Attention, Frame Condition and Decision Making Under Risk:
An Empirical Test of the Contingent Focus Model using an Eye Gaze Recorder

Satoshi Fujii1 & Kazuhisa Takemura2
1

Tokyo Institute of Technology, Japan
2

Waseda University, Japan

Abstract
Identical problems may give rise to different decisions, due to subjective decision framing inwhich the decision-making process depends on how the situation is described. This is called theframing effect. We applied the contingent focus model (Takemura, 1994a) to explain theframing effect. The model hypothesizes that risk attitude depends on the extent to which a
subject focuses on possible outcomes and probabilities (the focusing hypothesis), and that
focusing on possible outcomes and probabilities is, in turn, contingent on contextual factors
including positive/negative frame condition (the contingent focus hypothesis). These
hypotheses were tested by the eye movement data obtained from 33 participants using an eye
gaze recorder. The data indicated that participants whose ratio of total time gazing at words
representing possible outcomes to the total time gazing at words representing possible
outcomes and probabilities was higher preferred a risk-taking option. This ratio was higher
under negative frame conditions than under positive frame conditions.

1
Corresponding author: Satoshi Fujii, Department of Civil Engineering, Tokyo Institute of Technology,
1-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Tel: +81-3-5734-2590; Fax: +81-3-5734-2590; E-mail: fujii@plan.cv.titech.ac.jp1Introduction
Identical problems may lead to different decisions because of subjective decision
framing, in which the decision-making process depends on how the situation is described. Thisis called the framing effect (Tversky & Kahneman, 1981). For instance, when a decision needs
to be made concerning whether or not one agrees to undergo a surgical operation, the decision
may be different when a doctor tells one that there is a 95% probability of living following thesurgery, as compared to when one is told that there is a 5% probability of dying. This effectviolates the principle of description invariance, which states that different representations of thesame choice problem should yield the same preference (Tversky & Kahneman, 1986).
Tversky and Kahneman (1981) posed a question under the following two framing
conditions; this typical and well-known example, known as the Asian disease problem, allows
subjects to make a choice under each condition and results in the framing effect.
[Problem 1]
Positive frame condition:“Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected to kill
600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact
scientific estimates of the consequences of programs are as follows. Which of the two programs would you
favor?
If program A is adopted, 200 people will be saved.
If program B is adopted, there is 1/3 probability that 600 people will be saved, and 2/3 probability that nopeople will be saved. (p.193.)”
Negative frame condition:
The question is the same except for the description of programs, which were changed as follows:“If program C is adopted, 400 people will die.
If program D is adopted, there is 1/3 probability that nobody will die, and 2/3 probability that 600 people
will die. (p.193)”

Here, although the program descriptions are different, it is clear that programs A and C, and2

programs B and D, respectively, have equivalent meanings. “Be saved” equals “not die,” and“not be saved” equals “die.” Tversky and Kahneman (1981) reported that when a profitable
position was emphasized in the description of a positive frame condition, most subjects choserisk aversive programs, i.e., program A. But, if a losing position was emphasized in thedescription of a negative frame condition, most subjects chose the risk taking program, i.e.,
program D.
Tversky and Kahneman (1981, 1986) reported that the framing effect is a robust
phenomenon and suggested that, similar to visual illusion, the framing effect leads to aparadoxical result, even though the paradox may only be recognized afterwards. Framing
effects have been reported to occur in relation to medical judgments made by doctors (McNeil,
Pauker, Sox, & Tversky, 1982), in managerial decision making (Qualls & Puto, 1989), and inmany other decision making situations (Wang, 1996; Kühberger, 1998; Shafir & LeBoeuf,
2002; LeBoeuf & Shafir, 2003).

