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Attitude towards risk
Journal of Economic Behavior and Organization 21 (1993) 91-98. North-Holland
Attitude towards risk An empirical demonstration
of context dependence
Mir Anjum AltaP University of Karachi, Karachi, Pakistan Received June 1989, final version received February 1992
Following the breakdown of the consensus that marked the theory of choice under uncertainty there is an increasing realization of the importance of context-specific considerations in explaining risk preferences. This paper provides experimental evidence that one such consideration, the relative level of success with which participants enter a game, has a significant influence on attitudes towards risk.
1. Intr~u~tion
This paper explores the extent to which risk preferences are context dependent. March (1988, p. 5) has remarked that ‘[R]isk aversion is generally assumed in the formal literature on decision theory, where it is typically defined as a concavity in the utility for monetary (or other) return. . . . Most studies indicate, however, that risk preference is not fixed, but depends on the context of a choice’. In his survey of the field, Machina (1987, p. 121) observed that the consensus that surrounded the theory of choice under uncertainty has broken down. While no unified model has emerged to integrate various challenges to the expected utility model of preferences over random prospects, there is general agreement that the theory has to incorporate more context-specific considerations. In this paper I use a natural experiment to study one such factor suggested by March (1988, p. 20), the level of success at which different participants enter a game, which can be taken as a proxy for their historical experience relevant to the gaming situation. The experimental evidence supports the claim that such context-dependent considerations have a marked impact on the risk preferences of the participants. Correspondence to: Dr. Mir Anjum Altaf, Visiting Associate Professor, Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill, Chapel Hill, NC 275994060, USA. *I would like to thank an anonymous referee for comments that led to significant improvement in the paper and Dr. Richard Day for encouraging suggestions. I would also like to acknowledge the help of Shanzi Ke in the statistical analysis. 0167-2681/93~~06.~ 0 199%Elsevier
Science Publishers B.V. All rights reserved
92
2. Experimental
M.A. Altaf, Attitude towards risk
setting
The setting was provided by a course in Research Methods’ which introduced various types of models used in the social sciences and the concepts of probability, expected value, and choice under risk. The students participated in a game which essentially offered a choice between two gambles of equal expected values but different variances in a specific setting.’ In order to elicit serious responses from the students, it was announced that a small percentage of the normalized scores obtained in the game would count towards the final grade in the course.3 For reasons that are specific to the Pakistani academic environment and not relevant for this paper, out of the fifteen students enrolled, four obtained a clear pass in the course while the remaining eleven were eligible for a make-up examination. This provided a natural opportunity to test for the possible impact of varying success levels on attitude towards risk. A game, similar to the one conducted before, was administered to the students at the end of the course. The game had a two-part prize: all fifteen students were competing for a monetary prize which was to be distributed in proportion to the scores obtained in the game whereas the eleven students would, in addition, have a small proportion of the normalized score added to their final course grade. Once again the purpose of the prize was to elicit a serious response from all the students. The objective of the experiment was to see if the different level of success of the two groups in the course had an impact on their attitude towards risk in the second game and how this attitude compared with that revealed in the first game which was held prior to the declaration of the course result.
3. Description
of the games
Game I offered the choice yields were specified as under:
between
two
gambles
whose
Gamble
Outcome
Yield
Coin Gamble
Heads Tails ‘2’ or ‘4 ‘l’, ‘3’, ‘5’ or ‘6
100 0 400 - 125
Die Gamble
outcomes
and
points points points points
‘The course was taught as part of a Masters level degree program in Applied Economics at the Applied Economics Research Centre, University of Karachi, in Karachi, Pakistan. ‘The game was part of a research design, not known to the students, to study the impact of context-dependent considerations on attitudes towards risk. 3The course was graded in a normal fashion on the basis of homework, a mid-term, and a final examination, all designed to evaluate mastery of the course contents. None of these had anything to do with the game mentioned above.
