risky
choices in multiple-play conditions. In contrast, participants are not likely to use a
23 weighting and adding process to make risky choices in single-play conditions and are
more likely to use a heuristic process (Su et al., 2013).
However, the research of risky gamble decisions by Venkatraman, Payne and Huettel
(2014) supports the use of a simple heuristic that maximizes the overall probability of
winning (not losing) as a strategy for decision making involving complex (multiple
outcomes) mixed gambles. Another heuristic in decision making is supported by the
eye-tracking application in the experiment conducted by Hüsser and Wirt (2014). They
examine investors’ visual attention to parts of mutual fund disclosure. Results indicate
that prior fund performance, which is irrelevant normative information and non-useful in
predicting future performance, according to the authors’ opinion, receives considerable
attention from investors, and investors apparently believe in performance persistence.
Moreover, the participants are warned that past performance does not guarantee future
results at the beginning of the experiment.
In their investigation of how affective reactions influence investment decisions,
Rubaltelli, Agnoli and Franchin (2016) detect the impact of past performance in the
decision-making process. Taking into account individual differences regarding emo-
tional intelligence, the authors demonstrate that people who are more sensitive to af-
fective information have larger pupil dilation when looking at the past performance of a
stock fund. Additionally, the participants' larger pupil dilation has an impact on their in-
vestment decisions. Larger pupil dilation causes people to be more consistent and will-
ing to invest more money in a fund regardless of its past performance (positive or neg-
ative). Therefore, they indicate the impact of past performance and the trait of
emotional intelligence on investment decisions are significantly mediated by pupil
dilation.
This result is supported by another experiment conducted by Duclos (2015). In this ar-
ticle, he analyses how people process graphical displays of financial information (e.g.,
stock prices) to forecast future trends and invest accordingly. The results support that
the previous trading day bears in high importance on investment behaviour, even if no
real upward or downward trend can be identified by participants.
In their eye-tracking experiment and following after the verbal protocol on risky
gambling, Brandstatter and Korner (2014) establish direct relations between process
and choice and indicate that different components of a gamble attract different
amounts of attention depending on the participants' actual choice. Maximum losses
always have received most of the attention regardless of a choice (risky vs. safe
investment). Participants are concerned with the worst outcome in both loss/gain
games while simultaneously focusing on the probability of obtaining the best one. “This
effect was stronger for the loss than for the gain domain” (Brandstatter & Korner,
24 2014). Moreover, the last-fixated gamble but not the last-fixated reason predicts the
participants' choices that use cognitive processes similar to heuristics.
The decision making in economic gambles is the research topic of the recent article by
Kwak and his colleagues. They chose another angle to this problem, i.e. changes in a
human decision making over time. The authors examine the strategies used by ado-
lescents and young adults to resolve complex, multi-outcome economic gambles equa-
tions. The eye tracking data shows that prior to decisions being made, adolescents ac-
quire more information, and they engage in a more analytic processing strategy indica-
tive of trade-offs between decision variables and are more likely to make conservative,
loss-minimizing choices consistent with economic models (Kwak et al., 2015). In con-
trast, young adults' decisions are more consistent with heuristics that simplify the
decision-making process at the expense of analytic precision. Therefore, adolescents'
decisions are more consistent with rational-choice models, while young adults more
readily engage in task-appropriate heuristics because of lack of knowledge and experi-
ence (Kwak et al., 2015).
In the newly published article, Stewart, Hermens and Matthews (2016) conduct an eye-
tracking experiment on simple risky choices. They state the presence of gaze bias in
the decision-making process which is in contrast with prospect theory and the priority
heuristic. Additionally, they confirm that “the actually attributed values in the choice op-
tions are independent of the final choice” (Stewart, Hermens, & Matthews, 2016,
p.116). They specify that the participants chose the gamble they gazed at more often,
independently of the actual numbers they saw. Decision field theory, the decision by
sampling and the parallel constraint satisfaction model support the results of the
experiment.
It can be concluded from the preceding review that the application of eye tracking for
decision making is an approach which is developing rapidly and beginning to be uti-
lized more effectively in behavioural economics and the science of decision making
recently. This application shines some light on cognitive processes which underlie the
choice to understand the process of human decision making. The above-mentioned
publications of decisions in economics and finance under risk and uncertainty indicate
the following results: (1) decision makers separately compare values from probabilities
under time pressure and complex settings; (2) investors more focus on value change of
individual asset rather than on the performances of the overall aggregated portfolio or a
change in percentages; (3) they are concerned with the worst outcome in both
loss/gain games while simultaneously focusing on the probability of obtaining the best
one (second and third points support loss aversion tendency of investors); (4) investors
in their decisions rely on past performance of the fund; (5) visual attention influences a
25 choice or there is aptitude for the gaze cascade effect; (6) decision-making in multiple-
play conditions may be different than in single-play conditions; (7) adolescents'
decisions are more consistent with rational-choice models then young adults’
decisions.
2.2 Financial and investment decisions under uncertainty and time pressure
In this research paper, the review of previous publications on the decision under uncer-
tainty and time pressure is included even if the researchers did not employ eye-
tracking techniques in their experiments. The main reason for that is (1) to understand
the influence of time pressure on decisions under uncertainty employing the other
methods of behavioural and experimental economics and (2) to understand or estimate
if these studies can be supported with the outcomes of eye tracking applications.
Throughout the literature, it is affirmed that the decision maker is forced to select a
strategy that is less time consuming but also less accurate under time constraints and
time pressure (Ariely & Zakay, 2001). Earlier, Janis and Mann (1977) indicate that
emotional and stress factors affect the selection of a decision-making strategy.
However, many publications follow the approach as a decision maker changes his/her
criterion under time pressure rather than strategy (Albert, Aschenbrenner &
Schmalhofer, 1989; Aschenbrenner, Albert, & Schmalhofer, 1984; Busemeyer, 1985;
Busemeyer & Townsend, 1992, 1993; Diederich, 1995; Wallsten & Barton, 1982). The
previous publications also indicate that “time pressure is a very common feature of pro-
fessional and personal decision situations” including investment and financial decisions
(Maule & Endland, 2002).
The effects of time pressure on consumer supermarket shopping behaviour were
measured by Herrington and Capella as early as 1995. They observe that shopping
time and purchase amount are related. According to their results, supermarket shop-
pers tend to spend less time making any given purchase and more money in the over-
all time available to them. Moreover, time pressure overall decreases choice deferral,
but not when the choice involves low conflict or sets with common good and unique
bad features (avoidance‐avoidance conflict), according to Dhar and Nowlis (1999).
The research idea of Zur and Breznitz (1981) is comprehension of a risky choice under
time pressure. In their experiment of choosing between pairs of gambles, they observe
that subjects are less risky under high time pressure. Additionally, subjects tend to
spend more time observing the amount to loose and the probability of losing, whereas
they prefer observing their positive counterparts under low time pressure. This decision
behaviour is supported by prospect theory (Kahneman & Tversky, 1979), which states
that people put greater weight on losses rather than on gains.
26 Ordóñez and Benson III (1997) apply time constraints to both attractiveness ratings
and buying price tasks for a set of gambles and discover that decision makers multiply
probability and the amount information when stating buying prices with and without
being under time pressure, whereas they change their decision strategy when reporting
attractiveness ratings: they are using the same multiplicative decisions rather than
additive strategy as they tend to do without time pressure.
Although time pressure may influence risk taking, the precise nature of this influence
varies across different decision-making situations (Maule & Endland, 2002). Busemey-
er and Townsend in 1993 presented that the relationship between time pressure and
risk-taking is complex. Later Dror, Busemeyer and Basola (1999) state that participants
are less likely to take an action as risk levels increased; however, under time pressure,
participants are more conservative at the lower risk levels but are more inclined to take
risks at the higher levels of risk.
Similar results are provided by Huber and Kunz (2007) with quasi-realistic risky scenar-
ios where the initially risky alternative is chosen more often under time pressure.
Young and her colleagues support previous findings with the prospect theory frame-
work. They indicate that increases in time pressure lead to greater risk taking for posi-
tive and greater risk aversion for negative expected values. These findings suggest
that the risk preference under time pressure may depend on the overall expected value
among alternatives, whereby people are attracted to risks with positive expected value,
but averse to risks with negative expected value (Young et al., 2012).
Kocher, Pahlke and Trautmann (2013), who separated gain, loss and mixed prospects
(options), add to preceding results, such as an increase of gain seeking under time
pressure, the framing of the prospects. They point out that in cases of loss and mixed
prospects, the risk aversion attitude is increasing. Nursimulu and Bossaerts (2014) in-
dicate purchase impulsiveness under extreme time pressure on financial decisions.
However, sensitivity to expected reward does not depend on time according to the
researchers.
Will time pressure, in this case, reduce the quality and outcome of decision making?
This effect is noticed by Payne, Bettman and Johnson (1993), Bockenholt and Kroeger
(1993). They indicate that time pressure reduces the quality of decision making and
this reduction depends on the employed strategy (Maule and Endland, 2002). Howev-
er, Maule, Hockey and Bdzola (2000) analyse decision making under uncertainty and
show that time-pressured participants are more anxious, energetic and use a number
of different strategies to cope with the deadline. Kerstholt (1994) affirms in his study of
decision-making in dynamic situations under time pressure that information processing
is increasing with time pressure increasing. Nevertheless, the subject is not optimally
27 reacting to the time dimension of decision problems but waits until a specific value of
overall system performance is reached.
Mayer, Sonoda, and Gudykunst (1997) propose that the provision of information leads
to improved decision making, but time pressure has no effect on the quality of deci-
sions. Later Chu and Spires (2001) conclude that time-constrained decision makers
faster process information, although they manage less information and use less rigor-
ous decision strategies. However, properly designed decision support systems can
force decision makers to process more information and use more rigorous decision
strategies, which can result in enhanced performance. In support to that, Richardson,
Gregor and Heaney (2012) specify that with decision support even beginner level trad-
ers consistently outperformed those without support.
The effect of time pressure on description-based choice is different than experience-
based choice, as stated by Wegier and Spaniol (2015). If time pressure decreases risk
seeking for losses and increases for gains in description-based choice, there is no im-
pact of time pressure in outcomes that are learned through experience.
However, even experienced investors are comprised with behavioural biases, i.e. fram-
ing. Tversky and Kahneman (1981) compare the effects of frames on preferences to
the effects of perspectives on perceptual appearance. Svenson and Benson III (1993)
states that “the effects of time pressure were not as general as framing effect; when
there was an effect of time pressure, it was an interaction with the framing; when the
time was short, there was less or no effect of framing, and when time was long, there
was a stronger framing effect”. In line with this observation, Maule and Endland (2002)
found that the framing bias was weaker under time pressure. Therefore, some of the
publications mentioned above underline a better strategy and quality of investment de-
cisions under time pressure (Kerstholt, 1994; Maule, Hockey and Bdzola, 2000; Chu
and Spires, 2001). Unquestionably, the framing bias influences investment decisions
and is considered an important determinant of individual investment decisions, accord-
ing to Kumar and Lim (2006).
Throughout most of the publications on decision making under uncertainty and time
pressure, heuristics reflect as “efficient cognitive processes, conscious or unconscious,
that ignore part of the information” (Gigerenzer & Gaissmaier, 2011), or as decision
strategies that lack of complete relevant decisional information and therefore are seen
as less “rational” (Young et al., 2012). Gigerenzer and Gaissmaier (2011) indicate that
(a) individuals and organizations often rely on simple heuristics in an adaptive way, and
(b) ignoring part of the information can lead to more accurate judgments, for instance
for low predictability and small samples, than weighting and adding all information.
28 The research, that examines the effects of time pressure on decision making, has
found that a speed-accuracy trade-off can occur with time constraints. Investors
employ heuristic strategies, including acceleration, filtration of information, omission,
assessing across alternatives, changing in underlying decision rule and increased use
of attribute-based processing (Janis, 1983; Miller & Galanter, 1960; Verplanken, 1993;
Payne, Bettman, & Luce, 1996; Svenson, Edland, & Slovic, 1990; Zakay, 1993, Young
et al., 2012). Subjects seem to incline of using an ‘affect heuristic’, which improves
judgmental efficiency by deriving both risk and benefit evaluations from a common
source, as indicated by Finucane et al. (2000). In risky decisions, involving the possibil-
ities of both gains and losses, people often use a simple heuristic that maximizes the
overall probability of winning (Venkatraman, Payne & Huettel, 2014) and simplify the
decision problem at the expense of analytic precision (Kwak et al., 2015).