Prospect Theory and Reference Point
Tversky and Kahneman (1979) proposed prospect theory as a way of explaining
framing effects. They highlighted a difference in subjective values between gains and losses
associated with choice behavior. The value function in prospect theory is concave in the gainarea and convex in the loss area, which implies that a decision maker is risk averse in the gainarea but chooses to take risks in the loss area. Prospect theory also assumes that original pointsof the value functions, i.e., reference points, shift depending on the description of a decision
problem. Prospect theory explains framing effects by a shift of the reference point. When areference point is greater than an outcome, the outcome is interpreted as a gain. However, if thereference point shifts to be less than the outcome, it then comes to be regarded as a loss. Since
prospect theory assumes that subjects avoid risks when outcomes are framed as gains (i.e.,3positive frame), and that subjects take risks when outcomes are framed as losses (i.e., negative
frame), the theory predicts that risk attitudes change, depending on the frame condition.
A reference point is necessary for prospect theory to explain decision making underrisk because risk attitude, which determines a decision, depends on the relation between areference point and an outcome. This implies that one must be able to predict the position of areference point and its shift due to contextual factors, including positive/negative frame
conditions, in order to predict decision making under risk in an actual environment, in which
numerous contextual factors are embedded.
Does prospect theory, then, provide a theoretical and quantitative explanation for the shift of areference point per se? With respect to this question, Tversky and Kahneman (1981) stated briefly:"The frame that a decision maker adopts is controlled partly by the formulation of the problem and partly
by the norms, habits, and personal characteristics of the decision maker" (p. 453)

In line with this conjecture, Fischhoff (1983) reported an experiment that investigatedreference point positions while postulating the validity of prospect theory. However, he foundthat it was difficult, or even impossible, to identify a reference point position from external
observations, i.e., actual choices. In addition, he found an inconsistency between a reference
point that is derived from actual choice based on prospect theory, and a self-reported reference
point. To date, a methodology that identifies the reference point position does not seem to havebeen proposed.
While prospect theory postulates one reference point, a decision maker may actually
use multiple reference points. For instance, Takemura (2001) proposed the mental ruler theory
that postulates two reference points to explain numerical judgments. He confirmed that thetheory provides a better fit to judgmental data than other theories. In addition, Maule (1989)
collected verbal protocol data in decisions involving the Asian disease problem and found that
5 subjects out of 12 made their decisions while adopting two different reference points.

4

Contingent Focus Model
The reference point concept is useful with respect to explaining the framing effect.
However, it is difficult to define a reference point and to predict its position and shift;furthermore, prospect theory cannot explain decision making when a decision maker has
multiple reference points. For these reasons, one of the authors of the present study proposed
the contingent focus model, which does not employ the concept of reference point to explain theframing effect (Takemura, 1994a; Fujii & Takemura, 2000, 2001, 2003).
The basic assumption of the contingent focus model is that framing effects emerge, notwhen a reference point shifts, but when a decision maker changes focus on possible outcomesand probabilities, depending on the frame conditions of decision problems. As shown in Figure
1, under positive frame conditions, a decision maker is assumed to pay more attention toprobabilities than to possible outcomes, which results in the decision maker being risk averse.
On the other hand, under negative frame conditions, a decision maker is assumed to pay more
attention to possible outcomes than to probabilities, which results in the decision maker being
risk inclined. In other words, a decision maker is assumed to attend to negative outcomes (i.e.,loss) more intensely than to positive outcomes (i.e., gain).
This hypothesis is in line with the loss sensitivity principle (Gärling, et al., 1997;
Romanus & Gärling, 1999), which presumes that a decision maker is more sensitive to anegatively framed outcome (i.e., loss) than to a positively framed outcome (i.e., gain). Prospect
theory hypothesizes that the value function of outcomes is steeper for losses than for gains,which is also congruent with the hypothesis, since the curvature of the value function implies
the decision maker's sensitivity to outcome. Furthermore, Kahaneman & Tversky (1984) haveargued that "losses loom larger than gains (p. 348).” We can then infer that a decision makerpays more attention to outcomes under negative frame conditions than under positive frame
conditions, as is assumed in the contingent focus model.

5
Figure 1
As in prospect theory (Kahneman & Tversky, 1979) and subjective expected utility
theory (Von Neumann and Morgenstern, 1944; Savage, 1954), the contingent focus model also
describes decision making under risk. Within the contingent focus model, it is hypothesizedthat a decision maker chooses an alternative whose subjective decisional value is maximum
from among possible alternatives. The value is formulated as follows.
U(X, P) = F(X)aG(P) (1-a)(1)

