Competition, Superstition and the Illusion of Control
JEFFREY RUDSKI Muhlenberg College
The effects ,of reinforcement schedule and competition on generating superstitious behaviors and beliefs were examined in 72 people. Superstition was induced by hav- ing participants respond to turn on a tone under a concurrent 2-lever Variable Interval (VI) Extinction (EXT) schedule. During the session, stimulus lights would occasion- ally be illuminated, although they did not signal any change in contingency. Attribut- ing importance to the inactive lever, a pattern of switching between levers, or to the illumination of the lights were considered to be superstitious beliefs. Participants were either run alone or in pairs, and manipulation of the reinforcement schedule resulted in groups which were matched in probability of reinforcement, as well as in groups which were mismatched. Reinforcement schedule (VI 30” versus VI 60”) and com- petitive situation did not affect degree of superstitious belief, except when people were placed in a “winning” condition. However, Superstition was associated with participants’ belief in improved future performance and with participants’ perceived skill relative to their opponents. Results are discussed in terms of relationships be- tween superstition, the illusion of control, and self-efficacy. Differences between ex- perimentally-induced and commonly held superstitions are also discussed.
In operant behavior, an instrumental response is strengthened when it is followed by a desired consequence. Occasionally, the desired outcomes occur independently of actual responding, yet people still attribute a causal relationship between the two. Such an attribution can be called a superstitious belief. The resultant behavior, superstitious responding, can be defined as those instances in which responses are maintained through accidental correlation with reinforcement.
In the first thorough investigation of this phenomenon, Skinner (1948) provided food reinforcement to pigeons every 15 seconds, completely independently of their behavior. After only a few minutes the pigeons developed distinctive stereotyped rituals; one walked around in circles, another rubbed his face on the floor, etc. Skinner explained these idiosyncratic behaviors as resulting from the adventitious reinforce- ment of responses that were temporally contiguous with the presentation of the grain. Superstitious rituals resulting from similar schedules has also been reported in children (Wagner and Morris, 1987) and adults @no, 1987).
Superstitions can also arise in response-dependent situations, and are often seen when reinforcement is dependent upon behavior with the accidental correlation of one response for subsequent reinforcements for other responses (Catania & Cutts, 1963). In Catania and Cutts’ study, superstitious responding in humans was examined using a two-button situation. Presses on one button were reinforced with points on a Variable Interval (VI) 30” schedule (i.e., on the average of every 30 ,” a reinforcer was sched-
Current Psychology: Developmental l Leurning l Personality l Social Spring 200 1, Vol. 20, No. 1, 68-84.
uled and produced by the subsequent response) while presses on the other button had no consequences. This second button can be thought of as presenting an extinction (EXT) contingency. Despite the fact that reinforcement was independent of any re- sponding on the second button, responding on it was observed throughout sessions. Moreover, participants’ responding often revealed stereotyped patterns in their re- sponses across both buttons. The authors reported that this was likely due to presses on the inactive button frequently being followed by reinforced presses on the active button.
A qualitatively different type of superstition, termed. a sensory superstition, involves giving special importance to some feature of our surroundings (Vyse, 1997). What appears to be a salient aspect of the environment may turn out to be irrelevant, but gain associative meaning due to its temporal contiguity with reinforcement. For example, Morse & Skinner (1957) rewarded pigeons on a very lean reinforcement schedule (Le., VI 30’). At the start of the session, a blue light was illuminated. Occasionally, the blue light was changed to orange for 4-minute periods. Even though the reinforcement schedule was the same under the two colored lights, the pigeon treated them differ- ently, often altering its rate of responding when the orange light was illuminated. Starr & Staddon (1982) extended these results using several different colored lights and different reinforcement schedules. Once again, the pigeons responded with different rates in the presence of different colored lights, even though the lights did not set the occasion for a difference in the contingency. Similar findings with human participants have also been reported. Ono (1987) had participants respond under Fixed-or Vari- able-Time schedules (unlike Interval schedules, reinforcement is not contingent upon a response in Time schedules and reinfocers are delivered when scheduled). During the session, three different signal-light colors were presented in a random sequence, but matched for total number of presentations and duration. Changing of the colors had no bearing on the reinforcement schedule. Ono reported that 30 percent of his participants significantly altered their responding in a systematic fashion under these different stimulus conditions.