Thus, the publications, considered in this part of the literature review, suggest that time
pressure may change financial and investment decisions. However, the previous
studies indicate that these changes do not always take place in the same way, and
depend on (a) a decision maker strategy, (b) the types of options applied
(loss/gain/multi) and (c) the task structure of the experiment (Maule & Endland, 2002).
Therefore, (1) there is a relationship between time pressure and expected value (utility,
money), and (2) a tendency that decision makers under time pressure (a) take less risk
when the risk is lower, in case of losses, or negative values and (b) take more risk
when risk is higher, in case of gains, positive values, or impulse. (3) Time pressure al-
so has a complex impact on the quality of decisions, by reducing or increasing the
quality of decisions depending on (a) the employed strategy, (b) the additional provi-
sion of information provided or (c) other decision support. (4) Framing and loss aver-
sion biases under time constraints in some experiments are decreasing and on the
others are increasing, leaving open the question of the consequences of time pressure
on behavioural biases. (5) Throughout the previous publications, the idea of heuristics
is actively supported as a time-related strategy when a decision maker faces some
constraints, such as information overload, lack of knowledge and experience. In these
situations, investors (a) use the same methods as previous methods in their decisions,
(b) maximize the overall probability of winning, or (c) reason toward simplifying, accel-
erating and filtrating information to reach efficiency under time pressure.
To conclude the literature review, the author compares previous publications that utilize
eye-tracking techniques with other earlier methods of behavioural and experimental
economics. The following conclusion can be made which brings some discussion to
directions, depth and extensions of eye tracking applications in order to examine deci-
sion making under uncertainty and time pressure and constraints. Researchers who
29 are using eye tracking applications support some results of previous methods, for
example, optimizing choice strategies under time pressure, changes in loss aversion,
the impact of past performance in investment decision making or framing effects and
other biases. However, the cognitive biases require further explorations with different
sets and expected outcomes to test the sensitivity of biases dependent on environ-
ments under time pressure. In addition, eye tracking deepens the research on decision
making by observing the difference in decisions between simple-binary and multiple-
value-based choices, by comparing the influence of expected values separately from
probabilities in decision making under uncertainty and a value change of individual as-
sets from the performances of the overall aggregated portfolio. All of these studies be-
came possible due to eye tracking applications. The novel extensions of eye tracking
applications such as the gaze cascade effect where the decision-making process is
guided by visual attention and presentation of the information on the screen are only
some new directions in the analysis of the decision-making processes that are
discovered by using eye tracker applications.
Considering all the above mentioned background in this area of study, it can be
concluded that the previous studies (1) limit the experiment design by artificially
simplistic manipulated structure in order to measure one particular aspect of a
decision, (2) decision-making outcome or choice was the main research question of
prior experiments, not the decision-making process. Some recent studies investigate
the decision-making process however mostly from methodological application which is
discussed in detail in the next chapter. Therefore, this research is a single attempt in
applying eye tracking techniques to examine the decision-making process of obtaining
complex information from online stock marketplaces under time constraints to make a
decision to buy or short sell the stock. The author adapts natural online representation
of stock information as static screenshots to eliminate the influence of advertising pop-
ups and strictly defines and limits the areas of interest (AOI) to answer the stated re-
search questions. The following chapters of the research examine the methods and
measures that apply to the eye tracking data to test the research questions, i.e. delib-
eration of the information content under time constraints and heuristics in the decision-
making process.
30
3 METHODOLOGY OF THE RESEARCH
3.1 Methods and tools utilized in this area of research and justification of the adopted methods After evaluation of the publications in the area of decision making in economics and
finance under time constraints, it becomes evident that the extensive range of the pre-
vious research in this area are far from fulfilling the knowledge potential and discover-
ing the universal model of the decision-making process. Many aspects of the decision-
making process and models applicable to natural settings are not analysed or even
created yet. Taking into account these opportunities, the research, as mentioned in
previous chapters, focuses on the analysis of the information content deliberated by
participants of the experiment, and heuristics applied in the decision-making process.
Before providing the justification and describing the methods, technology, metrics and
tools adopted, the author presents a short overview of the previous methods that has
been utilized in this research area.
The decision-making area in economics and finance has progressed significantly. On
one hand, proclaiming rational logical methods of decision making founded on
expected utility theory, e.g. the neoclassical theorists such as von Neumann and
Morgenstern (1947) and Savage (1954) and, on the other hand, behavioural scientists
such as Edwards (1962), Kahneman and Tversky (1979) acknowledge the behavioural
principles behind the decision making process initiated by bounded rationality
principles. Since then a variety of methods has been developed to comprehend the
decision-making process in economics and finance. In greater detail, the difference be-
tween static vs. dynamic, normative vs. descriptive, deterministic vs. stochastic meth-
ods and models of the decision-making process are discussed in the works of
Busemeyer and Townsend (1993). Fiedler and Glöcker (2012) define two major clas-
ses of existing process models: simplifying heuristics and automatic integration models.
The complexity of the decision-making environments and time constraints require sim-
plifying and integrative approaches in the decision-making process to make a choice,
considering limited information-processing capacity (Payne, Bettman, & Johnson,
1993). Therefore, the heuristic methods previously studied by scholars can be defined
by the following features. First, the selection and filtration of information (Miller, 1960),
sequential choice (Gigerenzer & Goldstein, 1996) and finding the “satisficing” level of
reservation utility (Herbert Simons’ model, 1955) can have many different forms such
as using the preferential minimax or maximax heuristics (Brandstätter et al., 2006) or
choices decisions with an aspirational level (Luce, 1956; Simon, 1983). Second,
screening rather than acceleration in an information search task (Weenig & Maarleveld,
2002) or, third, search order (Caplin, Dean & Martin, 2011). Additionally, the previous
31 publications discussed repeatedly the recognition heuristic as more appropriate as ob-
served under time pressure (Klein, 1993). However, this heuristic can be only applied if
a decision maker has the previous knowledge or experience in regards to the subject
of the choice. Amos Tversky and Daniel Kahneman and their followers have committed
their research careers to the study of heuristics and biases (Kahneman & Tversky,
1974; Fiedler & von Sydow, 2015).
Even though heuristic methods accurately describe the decision processes in specific
conditions, the accuracy of these heuristics overall is questioned throughout the litera-
ture. For example, Gigerenzer and Brighton (2009) discuss the validity of fast and fru-
gal heuristics. Additionally, Kahneman and Tversky (1974) confirm that relying on heu-
ristics and biased approaches in the decision-making process leads to subjective
(overoptimistic or pessimistic) decisions in the stock marketplace; and the results are
price volatility or considerable loss in the portfolio. Fiedler and Glöcker (2012) state that
simple, non-compensatory models, such as the priority heuristics, lexicographic2, min-
imax, or maximax heuristics, do not predict search behaviour and processes in risky
decisions.
Another class of the decision methods, automatic integration models, is contrary to
heuristics and assumes that individuals “rely on powerful cognitive processes that allow
integration of considerable information very quickly and efficiently” (Fiedler & Glöcker,
2012). Evidence accumulation models of decision making under risk pertain to this
class. In this research, the author tests the hypotheses derived from decision field the-
ory (DFT, Busemeyer & Townsend, 1993) as an example of evidence accumulation
models. The hypotheses, based on DFT’s assumptions of the time limits, impose re-
strictions on the processing of information and therefore the “most prominent dimen-
sion tends to proceed, and the first alternative should be chosen more frequently”
(Busemeyer & Townsend, 1993, p.455). This approach will be discussed in greater de-
tail in the following part of the chapter. The following examples of evidence accumula-
tion models are the leaky competing accumulation model (LCAM, Usher & McClelland,
2004) and the parallel constraint satisfaction model (PCS, Glöckner & Herbold, 2011).
According to LCAM, information processing is a “gradual accumulation of intrinsically
noisy signals”. This model adds the effect of leakage (amplification of differences) in
the information accumulation process performed by the subject (Usher & McClelland,
2004, p.585). The PCS model identifies at least 3 steps in the decision-making
process: (1) activation of associated and relevant information in memory, (2)
parallelization of processes to maximize consistency in the context, for example by
2 Lexicographic strategy selects the alternative with the highest key value and with the highest validity (Gigerenzer, Todd, & ABC Research Group, 2000).
32 dominance structuring of information, (3) consulting mental representation with a
certain threshold, if it is fairly consistent, then a choice is made, if it is not analogous
then the next additional step (4) to change the decision on the basis of new
deliberations is considered (Glöckner & Hodges, 2011).
Some of the other noticeable methods of the evidence accumulation models are multi-
attribute decision field theory (MDFT, Diederich, 2003) and the attention drift-diffusion
model (aDDM) that are constructed hinge on a condition of certainty, i.e. purchasing
decision (Krajbich et al., 2012). Diederich’s MDFT assumes that a decision maker se-
quentially deliberates and compares attributes of alternatives over time. Therefore, un-
der time constraints, a decision maker modifies criterion rather than adjusts the strate-
gy of the decision. The aDDM method includes visual attention and the drift rate result-
ed from it, which “fluctuates continuously across time according to either a stationary or
Markov process” (Krajbich et al., 2012, p.10). Thus, visual attention accumulates more
evidence about the items to make a decision.
The short overview above demonstrates that the varieties of methods and models at-
tempt to explain inconsistencies of the static theories of the decision making. Most of
the recently developed models are indeed extensions or specifications or integrations
of simple heuristics or DFT. The author has reviewed only the most prominent methods
which applied to decision-making processes in economics and finance.
The authors’ decision toward the methods has a rational explanation rooted in the stat-
ed research questions and the capability of the SMI eye tracking technology. Taking
into account the features of the stimuli (information from online stock marketplaces)
and brainstorming possible correlations between visual attention to the financial
information, dynamics of the decision-making process and final decision, the author
assumes that the hypotheses and ideas of adaptive toolbox model (ATB) and decision
field theory (DFT) can explain the outcome of the experiment. ATB concept and DFT
are not only the most distinguished methods elucidating the decision-making process,
but they also apply to much complex decision-making processes. Therefore, noticing
that the experimental setting does not have an artificial, hypothetical content or ma-
nipulations of values in order to fit the outcome to a model, the research aims to test
hypotheses from ATB and DFT. May perhaps these models of the decision-making
process explain the outcome of the experiment? The real information content from the
online stock marketplaces was provided to participants of the experiment to test if the
models can explain a deliberation process of decision making, including attention to the
particular content of information and dynamics of the decision-making process. A more
detailed interpretation of the models and the motivation behind the decision of these
two models are given below.
33 In volatile equity markets, an investor has adaptive and goal-oriented behaviour. This
behaviour is a consequence not only of cognitive limits but first of all cognitive adapta-
tion (to time-space) limits. Having unlimited time and unlimited access, individuals po-
tentially can deliberate a rational and accurate decision based on specific goals and on
a specific time. Cognitive adaptation to the environment in order to make efficient deci-
sions employs various heuristics3. Gigerenzer and Gaissmaier (2011) demonstrate that
individuals often depend on “simple heuristics in an adaptive way”. Even though these
heuristics ignore part of the information in the decision-making process, they still lead
to accurate judgments in comparison with the time-consuming deliberation of weighting
and adding all available information. Adaptive toolbox model is adapted to the structure
of the applicable environment, i.e. “psychological plausibility, domain specificity and
ecological rationality” (Gigerenzer & Selten, 2002, p. 37). The author of this thesis con-
siders the premises of adaptive toolbox model that can be applied to the decision-
making process in the conducted experiment. The participants with the limited
knowledge and no experience deliberate the provided financial information from the
stock marketplaces to make a decision to buy or short sell the stock. This decision is
initially adaptive because of the complexity of unfamiliar information that the partici-
pants faced in the experiment. There is no comparison between the stocks, no recogni-
tion effects, i.e. the stocks chosen for the experiment are the offers of middle-size un-
noticed companies. The participants have to make a decision to buy or short-sell a
stock within one information block. What information content will be deliberated in the
decision-making process first, last and the most by participants? What will be ignored
and not considered at all in the decision? Will participants’ decisions be optimal, taking
into account (1) the goal of the experiment is to invest profitably and (2) participant’s
own goals and strategies? Which heuristics do participants use in this situation? All
these questions can be tested and answered within adaptive toolbox model. Therefore,
this method is considered as one of the most suitable in this type of the experiment.