where X denotes possible outcome, P denotes the probability that a decision maker gets X, U(X,P) denotes a subjective decisional value of an alternative of X and P, F(X) denotes the
subjective value of a possible outcome X (F(X) > 0), G(P) denotes the subjective value of P
(G(P) > 0), and a denotes a parameter (0 ≤ a ≤ 1) indicating the degree of focus on outcome X.
We label this parameter the focal parameter. As the focal parameter a approaches 1 from 0, a
decision maker makes riskier decisions. When a equals 1, only outcomes influence the decision
making, and a decision maker is making extremely risky choices. On the other hand, as aapproaches 0 from 1, a decision maker becomes risk averse. When a equals 0, only probabilities
influence the decision making, and a decision maker is extremely risk averse. This hypothesis,
which explains how focusing on possible outcomes and probabilities determines risk attitudes,is called the focusing hypothesis.
The hypothesis that focal parameter a changes depending on contextual factors,
including frame condition, is the contingent focus hypothesis. Thus, in the contingent focus
model, framing effects are ascribed to changes of the focal parameter a and not to reference
point shifts. This contingency of the focal parameter is formulated as follows:a = Ψ(θ)(2)

6where θ denotes a vector of contextual factors and Ψ( ) denotes a function indicating thecontingency of the focal parameter a on θ. Contextual factors (θ) include positive/negative
frame conditions. The basic contention within the contingent focus model, that a decision
maker attends to negative outcomes more intensely than to positive outcomes, indicates that the
focal parameter a will be larger under negative frame conditions than under positive frame
conditions.
Figure 2 summarizes the contingent focus model hypothesis that contextual factors,
including frame conditions, affect attention on possible outcomes and probabilities, and that
attention, in turn, determines risk attitudes.

Empirical Hypotheses
The hypotheses of the contingent focus model, i.e., the focusing hypothesis and the contingent
focus hypothesis, are supported by data from previous studies. Two experiments manipulated
the size of letters describing outcomes and probabilities in decision problems under risk (Fujii& Takemura, 2000). Results were compatible with predictions; that is, the subjects more
frequently selected risky options when outcomes were emphasized. The data from anexperiment using an information board technique, which manipulated time to display possible
outcomes and probabilities, also supported the hypothesis. Results indicated that participants
accepted more risk as possible outcomes were displayed longer (Takemura, Ｈｕ & Fujii, 2001).
We also applied the model to a psychometric meta-analysis of subjects' responses in 4
experiments of the Asian disease problem reported in Tversky & Kahaneman (1981),
Takemura (1994b) and Fujii & Takemura (2000). The results reported in Fujii & Takemura(2001) were also compatible with predictions derived from the hypotheses; a ratio developed by
calculating the weighting parameter of possible outcomes to probabilities under negative frame
conditions was significantly greater than that under positive frame conditions.
7

While the two hypotheses of the contingent focus model are supported byexperimental data, attention to possible outcomes and probabilities was not explicitly observedin previous studies.
In the present study, we used an eye gaze recorder to record the time that theparticipants gazed at words representing possible outcomes and probabilities in a decision
problem involving risk. Based on the contingent focus hypothesis, it was predicted that the ratioof time to gaze at words representing possible outcomes to time to gaze at words representing
probabilities would be greater under negative frame conditions than under positive frame
conditions (Hypothesis 1). Based on the focusing hypothesis, we predicted that the ratio of time
to gaze at possible outcome words to the time to gaze at probability words would be greater for
risk-taking participants than for risk-averse participants (Hypothesis 2).

MethodParticipants
Thirty-three undergraduate university students (25 men and 8 women) at the Tokyo Instituteof Technology participated in the experiment in return for the equivalent of $xx. The mean ageof the participants was 22.18 years (Sd = 1.97), within a range of 19 to 24 years. Subjects wererandomly assigned to two conditions: the negative frame condition (n = 18) and the positive
frame condition (n = 15)1.

Materials

1

There were 3 participants (out of 18 participants who were assigned to positive frame condition) whose eye
movement data we fail to obtain by eye gaze recorder. Therefore, we eliminate these 3 participant for the analysis,
and we report results from 15 participants for positive frame condition.
8

We adopted the Asian disease problem and reflection-effect problem used in Tversky and
Kahneman’s (1981) original framing study. Eye gaze recorder equipment (NAC EMR-8) wasused to test the present hypotheses. This equipment used the pupil-center/corneal reflection
method, which has the same function as the eye-tracking equipment used in previous decisionresearch (Lohse & Johnson, 1996; Boe, Selart, & Takemura, 2000; Selart, Boe, & Takemura,2000).
Procedure
Each participant was individually invited to an experimental room and sat in a chair placed 2
meters in front of a screen on the wall. The screen was approximately 1.5 meters high andapproximately 2 meters wide. After s/he sat in a chair, s/he put on a cap equipped with a small
camera to detect movement of the right eye. An experimenter then calibrated the eye gazerecorder to detect the participant’s eye movement, a process that averaged two minutes. The
eye movement was recorded in the video picture of the angular range of view that was
simultaneously captured by another camera. After the calibration, the participant was instructedto say “yes” immediately after s/he understood the instructions displayed on the screen, and was
also instructed to verbally answer the questions displayed on the screen immediately after
making a decision.
“Which do you choose if you have to choose from 2 alternatives?” was then displayedon the screen. If s/he said “yes,” the experimenter changed the display.
The following two options were displayed for the participants assigned to the positive
frame condition:[A]
certainly gain 20,000 yen[B]a lottery with a 50 % chance to gain 40,000 yen anda 50 % chance for no gain.