M.A. AltaJ Attitude towards risk
93
The objective of the game was to achieve a target score of 2,000 points in the least number of plays. Everyone started from an initial score of 300 and a maximum of 15 plays were allowed. In addition a player would forfeit participation in the game if his or her score fell below zero points. The final score was computed by dividing the target score by the number of plays. In Game II the choice was again between two gambles whose outcomes and yields were specified as under: Gamble
Outcome
Yield
Coin Gamble
Heads Tails ‘ 9 1 ‘3’ ‘6’ ‘2’, ‘4’ or ‘5’
100 0 600 60 - 360 0
Die Gamble
points points points points points points
The objective in the second game was to achieve a score of 1,750 in the least number of plays. Everyone started from an initial score of zero points and there was no limitation on the number of plays. In addition, a player would forfeit participation in the game if his or her score fell below zero points. The final score was computed by dividing the target score by the number of plays4 In each game both the gambles had equivalent expected values of 50 points while the die gamble had the higher variance. The indicator of risk preference used in the analysis was the proportion of total plays in which the die gamble was chosen: the higher the value of this indicator the higher the value of the risk preference revealed by an individual player.5
4. Results Performance in the course assigned the fifteen students enrolled into two distinct groups: the four students who passed formed one group (Group A) and the eleven who required a make-up examination formed the second group (Group B). The details of how each student played Games I and II (total plays, die throws, coin tosses, total score) are presented in the appendix. The above information is used for a number of comparisons of the risk preferences of the two groups as revealed in the two games. To mitigate for the small sample size multiple observations from each student are used. This 40n each play the participants wrote down their choice of gamble on a score sheet. A research assistant played out the appropriate gamble and recorded the outcome, the yield and the cumulative score on the score sheet. ‘While there were differences in the two games related to starting points, target values and limitations on the number of plays, there is no reason to suppose that these had a systematic effect on the risk preferences of the two groups in the target population.
94
M.A. AltaL Attitude Table Risk preferences
towards risk
1
revealed
in Game
1.
Group
Total number of plays
No. of plays on which die gamble was chosen
Risk preference indicator (% of die throws)
A B
59 160
20 84
33.9 52.5
type of repeated measures design is quite standard in educational research. However, since repeated plays by the same student are not independent of each other, an appropriate non-parametric test has to be used for statistical analysis of the data. We use the V test (a Rank-Sum test based on the Wilcoxon score) as the non-parametric alternative to the two-sample t test [Freund and Walpole (1987)]. Without having to assume that the two populations sampled have normal distributions, we can test the null hypothesis that we are sampling identical continuous populations.6 All the participants entered Game I (played prior to the declaration of the course results) with their risk preferences defined by factors exogenous to the game. For our purposes these could be considered given risk preferences. The results, in terms of the risk preference indicator defined earlier (proportion of die gambles in the total number of plays), are summarized for the two groups (defined subsequent to this game) in table 1. The table shows that Group B is more risk preferring on the average. However, using the individual data in the appendix the value of the V statistic is 10 while the critical value at the 0.05 level of significance is 6. Thus the null hypothesis that the two groups have the same risk preference cannot be rejected at the 5% level. The data in the appendix can also be used to show that the performance of the two groups in Game I was similar on the average. The average score per play was 95.3 for Group A and 82.7 for Group B. Although the participants therefore appear to have entered Game II with similar performances and similar risk preferences in Game I, Group A had achieved a higher success level in the course as a whole. What is of interest is to see if this difference prior to entering Game II affected the risk behavior of the players and, if so, in what way. The results of Game II are summarized in table 2. The null hypothesis that the risk preferences of the two groups in Game II are the same is overwhelmingly rejected at the 0.05 level of significance (V statistic= 1; critical value of V =6). Not only are the risk preferences statistically different, it is striking that Group B which was previously more 6The test is conducted
using the SAS non-parametric
test procedure
PROC
NPARIWAY.
M.A. Altaf, Attitude towards risk
95
Table 2 Risk preferences
revealed
in Game
II.
Group
Total number of plays
No. of plays on which die gamble was chosen
Risk preference indicator (% of die throws)
A B
79 439
37 48
46.8 10.9
Table 3 Risk preferences
of Group
A in Games
I and II.