Next, the author acknowledges decision field theory as a dynamic approach to decision
making in economics and finance. DFT principles explain numerous unclear
experimental results of individual decision-making processes in economics and finance
including “violations of stochastic dominance”, “violations of strong stochastic
transitivity”, “violations of independence between alternatives”, “serial position effects
on preference”, “speed-accuracy trade-off effects”, “the inverse relation between
decision probability and decision time”, “changes in the decisions of preferences under
3 The author of this paper agrees with Douglas H. on definition of “heuristic” as “an automatic perceptu-
ally based cognitive shortcut” and at the same time “conscious and effortful strategy that deliberately operate on a reduce amount of information and are guided by conscious stopping rules” (Douglas, 2016, p.135).
34 time pressure”, “slower decision times for avoidance as compared with approach
conflicts” and “preference reversals between decisions and prices” (Busemeyer &
Townsend, 1993, p.432). In other words, deriving their conclusions for DFT, Busemey-
er and Townsend step-by-step includes different conditions under which the decision-
making process can be changed.
In sum, preference direction, or attention can be switched from one event to another in
the decision-making process; the attention weight can vary caused by “difference in
subjective expected utilities” (Busemeyer & Townsend, 1993, p.336). In speed-
accuracy trade-off “the similarity or dissimilarity of the payoff produced by each action”
is taken into account (Busemeyer & Townsend, 1993, p.440). Prior knowledge or past
experience could be “an initial anchor point” that biases the decision under time con-
straints. However, when given a long time for sequential sampling processing of infor-
mation, the threshold bounds increase. The scholars demonstrate experimentally “the
inverse relation between decision probability and decision time” (Busemeyer & Town-
send, 1993, p.441). Moreover, the position of the sample has a greater effect on a
decision, and it takes a longer time to deliberate avoidance-avoidance rather than ap-
proach-approach decisions. Furthermore, the deliberation time is a continuous pro-
cess. Therefore, the changes in deliberation time, which is the main condition in the
experiment conducted by the author of this paper, leads to speed-accuracy trade-off,
unless there is a high threshold starting point. The participants do not have a high initial
anchor point to rely on their decision-making process. However, do they sequentially
deliberate information under time constraints or, as stated by Busemeyer and Town-
send, do they decrease the amount of attention allocated and deliberate only noticea-
ble information? Are there changes in attention over time? According to the DFT, neg-
ative values take more deliberation compared with positive values. Does the experi-
ment data support this assumption? If simple heuristics are applied in the decision-
making process, should the decrease in the accuracy of the decision take into account
low variance conditions (initial starting position)? Does the amount of time spend mak-
ing a decision affect the final decision? These are only the main questions that can be
answered to support or to contradict the model’s assumptions.
To sum up this part of the chapter, the author’s motivation behind the decision of
methods is based on (1) observability, e.g. presence of the most fundamental
principals in the models, (2) measurability, e.g. the capacity to explain the specific eye-
tracking data outcomes of the experiment, (3) reliability, e.g. the recognition and
successful adoption of these methods by the scientific society in economics and
finance. Therefore, ATB and DFT have been chosen as the fundamental methods of
this research paper.
35
3.2 Description of possible and applied eye-tracking techniques, software, metrics and tools Eye tracking technology, as mentioned in the introduction, is becoming a widespread
and accessible method in behavioural economics and finance recently. This approach
provides new crucial tools for measuring the actual dynamics of visual attention or
measure of where and when the eyes move during a complex task performance
(Godfroid, 2012).
Eye-tracking techniques are based on the main assumption that there is congruence
between visual attention and cognitive processes, or eye-mind relationships (Rayner,
2009). However, this assumption is a type of “Midas touch problem”, where the main
question is “how to differentiate attentive saccades with the intended goal of communi-
cation from the lower level eye movements that are just random or provoked by exter-
nal stimulation?” (Velichkovsky, Sprenger & Unema, 1997, p.509) In other words, is
there a robust correlation between visual attention to a stimulus and a cognitive pro-
cessing of information about this particular stimulus? However, this is a topic for anoth-
er research. Here, the author assumes that there is some correlation between visual
attention and the behaviours of the subjects.
Eye movements provide essential insights into comprehending human behaviour. Eyes
select and sample visual information (Horsley et al., 2014). The fixation locations de-
termine behaviour engagement with particular information and provide an objective
measure of ongoing cognitive processes during deliberation of the particular infor-
mation content (Horsley et al., 2014). Therefore, the assumption in regards to ongoing
cognitive processes and visual attention are carried out throughout the paper.
The experimental eye-tracking data can be scrutinized by a variety of statistical meth-
ods, as well as with visualization techniques provided by eye-tracking analytical soft-
ware such as BeGaze as used in this experiment (Blascheck et al., 2014). Eye tracking
equipment usually records the gaze points of the participants as raw data.
Subsequently, depending on a specified area and time span the gaze points are
spatially and temporally aggregated into fixations (or location and duration of gaze)
with an area of approximately 20-50 pixels and timespan between 200 and 300 ms;
saccades (location and length of eye movement) which are about 30 to 80 ms long;
and smooth pursuits with velocity around 10-30 degrees (Holmqvist et al, 2011). Spe-
cific regions of interest on the stimulus defined in the experiment such as areas of in-
terests (AOI) depend on the stated hypotheses (Blascheck et al., 2014). The author
follows the recommended measurements in the definition of fixation, saccades and
smooth pursuits. However, smooth pursuit data sets are not considered in this re-
36 search because smooth pursuit is initiated mostly by looking at a moving target and not
a static target.
Diversified methods and metrics have been developed throughout the previous studies
where an eye tracking device is adapted for collection of visual attention data, for
example, string editing algorithms (Duchowski, 2010), descriptive and inferential statis-
tical algorithms (Holmqvist et al., 2011) and visual analytics techniques (Andrienko,
2012). Visualization techniques are more explorative and qualitative compared with
statistical analysis, which largely provides quantitative results. Particularly, visual
methods specify different levels and spatiotemporal aspects in the analysis of complex
data. Additionally, the type of the stimuli used in the experiment influence on the design
of visualization techniques. The visual analysis can be point-based or AOI based
(Blascheck et al., 2014). This experiment used AOI based analysis, where correlations
between AOIs are more relevant to the aim of the stated research questions and point-
based or time binned growth curve analysis.
In this experiment, the raw data is directed from the Experiment Center to the BeGaze
software. This software simplifies the eye tracking data analysis not only by the visual
structuring of the data of the experiments but also by displaying the results of the ex-
periment in the different forms. Visualization of gaze plots and attention maps are
presented by scan path, bee swarm, gaze relay, focus map and heat map (BeGaze
Manual, 2014). If a scan path displays a gaze data overlay over a stimulus as a
sequence of alternating fixations and saccades, the focus and heat map shows gaze
patterns over a stimulus (BeGaze Manual, 2014). Preliminary to the detailed statistical
analysis, the author inspects the experimental data quality by BeGaze provided visual
data views. However, for deliberate study, the author has executed only statistical
analysis in R using raw data and event statistics.
Frequently, quantitative metrics of eye tracking data, such as fixation count, distribution
and position, saccadic amplitude, and pupil size specific to the AOI gives additional in-
formation about the decision-making strategies of the participants (Blascheck et al.,
2014). Common metrics for fixations are the number of fixations count, the fixation du-
ration in milliseconds and the fixation position given as x- and y-coordinates in pixels.
Fixation by itself does not provide meaning, only information where the participant fix-
ated. In general, fixation (percentage fixated, mean duration, position) is cross-
analysed with the AOI which indicates either interest to the AOI or perhaps difficulty in
understanding that AOI. Therefore, in this research, the fixation duration by itself can-
not be applied for analysis of participants’ interest to a particular area considering that
the graphical information is compared with textual required a significantly shorter dura-
tion (Granka, 2010). Additionally, the gaze cascade effect or duration of fixation is test-
37 ed to evaluate if it supports the stated hypotheses. Pupil dilation is an important pa-
rameter for determining cognitive load and the results of a shift of attention (Gamito,
2014). The author measures the mean of pupil dilation increase under time constraints
within and across trials to test the hypothesis of referencing to graphical information
and increase of cognitive activity under time constraints.
As mentioned previously, the following statistical software R was employed:
eyetracking R package and data.table, ezANOVA, ggplot, lmer packages. The
measures of central tendency such as mean, or the “balance point”, and median or the
“halving point” of fixation duration for a trial and each AOI is executed. Some of the
measures of position or location, such as quartiles and percentiles and measures of
dispersion such as standard deviation, range and the interquartile range illustrate the
degree of “spread” of the data and are provided in table format in the following chapter
(Godwin, 2016).
3.3 The design of the experiment
3.3.1 Participants
The author conducted an eye-tracking experiment to investigate the dynamics and
heuristics of investment decision making under time constraints. Twenty students from
the Hochschule Rhein-Waal participants’ pool completed the experiment (9 males and
11 females; age not recorded for participants, all are students of the University). Two
additional participants did not begin the experiment because they did not pass the
Screener Questionnaire suggested by Pernice and Nielsen (2015). They had eye-
related conditions that omitted them from participating. Data from two more students
had to be excluded from the analysis because their eye-tracking data was very low
quality (less than 40% tracking ratio)4. The students received a flat rate payment of
eight Euros for participation in the experiment. Decisions were not incentivized under
the assumption that the outcome of the investment decision is opportunistic. 40% of
the participants were assigned to sufficient time condition (given at least 10 minutes for
trial but not restricted), and 60% were limited by time in their decision-making process
(given 2.5 minutes for trial, or 30 seconds per stimulus). The participants had a 5-10
minute trial where they had time to familiarize themselves with the differences in the
layout of the online stock marketplaces.
4 The author uses tracking ratio applied by Amso, Markant and Haas (2014, p.3), or “the proportion of
time that the eye tracker recorded point of gaze coordinates over the entire task”, to improve quality of data. Participants with less than 40% tracking ratio contributes very little data and were excluded from analyses (1 male and 1 female).
38 3.3.2 Eye tracking apparatus and measures
Eye movements of the participants were recorded using the remote eye trackers (Sen-
soMotoric Instruments, SMI iView X RED250) while performing tasks. A five point cali-
bration is necessary to adapt the iView X eye tracking software to the participant's eye
characteristics. Additional points of validation to improve calibration quality were estab-
lished, and task stimuli were presented using the Experiment Center software
Integrated to SMI.
The experiment was carried out on three IBM-compatible desktop computers with built-
in SensoMotoric Instruments (SMI) software and the attached remote eye-trackers.
The stimuli were presented on three LCD monitors, which were controlled by Experi-
ment Center 2 (SMI). One was assigned to sufficient time conditions and the other two
were presented stimuli under time-constrained conditions. The viewing distance from a
participant to the monitor was approximately 70 cm. The participants’ eye movements
were recorded by the eye trackers with the infrared pupil and corneal reflex imaging
systems, at the sampling frequency of 120 Hz.
3.3.3 Stimuli
The following stimuli were presented in the experiment: screenshots from online stock
marketplaces as well as the questionnaire. Five screenshots for each of six companies
who trade their stock on the Deutsche Börse (the Frankfurt Stock Exchange), the Lon-
don Stock Exchange and the NASDAQ were presented as static stimuli on the display.
One day before the experiment, the information from the online stock marketplaces
were copied as screenshots except online advertising pop-ups which were deleted
from screenshots presentations. This approach is chosen to eliminate them as a dis-
traction to the decision-making process which is not aimed for analysis in this research.
The example of the screenshots is provided in Annex, Figure A.1. The first two compa-
nies are medium size, German engineering companies trading their equities on the
Deutsche Börse, for instance, ElringKlinger AG (market cap ≈ 1.38 b €) and KRONES
AG (market cap ≈ 3.22 b €) and were unfamiliar to most of the participants. The second
set of two companies is British financial companies who trade their stock on the Lon-
don Stock Exchange, such as III 3I GROUP PLC (market cap ≈ 4.36 b £) and FPO
FIRST PROPERTY GROUP PLC (market cap ≈ 60.59 b £), they were also unknown to
the participants. The third set of two companies, which also unfamiliar to the partici-
pants, is the U.S. biotechnology companies that trade their shares on the NASDAQ
Stock Market, such as ADMA Biologics Inc. (market cap ≈ 78.42 m $) and AMGN
Company (market cap 117.67 b $).