For the participants assigned to the negative frame condition, the following two options weredisplayed:9[A]certainly lose 20,000 yen[B]a lottery with a 50 % chance to lose 40,000 yen anda 50 % chance for no loss.

We labeled this the “reflection-effect problem”, as it is a version of a decision problem thatexhibits the reflection effect (Kahnemen & Tversky, 1979).
After s/he reported hers/his choice, the experimenter again changed the display so that
instructions for the Asian disease problem (Tversky and Kahneman, 1981) were displayed.
After the participant finished reading, s/he said “yes,” and the experimenter changed the display
to the following for the participants assigned to the positive frame condition:[program A]

200 people will be saved.
[program B]

there is 1/3 probability that 600 people will be saved,and 2/3 probability that no people will be saved.

For the participants assigned to the negative frame condition, the following was displayed:[program A]

400 people will die.
[program B]

there is 1/3 probability that nobody will die,and 2/3 probability that 600 people will die.

After s/he said “A” or “B,” the experiment was concluded.

Results
Choice Data
As can be seen in Table 1, participants preferred a risk-taking option to a risk-averse option in
the negative frame condition and preferred a risk-averse option to a risk-taking option in thepositive frame condition for both the reflection-effect problem and the Asian disease problem.
The results from the reflection-effect problem supported the reflection effect, and the resultsfrom the Asian disease problem supported the framing effect. A χ2 test was significant for the10reflection effect data (χ2 [df = 1] = 3.91, p < .05), but did not reach significance for the framing
effect data (χ2 [df = 1] = 13, p = .25).

Table 1

Recoding of the eye fixation data
We created the ROF variable, Rate of Outcome Focusing, for each choice problem using datafrom the eye gaze recorder.

ROF = T(outcome) / [T(outcome) + T(probability)]

where T(outcome) is the total time to gaze at possible outcome words after the participant readsentences on the screen and T(probability) is the total time to gaze at probability words after theparticipant read sentences on the screen. The possible outcome words in the reflection-effectproblem for both frame conditions were ”20,000 yen,” ”40,000 yen,” and “no.” The probability
words in the problem for both frame conditions were “certainly” and “50%.” The possible
outcome words in the Asian disease problem for the positive frame condition were “200people,” “600 people,” and “no people;” those for the negative frame condition were “400people,” “600 people,” and “nobody.” The probability words in the Asian disease problem forboth frame conditions were “1/3” and “2/3.” Since the time required to acquire information
using eye fixations varies between 200 ms to 400 ms (Russo, 1978; Card, Moran, &, Newell,1983), we defined “gazing at a word” as gazing at the word for more than 200 ms. We defined
the total time to gaze at a word as the sum of time to gaze at the word longer than 200 ms.

11Hypothesis 1
Table 2 presents ROFs for each condition and each decision problem. Data frominstances where eye movement data indicated that participants did not read sentences of each
option to the end were eliminated from the following analyses. The ROF was larger under thenegative frame condition than under the positive frame condition for both the reflection-effectproblem and the Asian disease problem. The difference in ROF for the reflection-effectproblem was significant (t [26] = 2.19 p < .019), and the difference for the Asian diseaseproblem was marginally significant (t [22] =1.56 p =.067). These results support Hypothesis 1that predicted, based on the contingent focus hypothesis, that decision makers attend more topossible outcomes under negative frame conditions than under positive frame conditions.