Game
Total number of plays
No. of plays on which die gamble was chosen
Risk preference indicator (‘A of die throws)
I II
59 79
20 37
33.9 46.8
Table 4 Risk preferences
of Group
B in Games
I and II.
Game
Total number of plays
No.-Lf plays on which die gamble was chosen
Risk preference indicator (‘A of die throws)
I II
160 439
84 48
52.5 10.9
risk preferring than Group A is now much more risk averse than Group A. The switch is quite dramatic. The interesting question to investigate is what caused the switch in risk preference? We can approach this question by examining the stability of risk preferences of the two groups over the two games. Tables 3 and 4 summarize the relevant information. The null hypothesis that there is no difference in the risk preference of Group A members over the two games cannot be rejected at the 0.05 level of significance (U statistic = 7; critical value = 0). The null hypothesis that there is no difference in the risk preference of Group B members over the two games is overwhelmingly rejected at the 0.05 level of significance (U statistic = 8.5; critical value = 30). The above results clearly suggest that those who entered Game II at a higher level of success (Group A) did not change their risk behavior while those who entered at a lower level of success (Group B) became very risk averse. The latter group had started out as being more risk preferring than the former but ended up as being more risk averse in relative terms. While
96
M.A. Altaf, Attitude towards risk
no generalizations are meant to be suggested regarding the specific direction of behavioral change in specific situations there is no doubt that a context effect exists and is significant. While it is not directly related to the central argument of this paper, the data do allow us to infer the impact of the swing in risk preference on relative performance in the games. For this we can use the average score per play as an indicator of performance. The value of the indicator for Group A in Game I was 95.3 and in Game II was 88.6. The corresponding values for Group B were 82.7 and 43.9, respectively. As mentioned earlier, there is little difference in the performance of the two groups in Game I (U statistic= 17; critical value=6). However, the same is not true for Game II (V statistic=OS; critical value = 6). In this specific situation the performance of the participants who entered Game II at a higher level of success remained stable (V statistic = 7; critical value = 0) while that of those at a lower level of success showed a marked deterioration (V statistic = 19; critical value = 30); the average score per play dropped from 82.7 to 43.9. Again, no generalizations are intended but the evidence suggests that context-dependence can affect behavior and thereby performance. 5. Discussion In evaluating the above results it should be recognized that the study is a ‘quasi-experiment’ since the condition which assigns the students to one of two groups is not the result of random assignment, but rather actual performance in the course. The term ‘quasi-experiment’ refers to a research design which has all the attributes of a true experiment - treatments, treated and untreated units, and outcome measures - but does ‘not use random assignment to create the comparisons from which the treatment-caused change is inferred’ [Cook and Campbell (1979, p. 6)]. Natural experiments of the type described in this study are generally quasiexperiments. Because full experimental control is lacking, it is imperative for internal validity to be aware of which specific variables the research design fails to control. For example, in this study it would be reasonable to ask if some other variable, related to performance in the course, could cause the observed changes. Were those who passed the course brighter, better-off, understood the game better, etc. and therefore performed differently in the second game? The experiment in this study conforms to the ‘nonequivalent group design’, one of twelve research designs discussed in Campbell and Stanley (1963). In such a design (‘one of the most widespread experimental designs in educational research’ [p. 471) two groups (termed experimental and control groups) are compared to each other. If the two groups are similar on tests before the experiment (pre-test), the criterion for a valid control group is met.