39 The reasons for choosing these particular companies are the following. First, in order
to diminish the familiarity bias, the author selects companies that unfamiliar to the par-
ticipants’ of the experiment. Second, the author randomizes the decision of the compa-
nies by their size, the first IPO (initial public offering) and performances. Moreover, the
author coordinates the screenshots with the information provided in each online stock
marketplace as (1-2) summary quote, (3) three years stock chart, (4) the company
information, including numerical performance and dividend information, and (5)
financial ratios in order to unify the analysis and comparison of stimuli. It should be
noted that the provided information is in a complex form which contains numbers,
words and visuals for each content defined AOI.
The displays of the companies were randomized, but the order of the stock information
was the same as enumerated above. To avoid confusion of obtaining information from
the displays, the author scaled the screenshots. Similar to the research conducted by
Stewart, Hermens, and Matthews (2015), the preliminary analysis of the data indicates
that the offsetting of the screenshots and randomization did not influence the decisions
or fixation durations.
The questionnaire includes some questions about participants’ attitudes and the strat-
egy they are going to use in the experiment and following at the end one additional
question about an actual strategy they applied in their deliberation of the stock infor-
mation. Each of six trials ends with the question about their decision between buying
and short selling a stock.
3.3.4 Procedure
Participants made six decisions between two options of buying or short selling stock in
the experiment. The information about the stock and company performance preceded
each decision. The author assumes that the price of the stock reflects all available in-
formation. The experiment lasted an average of 35 minutes which included the time to
answer the preliminary questionnaire, participation in a trial part, calibration phase, and
the eye tracking experiment. After signing up for the experiment, the participants were
required to answer the Screener Questionnaire. Successful candidates continued to
separate computers where they had approximately 5-10 minutes to browse chosen
online stock marketplaces to familiarize themselves with the layouts of each market-
place, i.e. the Deutsche Börse, the London Stock Exchange and the NASDAQ. Prac-
tice trials were obtained from a different set of stocks than those that applied to the
main task. This approach is a necessary step to prepare participants for the experiment
in order to optimize the decision-making process to prevent participant stress with the
40 complexity of the represented information and differences in the layout of the natural
settings.
Moreover, each participant was provided with the essential investor terminology
obtained from the NASDAQ Stock Exchange in order to fully inform participants of
stock exchange terminology such as earnings per share (EPS), EPS growth,
price/earnings ratio (PE) ratio, dividend yield, PEG (price/earnings to growth) ratio,
operating margin, return on capital employed, beta, market cap capitalization and 52
week high/low. They were not permitted to use the terminology cheat sheet during the
experiment, only during the trial. No eye tracking or any recordings were performed
during the trial. As soon as participants had experienced at least one trial with each of
the online stock marketplaces and understood the tasks, they proceeded to the main
session. Participants were asked to care about the decision that they were going to
make as if they were making the decision for them, i.e. take all given time, think delib-
erately and respond honestly.
The main part starts with a five-point calibration of the eye tracker and validation of the
calibration. Calibration was repeated as needed to obtain the best match. Participants
as aforementioned had to decide if they would buy or rather short-sell the stock. All the
information about the pricing and performance of the stock and company were
provided on the preceding five stimuli. The research is not only focused on the final
decisions but mostly in the processing of the provided information in order to make a
decision. Therefore, measures of attention and pupil dilation as a predictor of changes
in fixation durations are identified and investigated. The experiment is designed under
two conditions. Under the first condition, the participants had about 10 minutes to de-
liberate and search necessary information for the final decision. They had 2.5 minutes,
or 30 seconds per screen under time constrained conditions. The participants had the
option to return to any five previous stimuli if needed to review any of them in their
decision-making process. Therefore not only the dynamics across trials is intriguing to
examine but also within trials to determine, for example, the most referenced stimuli in
the decision-making process.
4 DESCRIPTION OF DATA
4.1 Detailed description of data collection, measures and recording
In the conducted experiment the participants' tasks are to evaluate the information
about the stock presented on the screen and decide if they would like to buy or short-
sell the particular stock. Students are usually considered as proxies for unsophisticated
investors (De Bondt & Thaler, 1985). Therefore, this research does not focus on a pro-
41 fessional decision-making strategy but on the decision-making process of a typical nov-
ice investor who is willing to invest his/her money via online stock marketplaces. Ac-
cording to the Bundesbank report, in 2013 approximately 11% (in middle quintile in-
come) of German households or about nine million people hold direct share investments.
In the experiment, each participant had six tasks with five static stimuli respectively per
task. The stimuli are organized sequentially according to the representation of the
stock information on the online stock marketplaces, i.e. (1-2) two summary pages
including stock quotes, volume, some ratios, in some cases company news headlines,
short information about the company and chart; (3) a three-year price chart chosen
against the provided interactive chart online, (4) the company information including
dividends, shareholders structure, market cap, company news; (5) financial ratios
together with some historical key data. Even though each of the five stimuli led to a de-
cision task, the participants could freely return to previous stimuli within a task if the
time allowed them to review the information again. The order of the trials was random-
ized to diminish the order effect. And as soon as a decision was made on the task, and
the participants began the next task, they could not return to the previous task to alter
their decision. Moreover, as mentioned in the previous chapter, the stocks are chosen
to be neutral in terms of familiarity to the participants.
According to Holmqvist, “a perfect experiment is one in which no factors systematically
influence the dependent variable (e.g. fixation duration) other than the ones controlled”
(Holmqvist, 2011, p.74). Therefore, the search5 for the content of the information to
make a decision is controlled by strictly defined and unified stimuli (AOIs), in conjunc-
tion with two different time conditions assigned to the participant to deliberate the dis-
played information in this experiment. On one hand, it is impossible to limit all of the
possible influential factors including emotional and physical differences or conditions to
simplify the complex nature of the decision-making process. However, on the other
hand by controlling the maximum possible conditions the results of the experiment can
be strictly applied only to the artificially controlled and manipulated settings which have
a detached relationship with the nature of the real world decision-making process.
Therefore, considering the particular design of the experiment, the eye movement data
was collected by the SMI’s Experiment Center 2 software with the following scope: (1)
movement measures, including variety of eye-movements and their properties; (2)
position measure, i.e. location, and “the properties of eye-movements at spatial
locations”; (3) numerical measure, particularly, “the number, proportion, or rate of any
countable eye-movement event”; and (4) latency measures, or “the duration from the
5 Information search means a deliberation process of obtaining relevant to the decision-making infor-mation in this paper.
42 onset of one event to the onset of a second event” (Holmqvist, 2011, p.3). The exam-
ples of the data collected represent direction, amplitude, duration, velocity, and accel-
eration of eye movements.
However, considering that the event data from the BeGaze software such as transition
matrices, scan path lengths and heat maps hinge on how fixations and saccades are
calculated by the software, e.g. filters in the velocity calculation, the author considers
mainly the raw data for the analysis. Additionally, the author does not apply any com-
plex measures that have not been validated by previous studies and have not been
linked to a particular cognitive process such as transition diagrams, position dispersion
measures, or scan path similarity measures. The other measurements such as smooth
pursuit gain and the anti-saccade measurement, even though executed extensively in
the preceding studies, they have been implemented in different fields of research, for
example, reading and scene perception. Recognizing that the validity of a dependent
variable is based on previous discoveries, no additional assumptions are made without
referring to the specific eye tracking research to support it. Moreover, in the selection of
measures and dependent variables, the author addresses certain points in time where
the participants are involved in the deliberation of the specific AOI, as recommended
by Holmqvist (2011), rather than prolonged gaze sequences.
Furthermore, the author takes into account the effect of how information is displayed,
i.e. that the participants tend to look more at the centre rather than the edges of the
monitor. Additionally, the participants make more horizontal than vertical saccades and
very few diagonal ones (Holmqvist, 2011). The representation effect and precision of
the samples are considered when the results are analysed in this paper because the
author does not manipulate or randomize the locations of the displayed information to
maintain the layout as it is online but varied them by representing the different online
stock marketplaces.
As stated by Andrienko and his colleagues (2012), eye tracking data can be assessed
by point-based or AOI-based approaches. If point-based measure considers the overall
eye movement and spatial or temporal distribution, then AOI-based metrics compare
the transition and relation between AOIs. The statistical analysis provided in this re-
search relies on both approaches: point-based (time binned) to investigate the dynam-
ics of the decision-making process and AOI-based techniques, to evaluate in what AOI
the participants are more fixated to make a decision.
The following noises are ignored in the experiment: (1) system-inherent noise because
the eye-tracker determines a spatial variance and not the researcher manually; (2)
43 oculomotor noise or jitter such as tremor, microsaccades, and drift6, and (3)
environmental noise, or “variation in the gaze position signal caused by external
mechanical and electromagnetic disturbances recording environment” (Holmqvist,
2011, p.34). Following Holmqvist’ recommendations such as “data quality results from
the combined effects of eye-tracker specific properties such as sampling frequency,
latency, and precision and participant-specific properties,” the author attempts to
mitigate possible noises in design and collection of data by following the suggestions
given in Experimental Center and BeGaze Manuals (Holmqvist, 2011. P.29). To im-
prove the quality of the dependent variables, all noisy and invalid data was removed,
for example, the invalid gaze data are originated from noise, eye blinks and extended
head movements that are beyond the eye tracker's range of detection. Conforming to
suggestions stated by Komogortsev (2010) and his colleagues, the author filtered long
duration invalid data of (more than 1,000 ms), noise and the blink duration data that are
less than 75 ms. Moreover, participants with a tracking ratio of less than 40% and a
calibration accuracy higher than 1° are not included in the analysis. Additionally, when
observing a less than ± 2° disparity in the participants’ right and left eye movements,
the same as Cornell and his colleagues (2003), and being convinced with the
conclusions of Eser and his fellows (2008) that approximately two-thirds of the people
have right eye dominance, the author analyses the data only from the right eye
movements in her research.
Providing details of the data collection process and measurements, the author briefly
reviews data recordings to demonstrate all available data forms for the analysis and
then defines the dependent variables which are considered for the research. As men-
tioned in the previous chapter, eye movement was recorded at the sampling rate of
120 Hz which means eye tracker recorded approximately 120 gaze points per second.
Considering 20 participants, six tasks and at least five stimuli per task (not including
options to browse between five stimuli if the given time permitted), the raw data col-
lected counts of over 1.5 million gaze points which afterward aggregated to the fixa-
tions, saccades, and blinks applying to the event detection algorithms. The following
statistical data was retrieved from BeGaze: raw data for each participant, fixation and
saccade parameters, AOI sequence, transition matrix, and event statistics with approx-
imately 100 statistical variables. However, the author relies only on raw data samples
to perform eye tracking analysis using R statistical software.
6 A drift is a systematic error or a disparity.
44
4.2 Definition of dependent variables
The experimental approach deals with the analysis of the effect of independent varia-
bles, e.g. displayed stimuli, on dependent variables measured as the participant’s reac-
tion to the stimulus, for instance, the examination of fixation durations or saccadic am-
plitude under controlled conditions of time constraints and sufficient time to make a de-
cision. The experiment demonstrates how manipulations of the independent variables
affect the dependent variables (Holmqvist, 2011).
The author is going to analyse the experimental data acquired over time and by the
AOIs, returning to the research questions stated in the introduction, to determine if they
are affected by time constraints. In this paper, the author has measured the attention
(mean percentage fixation duration) of the participants and pupil dilation provided in
BeGaze raw data sets. This approach allows the comparison of the chosen AOIs and
heuristics applied in the decision-making process under time constraints. In addition,
the author investigates a correlation between the AOIs and the final decisions.
A gain or loss as a consequence of the investment decision of each participant is
evaluated by the following stock performance: 25th of March stock price compared with
25th of January stock price as displayed in the experiment. The margin of safety princi-
ple is applied in this thesis to evaluate possible consequences of the decision. The
threshold for gain is a 20% increase (or decrease in the case of short selling) and a
10% decrease (or increase in the case of short selling) in price. The chosen approach
is explained in more detail in the next section of this chapter.