Table 2
Hypothesis 2
In order to test Hypothesis 2, which was derived from the focusing hypothesis, we
compared ROF means from those who chose a risk-taking option with those who chose arisk-averse option. According to Hypothesis 2, the ROF for those who chose the risk-taking
option would be greater than the ROF for those who chose the risk-averse option. Table 3
presents data that support this prediction. The mean ROF for risk-taking participants was
greater than 50 % for both decision problems, but the mean ROF for risk-averse participants
was less than 50 %. The difference in ROF between risk-taking participants and risk-averse
participants was significant for the reflection-effect problem (t [26] = 3.02, p <.005), and was
marginally significant for the Asian disease problem (t [22] = 1.57, p =.065).

Table 312

Mediational Analysis
We performed a set of binary logit analyses of the choice data. The results of the logit
analyses for the reflection-effect problem are presented in Table 4, and those for the Asian
disease problem are presented in Table 5. Frame condition had a significant effect on choice forthe reflection-effect problem, if ROF was not included in the model (Table 4). The effect of anegative-frame dummy was significantly positive for the case without ROF, which implies thatthe probability that participants will select the risk-taking option is larger under negative frame
conditions than under positive frame conditions, supporting the reflection effect. However,Table 4 also shows that the effect of frame condition disappeared if ROF was included as an
explanatory variable, while the effect of ROF was significantly positive, which indicates thatthe probability of choosing the risk-taking option increases as ROF increases. Since we foundthat frame condition was related to ROF in the reflection-effect problem (Table 2), the logit
analyses tell us that the effect of frame condition on choice in the reflection-effect problem (thereflection effect) was indirectly mediated by ROF.
Similar results were obtained for the Asian disease problem. Table 5 shows that thenegative-frame dummy had a negative effect on the responses, suggesting that participants are
more likely to select a risk-taking option under negative frame conditions than under positive
frame conditions. Although this framing effect did not reach significance, the standardized
coefficient for the framing effect and its t-statistics decrease when ROF was included as an
explanatory variable. ROF had a marginally significant positive effect, compatible with our
Hypothesis 2 derived from the focusing hypothesis. Since frame condition was related to ROF
in the Asian disease problem (Table 3), the logit analyses imply that the effect of frame
condition on choices in the Asian disease problem (the framing effect) was indirectly mediated13

by ROF.

Discussion
The contingent focus model incorporates two basic hypotheses: the focusing hypothesis and thecontingent focus hypothesis. The focusing hypothesis states that risk attitudes depend on theextent to which a subject focuses on possible outcomes and probabilities. The contingent focus
hypothesis states that focusing on possible outcomes and probabilities, or attending to possible
outcomes and probabilities, is contingent on decisional contexts. These hypotheses have been
supported by experimental data and psychometric tests (Fujii & Takemura, 2000. 2001, 2003;
Takemura, Hu, & Fujii, 2001). In the past, however, attention to possible outcomes andprobabilities was not explicitly observed, so in the current study we used an eye gaze recorderto observe eye movement during decision making, which may be related to attention to possible
outcomes and probabilities.
The choice data from the reflection-effect problem supported the reflection effect; thatis, participants preferred a risk-taking option more strongly under negative frame conditions
than under positive frame conditions. The choice data from the Asian disease problem indicatedthat more participants preferred a risk-taking option under negative frame conditions than underpositive frame conditions, although the difference between frame conditions was not significant.
The effect of frame condition on choice in the reflection-effect problem disappeared, and theeffect of frame condition on choice in the Asian disease problem decreased when eye
movement data were included as a covariate. These results imply that the effects of frame
condition on choice, i.e., the framing effect and the reflection effect, may be mediated byattention.
In the current study, ROF (the ratio of total time to gaze at possible outcome words
compared to the total time to gaze at possible outcome words and probability words) was used14

to analyze the eye movement data. For both the reflection-effect problem and the Asian diseaseproblem, ROFs were larger under negative frame conditions than under positive frame
conditions, and participants with higher ROFs were more likely to choose a risk-taking option
than those with lower ROFs. The former result supports the contingent focus hypothesis and thelatter supports the focusing hypothesis.
Results overall support the contingent focus model’s explanation of the reflection andframing effects; the decision maker attends to possible outcomes more strongly under negative
frame conditions than under positive frame conditions, and those who attend strongly topossible outcomes are likely to prefer a risk-taking option. Decision makers thus preferrisk-taking options more strongly under negative frame conditions than under positive frame
conditions.
It should be noted that although predicted effects for the reflection-effect problem
achieved significance, predicted effects for the Asian disease problem did not. Lack ofsignificance for the framing effect in the Asian disease problem is inconsistent with the original
experiment by Tversky and Kahneman (1981); in this respect, the “elaboration effect” (Fujii &Takemura, 2003; Takemura, 1992, 1993, 1994b) may provide an explanation. The elaboration
effect refers to the inhibition of the framing effect when decision makers are asked to elaborate
their decision making process. Participants in the current experiment might have elaborated
their decision making process in the Asian disease problem more than did participants in theoriginal experiment by Tversky and Kahneman (1981) because those in the current study wererequested to respond while alone in a experimental room. Although the framing effect was not
significant for the Asian disease problem, both the effect of frame condition on eye movement
and the effect of eye movement on decisions were marginally significant in the direction
compatible with the predictions of the contingent focus model.