While many studies have shown that superstitions can develop through adventitious reinforcement, fewer studies have examined various factors that may make it more or less likely that superstitious behavior or beliefs will develop. One variable that has received some attention is reinforcement schedule. For example, Vyse (199 1) reported that superstitious behavior increased when response requirements changed from a Fixed Ratio 1 to a Random Ratio 2 reinforcement schedule. Ono (1987) showed that more superstitious behavior occurred when people received points under a fixed time 30” schedule than under a fixed time 60” schedule. Finally, Rudski et al. (1999) demonstrated that the likelihood of people in generating fallacious rules linking spe- cific responses to random letter-digit combinations was positively related to probabil- ity of a desired outcome.
In a separate tradition of research into superstition, questionnaires containing vari- ous superstitious beliefs (e.g., belief in the occult or paranormal phenomena) are administered to people. Many factors have been examined in conjunction with these superstitious beliefs, typically revolving around individual or group differences. For example, people’s levels of agreement with various superstitious beliefs are reportedly
associated with having an external locus of control (Tobacyk & Milford, 1983), lower self-efficacy (Toabcyk & Schrader, 199 l), and a higher degree of hypnotic susceptibil- ity (Wagner & Ratzenberg, 1987). Among the group differences that have been exam- ined, it has been claimed that traditionally superstitious groups include athletes, gam- biers, soldiers, financial investors, and college students (Vyse, 1997). One element all of these groups have in common is the notion of competition. Some individuals win and others lose, and the majority of participants judge their performance relative to others. Despite this body of evidence, the direct effects of competition on experimen- tally-induced superstitious behavior or beliefs have received little attention.
The current study employed Catania and Cutts’ concurrent two-button VI EXT procedure (although the VI component was changed to a Random Interval, or RI schedule. In VI schedules, the possible intervals after which reinforcement is sched- uled are pre-programmed. In RI schedules they occur probabilistically). At specified intervals, a bank of lights was illuminated but the contingency was not altered. Super- stitious beliefs relating to the importance of the inactive lever and the significance of lights turning on and off over the course of sessions (i.e., sensory superstitions) were examined as a function of different reinforcement schedules on the active (VI) lever. Finally, in order to see if competition altered superstitious beliefs or behaviors, partici- pants were placed in cumpetitive or non-competitive situations, some of which guaran- teed “winners” and others “losers.”
METHODS
Participants
Seventy-two undergraduate students were used in the current study. All students attended a Division III college (i.e., no students attended college based on an athletic scholarship).
Apparatus
Two standard operant levers were mounted in a box, one on the right side and one on the left. Adjacent to the left lever was a bank of 3 stimulus lights (Model # El l-02, Coulboum Instruments, Allentown, PA) which were illuminated for the 4th through 6th and 10th through 12th minutes of the session. Situated midway between the levers was a “beeper” that generated either a 3000 or 6000 Hz (Model # E12-02, Coulbourn Instruments, Allentown, PA) for 1 second. Sessions were controlled and data were recorded using an IBM personal computer running Coulbourn L2T2 software.
Procedure
Participants (n = 12) were randomly assigned to one of six conditions, differing according to reinforcement schedule and competitive situation. Under all conditions responding on the left lever was controlled by an extinction schedule (i.e., responding
10. I have at least one ‘lucky’ object (e.g., charm, pen, article of clothing) which I occasionally use to bring me better luck?
11. I have a lucky number?
Yes No
Yes No
12. I occasionally refrain from saying something so as not to ‘jinx’ myself.
1 often
2 3 4 5 6 7 occasionally never
13. If I were to buy lottery tickets, I’m more likely to select numbers of personal significance than to let the computer randomly select the numbers for me.