The main terminology in eye-tracking research is fixation which is generally correlated
with visual attention. A fixation is an aggregation of gaze points measured by an eye
tracker. Typically gaze points are combined by a specified area of interest and
timespan. A fixation is the longest the eye gaze remains still over time. There are no
standardized aggregation areas or set timespans for a fixation but usually about 20 to
50 pixels and between 200 and 300 ms is observed according to the Holmqvist’s eye
tracking bible (Holmqvist et al., 2011). However, the identification of eye fixations main-
ly depends on a task and an approach. Previously Duchowski (2007) demonstrated
that information complexity and task complexity influence on fixation duration. For ex-
ample, “the average fixation duration during silent reading is approximately 225 milli-
seconds, while other tasks, including typing, scene perception, and music reading ap-
proach averages of 300-400 milliseconds” (Granka, Feusner, & Lorigo, 2008, p.3). The
average fixation duration in this research is around 300 ms. Fixations are classified us-
ing a 35-pixel tolerance and a minimum fixation time threshold of 75 ms as recom-
mended by the SMI Manual and the previous eye-tracking literature (Holmqvist et al.,
45 2011; Fiedler & Glöckner, 2012). Fixations are connected by saccades or continuous
and rapid movements of eye gazes. During the eye fixation, the following processes
take place, as mentioned by Viviani (2004), encoding of a visual stimulus, a sampling
of the periphery, and planning for the next saccade. Fixations in a particular AOI are
usually grouped together in mean fixation duration. The prevailing metrics for fixations
are the fixation duration in milliseconds, the fixation count (i.e. number of fixations), and
the fixation position specified as x- and y-coordinates in the pixel.
According to the previous studies, fixations reveal where the participant’s attention is
focused and represent the examples and the order of information acquisition and pro-
cessing (Rayner, 1998). The previous experimental findings evidence a very high cor-
relation between fixation on a displayed stimulus and exact thoughts about this stimu-
lus. In addition, the fixation duration on certain items directly links to the degree of cog-
nitive processing (Just & Carpenter, 1980). Depending on the type of displayed infor-
mation, the possible differences in fixation duration can be explained by the time and
speed required to absorb the information. While the eye moves rapidly during reading,
a participant typically grasps key information from certain regions in the visual search
which supports the idea of using heuristics in information processing (Sullivan et al.,
2012). The research on eye movements in reading proposes that fixation durations ex-
tend with the complexity of the text (Rayner et al., 2012).
AOI’s fixation percentage, mean proportion fixation (or mean proportion gaze) are the
main dependent variables in this research which identify the percentage of time fixated
at the specific AOIs during a trial. The study also considers relevant AOI fixation densi-
ty which defines the percentage of time fixated at the specific AOIs.
As mentioned briefly above, saccades are the continuous, ballistic and rapid move-
ments of eye gazes from one fixation to another (Purves, Augustine & Fitzpatrick,
2001). These extremely rapid movements last only 30-80 milliseconds with velocities
approaching 500 degrees per second. Again, there is no established standard for
length and velocities of the saccades. Therefore, the author follows the recommenda-
tions of BeGaze software to divide fixation from saccades and cross checks the results
with the other current studies in this area (Holmqvist et al., 2011). Humans are not
aware of saccadic movements. However, eye tracking data by measuring saccadic
movements can reach deep into information processing and absorption of new infor-
mation. The following typical metrics for saccadic movements are retrieved from Be-
Gaze software: the saccadic duration in milliseconds, the saccadic amplitude (i.e. the
distance the saccade traveled), and the saccadic velocity in degrees per second
(Blascheck, 2014). Certainly, no information is perceived and acquired during rapid
saccadic movement because of “the unstable image on the retina during eye move-
46 ments and other biological factors” (Granka, Feusner, & Lorigo, 2008, p.3). Saccadic
movements from one AOI to the next are called transition and scan paths. They illus-
trate a complete sequence of fixations and saccades to examine the information delib-
eration in the decision-making process. In this case, the sum of durations from all fixa-
tions and saccades, which hit the particular AOI, is defined as a dwell. However, even
though the transition matrix demonstrates search order regarding transition (or chang-
es in fixations), a maximum of two order transitions provided by BeGaze software limits
the horizon of estimates and accuracy of assumptions. Therefore, the author does not
consider a sequence of fixations and saccades as a final variable for this research.
Next, scan paths are a sequence of alternating fixations and saccades and illustrate
the pattern of eye movement across the visual stimulus. A straight line to a specified
AOI can be regarded as an ideal scan path. However, deviance from this ideal scan
path is interpreted as poor search by Goldberg and Kotval (1999). Examples of scan
path metrics are specified by Blascheck and his colleagues (2014), including scan path
length in pixels, or scan path duration in milliseconds and the convex hull (i.e. which area
is covered by the scan path). The participant’s scan path behaviour presents an insight
into their navigation through a visual stimulus. Preceding studies propose that scan
path movement is not random, but depends on a participant’s emotional state, expecta-
tions and purpose (Yarbus, 1967). This research does not analyse specific patterns in
scan paths that can explain the dynamics of decision making but applies the growth
curve analysis to confront the stated hypotheses.
The next dependent variable is pupil diameter or dilation which is defined as a measure
of active processing and often linked to task difficulty (Kahnemann & Beatty, 1966). A
larger diameter indicates an individual’s arousal or interest in the viewed content.
Therefore, if pupil dilation increases in the particular AOI, the author can assume that
this type of information is important in decision making. Previous studies compare the
average pupil dilation in a specific AOI and additionally the average pupil dilation over
an entire stimulus or experimental time to explain how participants might cognitively
process the matter of various content (Hess & Polt, 1960; Rayner, 1998; Duchowski,
2002). Kahneman stated in his interview with the German news magazine Der Spiegel
that “the pupils reflect the extent of mental effort in an incredibly precise way” (Kahne-
man, 2012). Moreover, recently Fiedler and Glöckner (2012) have demonstrated that
an increase in pupil dilation correlates with an increasing mean of expected value. Ad-
ditionally, pupil dilation increases over the duration of the experiment. Not only cogni-
tive but also emotional events lead to pupil constriction and expansion. In this re-
search, the author analyses the pupil diameter as a predictor of the logit and mixed-
effects models.
47 The author does not consider smooth pursuit movements for the analysis because
these movements are associated with a dynamic stimulus or moving objects which are
not used in this study. The other eye movements such as vergence movements are
also assumed to be negligible and not applicable to this research.
The last variable to be explained is the future value of the stock. As mentioned before,
the author does not calculate the expected value of the stock. Since all stock pricing
information is taken as screenshots directly from the online stock marketplaces without
any manipulations on the 25th of January, there was no reason to speculate a future
expected value because the stock markets provided the exact price of the stock on
March 25th. Therefore, the author knows the precise price of the stock three months
after the decisions were made by participants.
Additionally, the investment decision process does not end with a decision (buying or
short selling the stock), it continues until an investor will have a gain or loss. Consider-
ing this rational, the author assumes that immature investors try to follow the best
strategy recommended by analytics to manage his/her stock decision (purchase or
short-sell). Possibly by collecting more information about the company performance
he/she will be able to estimate the expected future value, his/her expected return, and
intrinsic value of the stock. The value of any share of stock finally rests on the present
value of the company's future cash flows. However, valuation will always hold a degree
of uncertainty. Even though all the calculations are precise, they reflect the value of the
stock at a specific moment in time. The news or any other changes in the company
performance can alter the perspectives. Therefore, an investor has to aim for a strate-
gy over time. These are the reasons why investors heavily rely on the margin of safety
concept in investing, that the Wall Street advisers favoured.
Accordingly, the author assumes that the immature investor also tries to use the mar-
gin of safety principle: sell the stock when it drops more than 10% and when it increase
in value more 20% depending on risk attitude. In contrary with short selling stock: buy
back if the price decreases 20% or more, or if price increase 10% or more, to mitigate
losses depending on risk tolerance (Calandro, 2011). This strategy (1) allows minimiz-
ing the possible loss from a mistaken decision, (2) considers that there is another bet-
ter option to invest in the market (3) is supported by recent statistics of investment
behaviour. According to LPL Financial, NYCE (2012) statistics, the average holding
period for stock decreased to less than one year compared with more than eight years
in 1960. (4) This strategy takes into account cognitive biases such as sunk cost,
confirmation, optimism or pessimism, etc., or finding the most difficult reasons to sell
the stock. (5) Based on intrinsic value calculation which is subjective in this case, the
margin of safety includes a cushion against errors in calculation.
48 It will be interesting to investigate the predicted outcome of this type of strategy com-
pared with others such as the more academic discounted cash flow (DCF) method, the
dividend discount model (DDM), etc. However, it is the topic of another research.
Thus, the author adopts the stock price developed in three months as the future stock
price and applies the margin of safety principle that a rational investor will employ in
his/her decision to buy or short sell a stock. The author judges the accuracy of the par-
ticipant’s decisions based on previous assumptions.
To sum up, this research analyses dependent measures of eye movement over the
entire decision-making time. The author investigates the dynamics of changes in
gazing at AOIs. Metrics such as fixation duration, the number of fixations, and pupil di-
lation (based on diameter), are described per each AOI such as “stock”, “chart”, “com-
pany”, and “ratios” and over time. Because the author uses different online stock mar-
ketplaces to diminish the order or the presentation of information effects on the
decision-making process, the AOIs’ definitions based on web pages is not consistent.
Therefore, the author determines the AOIs based on the content of the provided infor-
mation. First, the AOI stock contains pricing information such as bid-ask prices, spread,
52 weeks high-low prices, the stock trading information including volume and in some
cases stock price related ratios such as beta, alpha, EPS. This block of information is
numerical and minimally textual. Second, the AOI.visuals comprises a three-year price
chart, supportive graphs and visuals of the stock volume. The AOI company consists of
company information including address, industry, short descriptions, shareholders’ in-
formation, information about dividends, also latest news headlines. The AOI ratio in-
cludes all the key financial and historical ratios assisting in determining the intrinsic
value of the stock.
4.3 Data procedure
4.3.1 Cleaning and preparing data for R analysis
After modifying the AOI, the experimental data is adjusted to the eye tracking package
in R to examine the data set. EyetrackingR deals with initial raw data where each row
specifies a sample measure. Because the author operates the SMI eye tracker with the
sampling frequency of 120 Hz, each row of data represents an equally spaced amount
of time of 8 ms based on fixation position and timing information. The samples that are
more than 8 ms long are omitted.
The author focuses on the analysis of the gaze proportion across AOIs and within the
time bin of 100 ms. Therefore, non-AOI gazing data is not included into the comparison
between AOIs. As a result, all fixations to the white space (non-AOI determined fixa-
tions) are excluded from the analysis. Accordingly, the data examination focuses on
49 the trade-off between defined AOIs and determines the gaze to the single AOI across
conditions. Additionally, the author uses the first stimulus page and the last stimulus
page to test the stated hypotheses derived from the decision field theory (DFT) and
adaptive toolbox model (ATB). Thus, to calculate gaze proportion at the particular AOI,
the author computes “time looking to the AOI divided by time looking to all other AOIs”
by following an option given by Dink & Ferguson’s (2015) eye tracking package.
Both data files with no time constraints and under time constrained conditions passed
the following cleaning and adjusting process. The research concentrates only on delib-
eration of the provided online stock information and the decision-making process of this
information. Therefore, only stimuli from the online stock marketplaces remain for the
analysis, i.e. six companies with five pages of information for a company. Each of the
pages is framed with the particular AOIs as mentioned above. Additionally, the author
deletes the data of 2 participants with a tracking ratio less than the 40% to have
enough eye movement data for a participant to judge individual decision making. The
data that does not qualify as any AOI or is determined to be a white space is also
deleted from the analysis. Moreover, the data that do not qualify as fixation, blink or
saccade is not considered for the examination. Some data loss takes place when the
eye-tracker cannot track the participant’s eyes because a participant accidentally turns
his/her head or suddenly looks away from the screen to deliberate information or blinks
often, where the gaze location has very low efficacy.