15

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possible outcome

probability

possible outcome

probability

Decision Maker

Decision Maker(under positive frame condition)(under negative frame condition)

Figure 1. Contingent focus model (Takemura, 1994a)

19

contingent focus hypothesis

contextual factors
including positive/negative
frame condition

focusing hypothesis

attention on possible
outcome and probability ina decision problem

risk attitude(positive/negative)

Figure 2. Two hypotheses within the contingent focus model: the contingent focus hypothesis
and the focusing hypothesis.

20

Table 1. Distributions of participants’ choices between the risk-taking and risk-averse options
under negative and positive frame conditions.

reflection-effect problem
Asian disease problem


negative
positive
negative
positive
frame condition frame condition
frame condition frame condition(n = 18)(n = 15)(n = 18)(n = 15) 
 
risk-taking

11(61.1%)

4(26.7%)

12(66.7%)

7(46.7%)

risk-averse

7(38.9%)

11(73.3%)

6(33.3%)

8(53.3%)



21

Table 2. ROF (rate of outcome focusing) under negative and positive frame conditions.

reflection-effect problem
Asian disease problem


negative
positive
negative
positive
frame condition frame condition
frame condition frame condition(n = 15)(n = 13)(n = 12)(n = 12) 
 
M†1

65.0%

47.2%

59.0%

44.6%

SEM†2

(5.1%)(6.5%)(5.6%)(7.4%)


†1
mean
†2

standard error of the mean

22

Table 3. ROF (rate of outcome focusing) of risk-taking participants and risk-averse
participants.

reflection-effect problem
Asian disease problem


risk-taking
risk-averse
risk-taking
risk-averse(n = 13)(n = 15)(n = 14)(n = 10) 
 
M†1

69.1%

46.0%

58.0%

43.2%

SEM†2

(5.3%)(5.4%)(6.5%)(6.5%)


†1
mean
†2

standard error of the mean

23

Table 4. Estimation of logit regression analysis of choice†1 of the reflection-effect problem withand without ROF as an explanatory variable.

without ROF
with ROF


†2
β
t
p
β††
t
p






constant

-0.45

-0.93

.175

3.47

1.90

.028

negative-frame dummy†3

1.46

1.93

.027

-0.64

-0.71

.240

6.22

2.15

.016

ROF


sample size
33
28
L (C)†4-18.64-5.15-14.09-3.14
L (B)†5
†1

The dependent variable of the logit regression analysis = 1 if the risk-taking option waschosen, = 0 if the risk-averse option was chosen. Therefore, if an explanatory variable whose
coefficient is positive increases, the probability of choosing the risk-taking option increases.
†2
standardized coefficient.
†3= 1 if negative-frame condition, = 0 otherwise.
†4
log-likelihood for the model only with constant.
†5
log-likelihood for the model with constant and the other variables.

24

Table 5. Estimation of logit regression analysis of choice†1 of the Asian disease problem withand without ROF as an explanatory variable.

without ROF
with ROF


†2
β
t
p
β
t
p






constant

-0.69

-1.39

.083

1.70

1.17

.120

negative-frame dummy†3

0.83

1.15

.125

0.51

0.54

.794

3.50

1.53

.063

ROF


sample size
33
24
L (C)†4-15.61-3.90-14.19-3.22
L (B)†5
†1

The dependent variable of the logit regression analysis = 1 if the risk-taking option waschosen, = 0 if the risk-averse option was chosen. Therefore, if an explanatory variable whose
coefficient is positive increases, the probability of choosing the risk-taking option increases.
†2
standardized coefficient.
†3= 1 if negative-frame condition, = 0 otherwise.
†4
log-likelihood for the model with constant only.
†5
log-likelihood for the model with constant and the other variables.

25