M.A. AltuJ; Attitude towards risk
97
The groups are tested again after the intervention (post-test). The difference between the post-test results of the two groups is assumed to be the impact of the stimulus in the intervention. Careful examination of the two groups is of utmost importance: ‘the more similar the experimental and control groups are . . . and the more this similarity is confirmed . . . by pre-test, the more effective this control becomes’ (pp. 47-48). In this study, the risk preferences and performances of the two groups were statistically undifferentiated in Game I (the p&test). Thus, even if it were a fact that members of Group A were brighter than members of Group B (because they performed better in the course), this does not seem to have a bearing on the relative performance in the pre-test. This check, added to the fact that the games were of a simple gambling nature and therefore not highly intelligence dependent, lends credibility to the validity of the experiment. In addition, the preference swing was so dramatic that it is difficult to attribute the conclusion to anything else except the intervening effect under consideration. While this demonstration of context effect is interesting, it is not radically new. However, in general, research in this field has shown how structural features of the games themselves like response mode effects, framing, targets, reference points and anchoring effects [Kahneman and Tversky (1979), Machina (1987)] modify risk behavior. It has also been argued in the context of sequential games that performance in one segment of the sequence can affect behaviour in a subsequent segment. ‘Playing conservatively when losing, liberally when winning’ is an example of this type of context effect [Markowitz (1952, p. 156)J. The experiment described in this study shows that context-dependence has a wider ambit than recognized in these early studies in the sense that intervening events unrelated to the games themselves can have a significant impact on risk behavior. In this, the work is similar to that which shows the effect of variables like ‘mood’ on risk-taking behavior. In a fully randomized experiment, Arkes, Herren and Isen (1988) examined the influence of positive ‘affect’ on risk-taking behavior. Positive feelings were induced in an experimental group by a free gift of candy. Their results showed that positive feelings can foster both risk-prone behavior and riskaverse behavior. ‘When a positive-affect subject faces a risk situation in which the potential loss is emphasized, the subject demonstrates risk aversion; when the potential loss is minimized, then risk proneness is observed’ (p. 181). Our experiment can be interpreted in this theoretical framework. It can be argued tl?at failure to pass the course outright induced a negative affect in members of Group B (the experimental group) who were thereby subject to anxiety before playing Game II. No such anxiety was faced by members of Group A (the control group). The negative affect (anxiety) led to extreme risk
M.A. AltaA Attitude towards risk
98
aversion by members of the experimental group when faced with a situation of potential loss. The behavior of members of the control group remained unchanged. Appendix Data: Details of how individual candidates played games I and II. Game
number
I Number” of candidates
Coin tosses
II Die throws
Total plays
Total score
Coin tosses
Die throws
Total plays
Total score
1 2 3 4
11 12 10 6
3 3 5 9
14 15 15 15
2.200 1,575 600 1,250
7 12 9 14
10 11 4 12
17 23 13 26
1.750 1,750 1,750 1,750
5 6 7 8 9 10 11 12 13 14 15
10 11 2 9 5 1 7 11 0 6 8
5 4 10 6 8 8 8 4 15 9 7
15 15 12 15 13 15 15 15 15 15 15
1,025 925 2,200 500 2,225 750 1,175 1,025 1,050 950 1,400
23 22 51 30 28 28 65 27 41 44 32
13 4 7 6 1 0 11 1 1 2 2
36 26 58 36 29 28 76 28 42 46 34
1,750 1,750 1,750 1,750 1,750 1,750 1,750 1,750 1,750 1,750 1,750
“Candidates belonging to Group candidates belong to Group B.
A have
been
numbered
1 through
4. The
remaining
References Arkes, H.R., L.T. Herren and A.M. Isen, 1988, The role of potential loss in the influence of affect on risk-taking behavior, Organization Behavior and Human Decision Processes 42, 181-193. Campbell, D.T. and J.C. Stanley, 1963, Experimental and quasi-experimental designs for research (Rand McNally, Chicago, IL). Cook, T. and D. Campbell, 1979, Quasi-experimentation: Design and analysis for field settings (Houghton Miflin, Boston, MA). Freund, J.E. and R.E. Walpole, 1987, Mathematical statistics (Prentice-Hall, Englewood, NJ). Kahneman, D. and A. Tversky, 1979, Prospect theory: An analysis of decision under risk, Econometrica 47, 263-291. Machina, Mark J., 1987, Choice under uncertainty: Problems solved and unsolved, Journal of Economic Perspectives 1, 121-154. March, James G., 1988, Variable risk preferences and adaptive aspirations, Journal of Economic Behavior and Organization 9, 3-24. Markowitz, H., 1952, The utility of wealth, Journal of Political Economy 60, 151-158.