As indicated above, the experiment is designed around two-time conditions: the first
group of participants totaling nine students did not have any time constraints, but only
about 10 minutes per company was given to this group of participants; the second
group has the time constrained condition with 2.5 minutes or 30 sec per screen. No
one from the first group of students used the total given time condition of 10 minutes
per task. In the time-constrained condition of 2.5 minutes, a few participants attempted
to violate the time constrained condition by clicking forward and backward between the
pages. The data recorded at above 30 seconds duration per stimulus in the second
group is deleted, i.e. only for the two participants mentioned previously. Thus, approx-
imately one million gaze samples are considered for the eyetrackingR analysis after
cleaning the raw experimental data. The eye tracking package additionally (1) deter-
mines the amount of lost data in each trial and then (2) removes trials with over 25%
data loss. After analysis of the amount of lost data by participant and trials, approxi-
mately 402 trials are removed by the software and the additional two participants were
eliminated from the analysis. The author reports in Table B.1 the results of the lost data
per participant. As a result, the following data with the mean samples of 83.98% and
50 standard deviation (SD) equalling 3.00% contributed per trial, indicating that the devia-
tion of the data from the mean is minor.
4.3.2 Descriptive statistics and regression
In the next step, the author explains the results of the descriptive statistics analysis of
the data. The data summary provides the means and variance within each condition for
each participant or AOI, and some quick visualization of the variables. These graphs
represent the differences by plotting a line for each participant or AOI in each testing
condition. The provided descriptive statistics and plots correlate each participant and
trials to the different AOIs, time onset for a trial and pupil dilation by measuring pupil diame-
ter7 in mm.
Furthermore, the author performs a simple paired t-test using a single mean proportion
value (percentage of fixations to the particular AOI) for each time condition and each
participant. At this point, the author incorporates additional predictors into the analysis,
e.g. pupil dilation. After t-test, regression analysis additionally provides the following
dependent variables for the analysis, e.g. logit adjusted, empirical logit or corrected
logit transformed and arcsine square root transformed variables. The integration by
participants across the response window is realized by using arcsin function to trans-
form proportional data of dependent variables. However, this approach cannot inte-
grate one variable within another, for example, accumulated data by stimuli within par-
ticipants. In this case, the author follows with linear mixed-effect models applying lme4
package in R or empirical and adjusted logit transformed dependent variable. The au-
thor examines the fixation to the particular AOI (for example, the AOI stock) hinge on
the time condition of each trial, while computing for random intercepts and slopes
across trials and participants to determine if there are any significant differences be-
tween outcomes. In the end, the author tests an additional effect of pupil dilation that
may be correlated with changes in AOIs.
4.3.3 Growth curve analysis
Growth curve analysis is a multi-level regression model intended for the analysis of
time course or longitudinal data (Mirman, 2014). The previous analysis does not take
into account time course of the decision-making process across trials or participants.
Therefore, the author further advances the examination of data with growth curve anal-
ysis and visualization of data over the time course. In the decision-making process, the
changes in grasping particular information or focusing attention on the particular AOI
7 In this paper pupil dilation is measured by pupil diameter, which indicates the pupil size in a gaze sample.
51 demonstrates if participants develop some strategies or patterns that influence a final
decision and more effectively explain the decision-making process over time. Thus, for
the growth analysis, first, the data is separated into 100 ms time bins to calculate fixa-
tion proportion for each separate time bin over the course of the stimulus and statisti-
cally evaluate the bends in these curves (Dink & Ferguson, 2015). In other terms, this
model assesses raw gaze proportions or its transformations over time by simultaneous
regression of differences between time conditions. The author started with a linear time
model and further considers a non-linear change over time.
At this point, the author finalizes how the data analysis, previously explained, tests the
hypotheses stated in the introduction of this thesis. The following hypotheses were
formulated to test attention to the content of the provided information under time
constraints that influenced the decision. The author discusses them individually step-
by-step. First, the author following DFT assumes that the fixation duration is stable
over time, which is examined by fixation duration in each AOI per company and by
growth curve analysis. Second, the gaze cascade mechanism supports the decision
which indicates attentional bias. Participant based analysis of mean percentage fixation
duration tests this hypothesis. On average, how long is the participants’ gaze at the
particular AOI? This hypothesis furthermore is challenged with cross analysis of the
final decisions, i.e. if gaze cascade correlates with buying or short selling decision.
Third, visual information such as graphs and charts impacts the decision. The AOI
based determination of mean percentage fixation duration and regression across trials
and participants allows detection of time constrained conditions if they affect the fixa-
tion on the AOI visuals.
Additionally, the next three hypotheses verify the decision-making process under time
constraints or heuristics behind the decision dynamics. The fourth hypothesis states
that the most prominent dimension tends to be processed the most and the first com-
pare with others. The author assumes that the summary of the stock price or the AOI
stock’s stimuli impacts the decision process over time the most. However, how do the
effect of information presentation or the order impact the importance of the pricing in-
formation? Is the summary of a stock price prominent because it is presented on the
first page of all the online marketplaces, or because it is extremely valuable in decision
making and therefore presented the first? Fifth, according to DFT, the longest alterna-
tive should be chosen more frequently because of longer deliberation time. This hy-
pothesis has a different aspect than the attention bias concept. It conditions the time of
deliberation of information as an effective measure of a particular decision. Growth
curve analysis determines a change in the decision over time, which correlates with a
deliberation time. The last hypothesis is derived from DFT. However, if this hypothesis
52 is rejected, it supports adaptive toolbox model. Additionally upon rejection, the last hy-
pothesis affirms that changing to simple heuristics decreases the accuracy of the
decision. The author assumes that deliberation time reduces significantly under time
constraints. Therefore, simple heuristics are expected to be applied in the decision-
making process. The final decision accuracy directly depends on the hypothesis ac-
ceptance. The author regresses participant times in task duration (a decision to buy or
short-sell a stock) against their decision accuracy that is determined as mentioned be-
fore by a margin of safety principle to minimize the downside risk.
5 RESULTS
The analysis of the dependent measures elaborates and deepens over three main
steps of the data examination. The author starts with descriptive statistics providing a
description and summary of the data statistics such as mean, standard deviation (SD)
and variance. The next step is performing step-by-step regression and testing of the
eye tracking data with arcsin square root transformation to logit modelling to discover
nonlinear correlations and significant relations of the data set. Third, examining how
the differences and correlations between variables emerged over time by completing
the scrutinizing of the data with growth curve analysis. The last part summarizes the
results in connection with the assumed hypotheses.
[…Please send me email to receive visual and analytical part of this chapter.
Thank you!]
5.4 Summary of the results
To conclude the above provided statistical analysis of the gazing data samples, the au-
thor summarizes the findings by following the formulated hypotheses. However, it
should be mentioned beforehand, that there are some differences between laboratory
and field, the complexity of naturalistic decision making cannot be directly concluded
only based on the experimental founding. The experimental settings and the decision-
making conditions presumably affect the experimental results. Therefore, the summary
is based on step-by-step specifics of design, collection and analysis of data.
According to the research questions, this paper intends to analyse the information con-
tent and heuristics behind the decision-making process. Therefore, the following hy-
potheses are developed based on DFT and ATB models of the decision-making pro-
53 cess. The provided statistical analysis tests these specifically stated hypotheses in this
chapter.
Thus, the first hypothesis states that fixation duration is stable over time. The author
observes the complexity of this assumption in both conditions. Fixation duration as ap-
proximated around 200-300 ms can be considered as stable. However, the author indi-
cates in the previous analysis that fixation duration links to the information content or
depends on the presented stimulus (the AOI). The mean percentage fixation is varied
depending from the presented AOI and significantly impacted by time conditions.
Moreover, as mentioned in the previous research, fixation duration is idiosyncratic and
varies from participant to participant. Therefore, within the trials and as more simplistic
and familiar information is given, the fixation duration averages and remains more sta-
ble than observed by previous experiments (Horstmann et al., 2009). As presented by
the growth curve analysis the fixation is not precisely stable over time and slightly dif-
ferentiated because of the complexity and variety of the displayed information. Howev-
er, the author would agree with Glöckner and Herbold (2011) that the later fixations are
longer (Figure 5.3.1, graph number 4).
The next hypothesis asserts influence of attention or the gaze cascade effect over de-
cision making. The longer the gaze on a particular AOI the more preferences will be
given to it (Shinsuke Shimojo et al., 2003). In order to test this hypothesis, the author
regresses the decision made results against gaze proportions and additionally includes
growth curve analysis. The results support this hypothesis, especially in the given time
constrained condition, where the participants’ decisions are correlated directly with the
fixation duration over the particular company. Moreover, the previous results demon-
strate that the attention bias positively affects the final decision under time constraints,
where the effect is much higher or lower with sufficient time. The participants without
time constraints have plenty of time to deliberate information content; therefore, they
contrast their decisions despite the attention because of the negative or pessimistic
information content.
The third and fourth hypotheses are the levelled extensions of the gaze cascade
mechanism where the author analyses if fixation duration to the particular AOIs affects
the final decision. The results indicate that focus on visual information is only a little
higher under time constraints, but not significant in comparison with the other AOIs.
However, it should be taken into account the nature of cognitive processing of visual
information that requires less fixation duration in the stage of grasping the visuals.
Nevertheless, it increases with focusing on key information obtained from the graph or
chart. Growth curve analysis supports this reasoning. Furthermore, the author ob-
serves that there is not a significant impact on AOI stock over a decision under time
54 constraints. Nevertheless, the order of the stimuli might reduce the significance of this
AOI on a decision. Moreover, the pupil diameter changes over time. The correlation
between these changes in pupil diameter and fixation duration in each AOI confirms
the similar trend in each AOI. However under time constraints, the difference in gazing
at the specific AOI is more varying from trial to trial because participants become more
familiar with the information content and task, more confident in their strategy, more
selectively observe the information in order to fit into the given time frame. And these
changes overcome individual changes within the trial and between AOIs. Therefore,
the author rejects the third and fourth hypotheses.
The fifth hypothesis includes the deliberation time in the decision-making process and
states the tendency between deliberation time, fixation duration, and final decision.
Time conditions do not significantly impact the decision. The result demonstrates that
even though participants spent more time to gaze at a particular company stock, they
finally decided to short-sell the stock (despite the attention bias and deliberation time).
Therefore, the influence of unfavourable information such as a downside trend of the
stock price or other pessimistic information about the company’s future performance
can challenge the final decision against attention bias in cases of extended deliberation
time. The fifth hypothesis is also rejected.
Finally, the sixth hypothesis assumes a correlation between decision accuracy and
given time. Under time constraints, the participants employ simple heuristics which
eventually decrease the accuracy of their decisions. The statistical analysis of the eye-
tracking data does not support this hypothesis. There is no distinct difference between
gazing at the particular company to make a decision to buy or short-sell it and accuracy
of the decision over time. However, considering growth curve analysis the author takes
a glimpse at the sublevel of the decision accuracy depending on the particular AOIs
observed by the participants. It concludes that under time constraints the participant
who focused more on ratios and the summary of the stock better predicted the future
price of the stock. Additionally, participants, who had extra time to read over company
information, evaluated a possible future stock price better than participants under time
constraints.
55
6 CONCLUSION
6.1 Overview of the research
Decision making in economics and finance is a novel and at the same time very di-
verse area of research. In spite of some important advances, the decision-making pro-
cess is still an enigma that imposes significant challenges on research. Forasmuch in-
triguing as the topic contains and recognizing the complexity of subject matter; the au-
thor attempts to input originality to the research by designing and conducting an own
experiment to analyse the investment decision-making process under time constraints
exploiting the information from the online stock marketplace as stimuli for the experi-
ment.
In order to justify the motivation and topic importance, the author devotes the whole
introduction section to introduce step-by-step the definitions of the topic and back-
ground behind each term. The pathway from neoclassical principles of von Neumann–
Morgenstern (1944) to the behavioural matter of Kahneman and Tversky (1979) in
economics and finance is only about 35 years old, but it changes the perception and
approach including behavioural aspects of the agent or “utility maximizer” in pursuance
of improving economic models. Following after, the author gave the overview of the
progress in decision theory and how it directly relates to economics. Shifting from the
static model of Edwards (1954) to the dynamic model of Busemeyer and Townsend
(1993) is the way to recognize the complexity of the decision-making matter which is
no longer associated with the only outcome but opens the black box of inside pro-
cessing.