Attitude towards risk An empirical demonstration
of context dependence
Mir Anjum AltaP University of Karachi, Karachi, Pakistan Received June 1989, final version received February 1992
Following the breakdown of the consensus that marked the theory of choice under uncertainty there is an increasing realization of the importance of context-specific considerations in explaining risk preferences. This paper provides experimental evidence that one such consideration, the relative level of success with which participants enter a game, has a significant influence on attitudes towards risk.
1. Intr~u~tion
This paper explores the extent to which risk preferences are context dependent. March (1988, p. 5) has remarked that ‘[R]isk aversion is generally assumed in the formal literature on decision theory, where it is typically defined as a concavity in the utility for monetary (or other) return. . . . Most studies indicate, however, that risk preference is not fixed, but depends on the context of a choice’. In his survey of the field, Machina (1987, p. 121) observed that the consensus that surrounded the theory of choice under uncertainty has broken down. While no unified model has emerged to integrate various challenges to the expected utility model of preferences over random prospects, there is general agreement that the theory has to incorporate more context-specific considerations. In this paper I use a natural experiment to study one such factor suggested by March (1988, p. 20), the level of success at which different participants enter a game, which can be taken as a proxy for their historical experience relevant to the gaming situation. The experimental evidence supports the claim that such context-dependent considerations have a marked impact on the risk preferences of the participants. Correspondence to: Dr. Mir Anjum Altaf, Visiting Associate Professor, Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill, Chapel Hill, NC 275994060, USA. *I would like to thank an anonymous referee for comments that led to significant improvement in the paper and Dr. Richard Day for encouraging suggestions. I would also like to acknowledge the help of Shanzi Ke in the statistical analysis. 0167-2681/93~~06.~ 0 199%Elsevier
Science Publishers B.V. All rights reserved
92
2. Experimental
M.A. Altaf, Attitude towards risk
setting
The setting was provided by a course in Research Methods’ which introduced various types of models used in the social sciences and the concepts of probability, expected value, and choice under risk. The students participated in a game which essentially offered a choice between two gambles of equal expected values but different variances in a specific setting.’ In order to elicit serious responses from the students, it was announced that a small percentage of the normalized scores obtained in the game would count towards the final grade in the course.3 For reasons that are specific to the Pakistani academic environment and not relevant for this paper, out of the fifteen students enrolled, four obtained a clear pass in the course while the remaining eleven were eligible for a make-up examination. This provided a natural opportunity to test for the possible impact of varying success levels on attitude towards risk. A game, similar to the one conducted before, was administered to the students at the end of the course. The game had a two-part prize: all fifteen students were competing for a monetary prize which was to be distributed in proportion to the scores obtained in the game whereas the eleven students would, in addition, have a small proportion of the normalized score added to their final course grade. Once again the purpose of the prize was to elicit a serious response from all the students. The objective of the experiment was to see if the different level of success of the two groups in the course had an impact on their attitude towards risk in the second game and how this attitude compared with that revealed in the first game which was held prior to the declaration of the course result.
3. Description
of the games
Game I offered the choice yields were specified as under:
between
two
gambles
whose
Gamble
Outcome
Yield
Coin Gamble
Heads Tails ‘2’ or ‘4 ‘l’, ‘3’, ‘5’ or ‘6
100 0 400 - 125
Die Gamble
outcomes
and
points points points points
‘The course was taught as part of a Masters level degree program in Applied Economics at the Applied Economics Research Centre, University of Karachi, in Karachi, Pakistan. ‘The game was part of a research design, not known to the students, to study the impact of context-dependent considerations on attitudes towards risk. 3The course was graded in a normal fashion on the basis of homework, a mid-term, and a final examination, all designed to evaluate mastery of the course contents. None of these had anything to do with the game mentioned above.