However, pondering further the nature of the decision-making process, the author indi-
cates that the time constraints that impose limitations and tangible drawback need to
be taken into account and investigated. Moreover, the author is interested in the cogni-
tive processes behind decision-making and hence applies the eye tracking techniques
to the research. Certainly, there are some assumptions to be made between eye
movement, attention and behaviour. However, the eye tracking techniques are
improving, and the eye tracking analysis is obtaining deeper levels. It might not be a
direct causal correlation between behaviour and gazing, but the eyes are one way to
understand the mind which impacts individual behaviour. Additionally, nowadays the
financial markets are no longer restricted to brokers; investors with different experience
and knowledge are trading shares by the click of the computer mouse. Therefore, all of
the above mentioned and furthermore indicated in this thesis have motivated the au-
thor to select this topic for the master’s thesis.
56 The main two research questions that the author focuses on in this study are (1) which
information content is more attentive in making decisions with time constraints and (2)
what heuristics are employed in the decision-making process under time constraints.
The author designed the eye tracking experiment to keep the natural settings of the
online stock marketplaces to a maximum. However, in order to formulate and test the
precise hypothesis, the author meticulously chose (1) identical content for each
company and online stock marketplace based AOIs, (2) three different layouts to
minimize the order effect on the decision, (3) six middle sized and little known to the
public companies to minimize recognition bias in decision-making.
Furthermore, the research requires grounds as to what was discovered and investigat-
ed in this area before. Therefore, in the next step, the author reviews previous publica-
tions in economics, finance and business that employ eye-tracking techniques under
time pressure and constraints, including consumer economic decisions as a purchase
choice and decision making under uncertainty and time pressure and constraints. Be-
cause the terms are not distinguished precisely in previous publications, the author
overviews the literature on time pressure and time constraints. Additionally, the litera-
ture review comprises of decision making in economics and finance under uncertainty
and time pressure and constraints. This approach is chosen to overview the extension
of previous studies in this area and the utilization of different methods and applications
and to demonstrate that this research is unique in applying eye tracking techniques to
examine the decision-making process of obtaining information from online stock mar-
ketplaces under time constraints.
After outlining this vast area of research in decision making, the author identifies and
discusses the previous methodology, methods and models that are utilized in this area
of study and reasons the adopted methods for the research. Following Fiedler and
Glöcker (2012), the author defines two major classes of existing process models: heu-
ristics models and automatic integration models. Most of the recently developed mod-
els are indeed extensions, specifications or integrations of simple heuristics or DFT
models.
The authors’ choice of the methods has a rational explanation rooted in the stated re-
search questions and the capability of the SMI eye tracking technology. Taking into
account the features of the stimuli (information from online stock marketplaces) and
brainstorming possible correlations between visual attention to the financial
information, dynamics of the decision-making process and final choice, the author
assumes that the hypotheses and ideas of adaptive toolbox model (ATB) and decision
field theory (DFT) can explain the outcome of the experiment.
57 To design the experiment, measure the attention of the participant and collect the eye
tracking data for the subsequent examination, the author utilizes SensoMotoric Instru-
ments, SMI iView X RED250, an eye tracker and Experiment Suite 360 software bun-
dle which includes Experimenter Center 2 and BeGaze 3.5.10 in it. To conclude the
design, 20 participants were exposed to 30 stimuli with six tasks to decide to buy or
short-sell based on observed and deliberated information provided on the screen. More
than 1.5 million samples of raw gaze data collected undergo a rigorous cleaning pro-
cess by only selecting measurable outcomes resulting in around one million gaze sam-
ples are being selected for eyetrackingR analysis.
The dependent variables such as fixation percentage mean and fixation density per
trial, task and participant are considered for evaluation of stated hypotheses. In this
research, the author also analyses the pupil diameter including this variable as a pre-
dictor of the logit and mixed-effects models. Taking into account the developed stock
price and the rationale behind the margin of safety principle, the author assigns the ac-
curacy factor to the each decision and uses it as another dependent variable to analyse the
hypothesis.
The R analysis tested six stated hypotheses derived from DFT and ATB models which
are widely discussed in previous publications: (1) fixation duration is stable over time;
(2) the gaze cascade mechanism supports the decision; (3) visual information impacts
the decision; (4) the AOI stock summary impacts the decision; (5) decision outcome
correlates with the deliberation time; (6) decision accuracy is decreasing under time
constraints. To deliver a thorough analysis, the author step-by-step expands the en-
quiry to find correlations between dependent and independent variables in order to ex-
plain the decision-making process.
First, the author begins with the summary of the data and descriptive statistics. Sec-
ond, the data are subjected to the simple t-test, regression, and linear modelling.
However, dealing with binary data, e.g. contrasting one AOI against others, the author
applies logistic regression to the research to convert the proportional scale of the
dependent variables to a logarithmic scale or logit transformed as well as to perform
the analysis on the transformed values in order to capture another level by aggregating
data by participants within trials. The author then examines if gazing at the specific AOI
under time conditions can be explained by the linear mixed-effects model. In this step
of multilevel modelling, the author is able to include random factors and estimate the
maximum likelihood of deviations from it. However, one step further attempted in the
analysis is to reveal the changes in dependent variables over time by performing the
growth curve analysis for each AOI, trial and participant duration gaze under time con-
ditions.
58
6.2 Findings and limitations
According to the research questions, this paper intends to analyse the information con-
tent and heuristics behind the decision-making process. The hypotheses derived from
DFT and ATB models are assessed in this paper. However, the thorough analysis indi-
cates a complexity of the stated hypotheses as a more sub-levelled examination of de-
pendent variables is discovered. The fixation duration is stable over time for the simple
homogeneous tasks. However, fixation duration links to the information content of the
AOIs, complexity of stimuli and is significantly impacted by time constraints. Within
trials, as more familiar information becomes evident, the fixation duration averages and
stays more stable. Moreover, fixation duration is idiosyncratic and therefore not stable
for each participant over time. The attention or gaze cascade affects the decision-
making process significantly under time constraints. The participants without time con-
straints have plenty of time to deliberate information content; therefore, they may con-
trast their decisions despite the attention bias because of negative or pessimistic in-
formation content. Moreover, the results do not support the assumption that visual in-
formation and the summary of stock quotes impact decision making under time con-
straints. However, it should be taken into account the nature of the processing of visual
information that requires fewer fixation durations in the stage of grasping the visuals.
However, it increases with focusing on key information obtained from the graph or
chart. Growth curve analysis demonstrates this effect. Time conditions do not signifi-
cantly impact the decision. The results reveal that even though participants spent more
time to gaze at a particular company stock, they finally decided to short-sell the stock
(despite the attention bias, and deliberation time). Finally, there are no distinct differ-
ences between gazing at the particular company to make a decision to buy or short-sell
this stock and accuracy of the decisions over time. To sum up, the outcomes indicate
that under the natural complexity of the provided financial information, the participants
rely on simple heuristics rather than accumulation information models in the decision-
making processes under time constraints. The content of the information impacts the
decision-making process of participants under both time conditions.
This work is a subject, similar to the other experimental analyses in the area of
behavioural economics and finance, of certain limitations such as the small sample
size of 20 participants who are students and cannot be considered as representatives
of the general population. Moreover, even though the author intends to mitigate meas-
urement precision and accuracy of the eye-tracking hardware and to increase synchro-
nization between stimulus presentation and eye movement recordings following the
recommendation of the experts, some errors may occur due to the author’s overlook
considering the 1.5 million data elements per participant. Moreover, the assumption
59 between attention and fixations is still a topic for ponderable argumentations according
to the recent literature. Therefore, considering the limitation mentioned above, possible
technical errors, and the assumption the results of the research indicate the tendency
of the decision-making process under certain experimental conditions and samples to
be in line and consistent with previous publications.
6.3 Importance and further research questions
To sum up, the eye tracking research in the area of decision making is crucial in order
to understand the investors’ behaviour and processes behind the decisions which con-
sequently facilitate the investors to make better investment decisions in the extremely
complex and complicated financial markets. Moreover, the stock offering companies
from all around the world strive to make improvements in data representation available
on their websites. The results of this research are a first attempt to demonstrate what
kind of information and data are more attentive in investment decisions under time
constraints.
A future research in this area perhaps will increase the understanding of investment
decision-making processes by conducting experiments involving different levels of in-
vestors according to their experience and knowledge, risk attitudes and even cultural
backgrounds. Moreover, the new techniques and a multiple-systems approach can be
added to the future research to delve deeper into the decision-making process. Finally,
the integration of these multidisciplinary approaches and methodologies helps to de-
velop more accurate models of decision-making in economics and finance.
60
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69
ANNEX
Appendix A
Figure A.1: Example of the stimulus provided in the experiment
Figure A.2: Growth curve analysis of gazing over time at the AOIs
AOI stock
AOI visuals
AOI company
AOI ratios
70
Appendix B Table B.1: Loss of eye tracking data per participant (%)
Participant Trackloss (%)
p02 0.16
p03 0.15
p04 0.12
p05 0.17
p06 0.16
p07 0.17
p08 0.13
p10 0.13
p11 0.12
p12 0.22
p13 0.16
p14 0.14
p15 0.17
p16 0.14
p17 0.19
p18 0.16
p19 0.23
p20 0.17
Mean 0.84
SD 0.03
The eye tracking data of two additional participants were removed to follow 25% tracking loss threshold.