M.A. AltaJ Attitude towards risk
93
The objective of the game was to achieve a target score of 2,000 points in the least number of plays. Everyone started from an initial score of 300 and a maximum of 15 plays were allowed. In addition a player would forfeit participation in the game if his or her score fell below zero points. The final score was computed by dividing the target score by the number of plays. In Game II the choice was again between two gambles whose outcomes and yields were specified as under: Gamble
Outcome
Yield
Coin Gamble
Heads Tails ‘ 9 1 ‘3’ ‘6’ ‘2’, ‘4’ or ‘5’
100 0 600 60 - 360 0
Die Gamble
points points points points points points
The objective in the second game was to achieve a score of 1,750 in the least number of plays. Everyone started from an initial score of zero points and there was no limitation on the number of plays. In addition, a player would forfeit participation in the game if his or her score fell below zero points. The final score was computed by dividing the target score by the number of plays4 In each game both the gambles had equivalent expected values of 50 points while the die gamble had the higher variance. The indicator of risk preference used in the analysis was the proportion of total plays in which the die gamble was chosen: the higher the value of this indicator the higher the value of the risk preference revealed by an individual player.5
4. Results Performance in the course assigned the fifteen students enrolled into two distinct groups: the four students who passed formed one group (Group A) and the eleven who required a make-up examination formed the second group (Group B). The details of how each student played Games I and II (total plays, die throws, coin tosses, total score) are presented in the appendix. The above information is used for a number of comparisons of the risk preferences of the two groups as revealed in the two games. To mitigate for the small sample size multiple observations from each student are used. This 40n each play the participants wrote down their choice of gamble on a score sheet. A research assistant played out the appropriate gamble and recorded the outcome, the yield and the cumulative score on the score sheet. ‘While there were differences in the two games related to starting points, target values and limitations on the number of plays, there is no reason to suppose that these had a systematic effect on the risk preferences of the two groups in the target population.
94
M.A. AltaL Attitude Table Risk preferences
towards risk
1
revealed
in Game
1.
Group
Total number of plays
No. of plays on which die gamble was chosen
Risk preference indicator (% of die throws)
A B
59 160
20 84
33.9 52.5
type of repeated measures design is quite standard in educational research. However, since repeated plays by the same student are not independent of each other, an appropriate non-parametric test has to be used for statistical analysis of the data. We use the V test (a Rank-Sum test based on the Wilcoxon score) as the non-parametric alternative to the two-sample t test [Freund and Walpole (1987)]. Without having to assume that the two populations sampled have normal distributions, we can test the null hypothesis that we are sampling identical continuous populations.6 All the participants entered Game I (played prior to the declaration of the course results) with their risk preferences defined by factors exogenous to the game. For our purposes these could be considered given risk preferences. The results, in terms of the risk preference indicator defined earlier (proportion of die gambles in the total number of plays), are summarized for the two groups (defined subsequent to this game) in table 1. The table shows that Group B is more risk preferring on the average. However, using the individual data in the appendix the value of the V statistic is 10 while the critical value at the 0.05 level of significance is 6. Thus the null hypothesis that the two groups have the same risk preference cannot be rejected at the 5% level. The data in the appendix can also be used to show that the performance of the two groups in Game I was similar on the average. The average score per play was 95.3 for Group A and 82.7 for Group B. Although the participants therefore appear to have entered Game II with similar performances and similar risk preferences in Game I, Group A had achieved a higher success level in the course as a whole. What is of interest is to see if this difference prior to entering Game II affected the risk behavior of the players and, if so, in what way. The results of Game II are summarized in table 2. The null hypothesis that the risk preferences of the two groups in Game II are the same is overwhelmingly rejected at the 0.05 level of significance (V statistic= 1; critical value of V =6). Not only are the risk preferences statistically different, it is striking that Group B which was previously more 6The test is conducted
using the SAS non-parametric
test procedure
PROC
NPARIWAY.
M.A. Altaf, Attitude towards risk
95
Table 2 Risk preferences
revealed
in Game
II.
Group
Total number of plays
No. of plays on which die gamble was chosen
Risk preference indicator (% of die throws)
A B
79 439
37 48
46.8 10.9
Table 3 Risk preferences
of Group
A in Games
I and II.
Game
Total number of plays
No. of plays on which die gamble was chosen
Risk preference indicator (‘A of die throws)
I II
59 79
20 37
33.9 46.8
Table 4 Risk preferences
of Group
B in Games
I and II.
Game
Total number of plays
No.-Lf plays on which die gamble was chosen
Risk preference indicator (‘A of die throws)
I II
160 439
84 48
52.5 10.9
risk preferring than Group A is now much more risk averse than Group A. The switch is quite dramatic. The interesting question to investigate is what caused the switch in risk preference? We can approach this question by examining the stability of risk preferences of the two groups over the two games. Tables 3 and 4 summarize the relevant information. The null hypothesis that there is no difference in the risk preference of Group A members over the two games cannot be rejected at the 0.05 level of significance (U statistic = 7; critical value = 0). The null hypothesis that there is no difference in the risk preference of Group B members over the two games is overwhelmingly rejected at the 0.05 level of significance (U statistic = 8.5; critical value = 30). The above results clearly suggest that those who entered Game II at a higher level of success (Group A) did not change their risk behavior while those who entered at a lower level of success (Group B) became very risk averse. The latter group had started out as being more risk preferring than the former but ended up as being more risk averse in relative terms. While
96
M.A. Altaf, Attitude towards risk
no generalizations are meant to be suggested regarding the specific direction of behavioral change in specific situations there is no doubt that a context effect exists and is significant. While it is not directly related to the central argument of this paper, the data do allow us to infer the impact of the swing in risk preference on relative performance in the games. For this we can use the average score per play as an indicator of performance. The value of the indicator for Group A in Game I was 95.3 and in Game II was 88.6. The corresponding values for Group B were 82.7 and 43.9, respectively. As mentioned earlier, there is little difference in the performance of the two groups in Game I (U statistic= 17; critical value=6). However, the same is not true for Game II (V statistic=OS; critical value = 6). In this specific situation the performance of the participants who entered Game II at a higher level of success remained stable (V statistic = 7; critical value = 0) while that of those at a lower level of success showed a marked deterioration (V statistic = 19; critical value = 30); the average score per play dropped from 82.7 to 43.9. Again, no generalizations are intended but the evidence suggests that context-dependence can affect behavior and thereby performance. 5. Discussion In evaluating the above results it should be recognized that the study is a ‘quasi-experiment’ since the condition which assigns the students to one of two groups is not the result of random assignment, but rather actual performance in the course. The term ‘quasi-experiment’ refers to a research design which has all the attributes of a true experiment - treatments, treated and untreated units, and outcome measures - but does ‘not use random assignment to create the comparisons from which the treatment-caused change is inferred’ [Cook and Campbell (1979, p. 6)]. Natural experiments of the type described in this study are generally quasiexperiments. Because full experimental control is lacking, it is imperative for internal validity to be aware of which specific variables the research design fails to control. For example, in this study it would be reasonable to ask if some other variable, related to performance in the course, could cause the observed changes. Were those who passed the course brighter, better-off, understood the game better, etc. and therefore performed differently in the second game? The experiment in this study conforms to the ‘nonequivalent group design’, one of twelve research designs discussed in Campbell and Stanley (1963). In such a design (‘one of the most widespread experimental designs in educational research’ [p. 471) two groups (termed experimental and control groups) are compared to each other. If the two groups are similar on tests before the experiment (pre-test), the criterion for a valid control group is met.