Table B.2: Summary statistic of raw data adjusted for the R software analysis
Participant Decision Accuracy Gender TrialNum Trials TimeFromTrialOnset
p04 :116338 Buy :625163 Min. :0.0000 F:542781 Min. : 1.00 dEKPage1: 61043 Min. : 0
p03 :109904 Sell:460596 1st Qu.:0.0000 M:542978 1st Qu.: 7.00 dKrPage1: 56530 1st Qu.: 4208
p08 : 93110 Median :0.0000 Median :14.00 dKrPage5: 55628 Median : 9904
p06 : 78460 Mean :0.4763 Mean :14.34 l3IPage1: 54795 Mean : 14041
p14 : 76078 3rd Qu.:1.0000 3rd Qu.:21.00 nAmPage1: 53003 3rd Qu.: 19192
p11 : 75733 Max. :1.0000 Max. :30.00 lFPPage2: 51946 Max. :116616
(Other):536136 (Other) :752814
TimeFromParticipantOnset AOIGroup AOI.stock AOI.visuals AOI.company AOI.ratios
Min. : 0 White Space:288496 Mode :logical Mode :logical Mode :logical Mode :logical
1st Qu.:108568 ratios :213251 FALSE:639644 FALSE:627881 FALSE:651986 FALSE:575754
Median :227864 visuals :160718 TRUE :147240 TRUE :159003 TRUE :134898 TRUE :211130
Mean :278488 stock :148886 NA's :298875 NA's :298875 NA's :298875 NA's :298875
3rd Qu.:410400 company :135864
Max. :930696 other :135812
(Other) : 2732
AOI.other Condition Opinion Category Trackloss Index PupilDiameter
Mode :logical Min. :1.000 DB :445179 Blink :126672 Mode :logical Min. : 0.00 Min. :0.00
FALSE:652271 1st Qu.:1.000 LSE :284085 Fixation:848218 FALSE:786884 1st Qu.: 9.00 1st Qu.:3.13
TRUE :134613 Median :3.000 NASDAQ:356495 Saccade : 80525 TRUE :298875 Median : 27.00 Median :3.48
NA's :298875 Mean :2.103 NA's : 30344 NA's :0 Mean : 38.61 Mean :3.10
3rd Qu.:3.000 3rd Qu.: 54.00 3rd Qu.:3.71
Max. :3.000 Max. :340.00 Max. :6.98
71
Table B.3: Summary statistics for the numerical variables
Mean SD Variance
Accuracy (between 0 and 1) 0.50 0.48 0.25
TrialNumber 14.34 8.49 72.02
TimeFromTrialOnset (ms) 14041.45 14654.66 214759040
TimeFromParticipantOnset (ms) 278487.50 212192.50 45025645671
PupilDiameter (mm) 1.22 3.10 1.50
Table B.4: Example of descriptive data for each AOI of the AD stock
Target.ad Condition Mean SD Var Min Max N NumTrials
(fctr) (int) (dbl) (dbl) (dbl) (dbl) (dbl) (int) (int)
1 AD 1 0.18922840 0.3916988 0.15342797 0 1 25586 5
2 AD 3 0.02892717 0.1676050 0.02809145 0 1 30326 4
3 Otherc 1 0.18098851 0.3850100 0.14823270 0 1 169418 18
4 Otherc 3 0.16175130 0.3682236 0.13558860 0 1 204099 20
Target.ad Condition Mean SD Var Min Max N NumTrials
(fctr) (int) (dbl) (dbl) (dbl) (dbl) (dbl) (int) (int)
1 AD 1 0.2974884 0.4571636 0.2089985 0 1 25586 5
2 AD 3 0.2413106 0.4278863 0.1830867 0 1 30326 4
3 Otherc 1 0.1630616 0.3694232 0.1364735 0 1 169418 18
4 Otherc 3 0.1752793 0.3802069 0.1445573 0 1 204099 20
Target.ad Condition Mean SD Var Min Max N NumTrials
(fctr) (int) (dbl) (dbl) (dbl) (dbl) (dbl) (int) (int)
1 AD 1 0.1924018 0.3941959 0.1553904 0 1 25586 5
2 AD 3 0.2680936 0.4429749 0.1962268 0 1 30326 4
3 Otherc 1 0.2795828 0.4487958 0.2014177 0 1 169418 18
4 Otherc 3 0.2152614 0.4110048 0.1689249 0 1 204099 20
Target.ad Condition Mean SD Var Min Max N NumTrials
(fctr) (int) (dbl) (dbl) (dbl) (dbl) (dbl) (int) (int)
1 AD 1 0.3208813 0.4668259 0.2179264 0 1 25586 5
2 AD 3 0.4616687 0.4985379 0.2485401 0 1 30326 4
3 Otherc 1 0.3763671 0.4844755 0.2347165 0 1 169418 18
4 Otherc 3 0.4477080 0.4972595 0.2472670 0 1 204099 20
Table B.5: Example of descriptive statistics of aggregating data with three target conditions: a company, accuracy of decision and time condition Target.kr Accuracy Condition Mean SD Var Min Max N NumTrials
(fctr) (int) (int) (dbl) (dbl) (dbl) (dbl) (dbl) (int) (int)
1 Kr 0 1 11549.462 7510.999 56415103 0 30000 21443 3
2 Kr 0 3 21182.228 15886.446 252379161 0 63152 21680 3
3 Kr 1 1 13508.303 8547.276 73055930 0 30000 24522 3
4 Kr 1 3 11718.390 7856.116 61718557 0 33584 16161 4
5 Otherc 0 1 10777.738 8186.546 67019531 0 30000 71666 17
6 Otherc 0 3 24431.725 23596.779 556807959 0 114944 91342 11
7 Otherc 1 1 9547.759 7673.486 58882394 0 30000 77373 17
8 Otherc 1 3 20544.610 15861.510 251587488 0 62272 105242 16
Table B.6: Examples of paired t-test between conditions with the predictor, pupil diameter, for AOI.stock Target.t Mean SD Var Min Max N NumTrials
(fctr) (dbl) (dbl) (dbl) (dbl) (dbl) (int) (int)
1 limit 0.2664829 0.5291146 0.2799623 0 1.570796 4638 23
2 time 0.2052875 0.4766350 0.2271809 0 1.570796 3855 24
72
Welch Two Sample t-test
data: ArcSin by Target.t
t = 5.4032, df = 7847.7, p-value = 6.737e-08
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.03899405 0.08339670
sample estimates:
mean in group limit mean in group time
0.2664829 0.2052875
term estimate std.error statistic p.value
1 (Intercept) 0.28572233 0.008160435 35.013125 8.630548e-250
2 Target.ttime -0.09702919 0.011929690 -8.133421 4.810016e-16
3 PupilDiameterC -0.06489075 0.009485137 -6.841309 8.433390e-12
4 Target.ttime:PupilDiameterC -0.01723911 0.014798998 -1.164883 2.441014e-01
Welch Two Sample t-test
data: ArcSin by Target.ek
t = 5.2436, df = 2863.5, p-value = 1.689e-07
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.05267783 0.11560521
sample estimates:
mean in group EK mean in group Otherc
0.3587714 0.2746299
term estimate std.error statistic p.value
1 (Intercept) 0.283858093 0.01187340 23.9070589 4.225964e-118
2 Target.ekOtherc 0.005866971 0.01500058 0.3911164 6.957322e-01
3 PupilDiameterC 0.100034269 0.01274910 7.8463805 5.469226e-15
4 ConditionC 0.072804366 0.01170475 6.2200726 5.485125e-10
5 Target.ekOtherc:PupilDiameterC -0.205524098 0.01695341 -12.1228798 3.081747e-33
6 Target.ekOtherc:ConditionC -0.210829745 0.01491142 -14.1388071 2.582063e-44
7 PupilDiameterC:ConditionC -0.200595306 0.01258430 -15.9401267 1.721437e-55
8 Target.ekOtherc:PupilDiameterC:ConditionC 0.326966457 0.01689430 19.3536561 8.332160e-80
Table B.7: Example of fitting the data to mixed-effects models for the AOIs.
Model:AOI.stock
Elog ~ TargetC * PupilDiameterC + (1 + TargetC | Participant) +
(1 | Trials)
Df AIC LRT Pr(Chi)
<none> 54798
TargetC 1 54796 0.247 0.6193
PupilDiameterC 1 55029 232.512 < 2.2e-16 ***
TargetC:PupilDiameterC 1 54837 41.020 1.507e-10 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Model:AOI.visuals
Elog ~ TargetC * PupilDiameterC + (1 + TargetC | Participant) +
(1 | Trials)
Df AIC LRT Pr(Chi)
<none> 56712
TargetC 1 56711 0.268 0.6047
PupilDiameterC 1 56925 214.331 <2e-16 ***
73 TargetC:PupilDiameterC 1 56710 0.023 0.8800
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Model:AOI.company
Elog ~ TargetC * PupilDiameterC + (1 + TargetC | Participant) +
(1 | Trials)
Df AIC LRT Pr(Chi)
<none> 56158
TargetC 1 56161 5.36 0.02064 *
PupilDiameterC 1 56478 321.55 < 2e-16 ***
TargetC:PupilDiameterC 1 56157 0.69 0.40464
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Model:AOI.ratios
Elog ~ TargetC * PupilDiameterC + (1 + TargetC | Participant) +
(1 | Trials)
Df AIC LRT Pr(Chi)
<none> 55831
TargetC 1 55829 0.198 0.6561267
PupilDiameterC 1 55910 81.542 < 2.2e-16 ***
TargetC:PupilDiameterC 1 55843 14.494 0.0001406 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Table B.8: Example of growth curve analysis in R. (1) AOI stock
term estimate std.error statistic
1 (Intercept) 133.4448 25.75525 5.181265
2 TargetC 297.8906 56.64898 5.258534
3 ot1 5650.3265 1077.04105 5.246157
4 ot2 3561.4743 680.94226 5.230215
5 ot3 1283.1601 247.16730 5.191464
6 ot4 211.8076 41.31009 5.127260
7 TargetC:ot1 12447.4293 2369.22041 5.253808
8 TargetC:ot2 7835.4326 1497.90220 5.230937
9 TargetC:ot3 2814.0608 543.70173 5.175744
10 TargetC:ot4 462.0614 90.86856 5.084943
Model:
Elog ~ TargetC * (ot1 + ot2 + ot3 + ot4) + (1 | Participant) +
(1 | Trials)
Df AIC LRT Pr(Chi)
<none> 124273
TargetC 1 124298 27.641 1.461e-07 ***
ot1 1 124298 27.511 1.562e-07 ***
ot2 1 124298 27.344 1.703e-07 ***
ot3 1 124298 26.941 2.098e-07 ***
ot4 1 124297 26.279 2.955e-07 ***
TargetC:ot1 1 124298 27.591 1.499e-07 ***
TargetC:ot2 1 124298 27.352 1.696e-07 ***
TargetC:ot3 1 124297 26.778 2.282e-07 ***
TargetC:ot4 1 124297 25.847 3.696e-07 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(2) AOI visuals
term estimate std.error statistic
1 (Intercept) -28.93364 27.86663 -1.0382898
74 2 TargetC -61.12665 61.29117 -0.9973159
3 ot1 -1124.62527 1165.30104 -0.9650942
4 ot2 -664.87458 736.74304 -0.9024511
5 ot3 -212.62616 267.42164 -0.7950971
6 ot4 -23.14054 44.69525 -0.5177403
7 TargetC:ot1 -2477.07977 2563.37024 -0.9663371
8 TargetC:ot2 -1448.95815 1620.64992 -0.8940599
9 TargetC:ot3 -451.51612 588.25587 -0.7675506
10 TargetC:ot4 -56.39763 98.31481 -0.5736432
Model:
Elog ~ TargetC * (ot1 + ot2 + ot3 + ot4) + (1 | Participant) +
(1 | Trials)
Df AIC LRT Pr(Chi)
<none> 129703
TargetC 1 129702 0.99461 0.3186
ot1 1 129701 0.93138 0.3345
ot2 1 129701 0.81440 0.3668
ot3 1 129701 0.63216 0.4266
ot4 1 129701 0.26805 0.6046
TargetC:ot1 1 129701 0.93378 0.3339
TargetC:ot2 1 129701 0.79932 0.3713
TargetC:ot3 1 129701 0.58912 0.4428
TargetC:ot4 1 129701 0.32906 0.5662
(3) AOI company
term estimate std.error statistic
1 (Intercept) 2.258072 26.03137 0.08674425
2 TargetC 8.113472 57.26241 0.14168933
3 ot1 154.478185 1089.06712 0.14184450
4 ot2 101.460563 689.14658 0.14722639
5 ot3 44.568766 250.46285 0.17794561
6 ot4 14.262627 42.12678 0.33856439
7 TargetC:ot1 339.826769 2395.80336 0.14184251
8 TargetC:ot2 216.368812 1515.74019 0.14274795
9 TargetC:ot3 84.787130 550.60077 0.15399021
10 TargetC:ot4 14.653497 92.24302 0.15885752
Model:
Elog ~ TargetC * (ot1 + ot2 + ot3 + ot4) + (1 + ot1 + ot2 + ot3 +
ot4 | Trials) + (1 + ot1 + ot2 + ot3 + ot4 | Participant)
Df AIC LRT Pr(Chi)
<none> 124235
TargetC 1 124219 -13.1727 1.0000
ot1 1 124229 -3.5894 1.0000
ot2 1 124235 1.9977 0.1575
ot3 1 124210 -23.0749 1.0000
ot4 1 124227 -6.1084 1.0000
TargetC:ot1 1 124223 -9.9579 1.0000
TargetC:ot2 1 124230 -2.8079 1.0000
TargetC:ot3 1 124230 -2.6898 1.0000
TargetC:ot4 1 124222 -10.1668 1.0000
(4) AOI ratios
term estimate std.error statistic
1 (Intercept) 82.62818 17.01007 4.857603
2 TargetC 183.96892 37.40838 4.917853
3 ot1 3511.90221 711.47901 4.936059
4 ot2 2237.11599 450.22397 4.968896
5 ot3 830.21644 163.60920 5.074387
75 6 ot4 146.37337 27.42502 5.337219
7 TargetC:ot1 7704.08558 1565.07121 4.922514
8 TargetC:ot2 4877.22898 990.16645 4.925666
9 TargetC:ot3 1763.48251 359.72209 4.902347
10 TargetC:ot4 286.58147 60.20393 4.760179
Model:
Elog ~ TargetC * (ot1 + ot2 + ot3 + ot4) + (1 + ot1 + ot2 + ot3 +
ot4 | Trials) + (1 + ot1 + ot2 + ot3 + ot4 | Participant)
Df AIC LRT Pr(Chi)
<none> 95180
TargetC 1 95208 29.610 5.284e-08 ***
ot1 1 95200 21.481 3.574e-06 ***
ot2 1 95198 19.107 1.236e-05 ***
ot3 1 95176 -2.895 1.00000
ot4 1 95201 22.461 2.145e-06 ***
TargetC:ot1 1 95207 28.195 1.097e-07 ***
TargetC:ot2 1 95210 31.982 1.556e-08 ***
TargetC:ot3 1 95183 4.268 0.03884 *
TargetC:ot4 1 95211 33.053 8.966e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