M.A. AltuJ; Attitude towards risk
97
The groups are tested again after the intervention (post-test). The difference between the post-test results of the two groups is assumed to be the impact of the stimulus in the intervention. Careful examination of the two groups is of utmost importance: ‘the more similar the experimental and control groups are . . . and the more this similarity is confirmed . . . by pre-test, the more effective this control becomes’ (pp. 47-48). In this study, the risk preferences and performances of the two groups were statistically undifferentiated in Game I (the p&test). Thus, even if it were a fact that members of Group A were brighter than members of Group B (because they performed better in the course), this does not seem to have a bearing on the relative performance in the pre-test. This check, added to the fact that the games were of a simple gambling nature and therefore not highly intelligence dependent, lends credibility to the validity of the experiment. In addition, the preference swing was so dramatic that it is difficult to attribute the conclusion to anything else except the intervening effect under consideration. While this demonstration of context effect is interesting, it is not radically new. However, in general, research in this field has shown how structural features of the games themselves like response mode effects, framing, targets, reference points and anchoring effects [Kahneman and Tversky (1979), Machina (1987)] modify risk behavior. It has also been argued in the context of sequential games that performance in one segment of the sequence can affect behaviour in a subsequent segment. ‘Playing conservatively when losing, liberally when winning’ is an example of this type of context effect [Markowitz (1952, p. 156)J. The experiment described in this study shows that context-dependence has a wider ambit than recognized in these early studies in the sense that intervening events unrelated to the games themselves can have a significant impact on risk behavior. In this, the work is similar to that which shows the effect of variables like ‘mood’ on risk-taking behavior. In a fully randomized experiment, Arkes, Herren and Isen (1988) examined the influence of positive ‘affect’ on risk-taking behavior. Positive feelings were induced in an experimental group by a free gift of candy. Their results showed that positive feelings can foster both risk-prone behavior and riskaverse behavior. ‘When a positive-affect subject faces a risk situation in which the potential loss is emphasized, the subject demonstrates risk aversion; when the potential loss is minimized, then risk proneness is observed’ (p. 181). Our experiment can be interpreted in this theoretical framework. It can be argued tl?at failure to pass the course outright induced a negative affect in members of Group B (the experimental group) who were thereby subject to anxiety before playing Game II. No such anxiety was faced by members of Group A (the control group). The negative affect (anxiety) led to extreme risk
M.A. AltaA Attitude towards risk
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aversion by members of the experimental group when faced with a situation of potential loss. The behavior of members of the control group remained unchanged. Appendix Data: Details of how individual candidates played games I and II. Game
number
I Number” of candidates
Coin tosses
II Die throws
Total plays
Total score
Coin tosses
Die throws
Total plays
Total score
1 2 3 4
11 12 10 6
3 3 5 9
14 15 15 15
2.200 1,575 600 1,250
7 12 9 14
10 11 4 12
17 23 13 26
1.750 1,750 1,750 1,750
5 6 7 8 9 10 11 12 13 14 15
10 11 2 9 5 1 7 11 0 6 8
5 4 10 6 8 8 8 4 15 9 7
15 15 12 15 13 15 15 15 15 15 15
1,025 925 2,200 500 2,225 750 1,175 1,025 1,050 950 1,400
23 22 51 30 28 28 65 27 41 44 32
13 4 7 6 1 0 11 1 1 2 2
36 26 58 36 29 28 76 28 42 46 34
1,750 1,750 1,750 1,750 1,750 1,750 1,750 1,750 1,750 1,750 1,750
“Candidates belonging to Group candidates belong to Group B.
A have
been
numbered
1 through
4. The
remaining
References Arkes, H.R., L.T. Herren and A.M. Isen, 1988, The role of potential loss in the influence of affect on risk-taking behavior, Organization Behavior and Human Decision Processes 42, 181-193. Campbell, D.T. and J.C. Stanley, 1963, Experimental and quasi-experimental designs for research (Rand McNally, Chicago, IL). Cook, T. and D. Campbell, 1979, Quasi-experimentation: Design and analysis for field settings (Houghton Miflin, Boston, MA). Freund, J.E. and R.E. Walpole, 1987, Mathematical statistics (Prentice-Hall, Englewood, NJ). Kahneman, D. and A. Tversky, 1979, Prospect theory: An analysis of decision under risk, Econometrica 47, 263-291. Machina, Mark J., 1987, Choice under uncertainty: Problems solved and unsolved, Journal of Economic Perspectives 1, 121-154. March, James G., 1988, Variable risk preferences and adaptive aspirations, Journal of Economic Behavior and Organization 9, 3-24. Markowitz, H., 1952, The utility of wealth, Journal of Political Economy 60, 151-158.