14. Please Circle all that apply to you: College Varsity Athlete College Intramural Athlete
High School Varsity Athlete None
had no consequence). All participants were instructed that their task was to “figure out how lever pressing is related to turning on the tone.” Participants in the Alone-30 group had their responding on the right lever reinforced according to a random interval (RI) 30” schedule (i.e., on the average of every 30 seconds, a tone was scheduled to occur following the next press of the right lever). Participants in the Alone-60 group had their right-lever responses reinforced under a RI 60” schedule. For the other conditions, participants were run in pairs. Participants in the “Pair” group were told that they were to independently discover the rule, and their responses were reinforced under a RI 30” schedule. Participants in the “Opponent” group responded under a similar schedule. However, their instructions differed in that they were told that they were competing with each other to see who could best find out and approximate the “rule .” In the other two groups, participants were run concurrently on unequal rein- forcement schedules. Participants’ responses in the “Winner” group were reinforced under a RI 30” schedule while their opponents’ responses in the “Loser” group were reinforced under a RI 60” schedule. The discrepancy between these schedules results in the “Winners” receiving on average twice as many reinforcers as the “Losers.”
Belief in lights signaling a change in contingencies 40
Adoption of at least one of the above beliefs 74
After spending 12 minutes on the free-operant task, participants were asked to fill out a brief survey (see Appendix). The survey contained a Likert-type question that asked about belief in improved future performance (1 to 7 scale, 1 = not better at all, 4 = somewhat better, 7 = much better), and questions related to beliefs in the importance of each lever in producing points (1 to 9 scale, 1 = strongly disagree, 5 = undecided, 9 = strongly agree) under the lights-on and lights-off conditions. Two questions (1 to 9 scale) directly assessed superstitious beliefs. The first asked for degree of agreement regarding whether a pattern of switching was important in producing points, and the second asked whether the lights signaled a change in the instrumental contingency. Participants were also asked whether or not they had a lucky object, lucky number, and consciously refrained from “jinxing” themselves. Finally, participants were asked to assess their level of competitiveness (1 to 9 scale), their level of skill at the task relative to their partner/opponent (1 to 9 scale, only asked for the groups run in pairs) and to indicate their degree of athletic participation (maximum of 4 points) in second- ary school (1 point) and college (1 point for participation in intramural competition, and 2 points for participation in varsity athletics). (Table 1)
RESULTS
Seventy-one of 72 participants kept on pressing the inactive (i.e., left) lever throughout the experiment, thus demonstrating some degree of superstitious behavior. The most common superstitious belief as defined as any degree of agreement (i.e., a score of 6 or higher on the survey) involved the importance of a pattern of switching between levers (40 of 72 participants). Twenty-nine participants believed that the lights sig- naled some switch in contingencies. Fifty-three participants (73.6%) adopted at least one of these beliefs (Table 2).
All groups reported that the active (i.e., right) lever was more important in produc- ing points (M = 6.17, SD = 1.86 and M = 5.90, SD = 1.86 for the lights on and lights off conditions, respectively) than the inactive lever (M = 4.32, SD = 1.96 and M = 4.2 1, SD = 1.98 for the lights on and lights off conditions, respectively; see Table 3).
Despite the increased importance placed on the active lever, over the session approxi- mately the same number of responses were emitted on each lever (51.5% on the active lever and 48.5% on the inactive lever averaged across all groups).
One might expect that as the session progressed, participants would emit a lower percentage of their responses on the inactive lever. Responses were analyzed in terms of four 3-minute bins with a repeated measures analysis of variance. A reverse trend indicating percentage of responding on the inactive lever was obtained that approached statistical significance (F (3, 198) = 2.34, p = 0.075).
Finally, agreement with the necessity of a specific pattern in producing points was associated with agreement with the lights indicating an alteration in the instrumental contingency (r (72) = 0.34,~ = 0.003).
Group Assignment
Experimental condition effected the number of responses (F (5 $6) = 4.92, p = 0.001). Group assignment also affected the degree of agreement with the statement that a pattern of switching between levers was necessary (F (5,66) = 3.30, p = O.Ol), but did not effect the degree of agreement related to the importance of the light as indicating a change in the instrumental contingency, nor the importance assigned to each lever in producing points. Moreover, examining the direct behavioral measures (i.e., percentage of responses on the inactive lever, or different percentages of re- sponses on each lever under the lights-on/lights-off conditions) revealed no significant differences between groups. It is also interesting that group assignment produced no main effects on the belief that performance could be improved if allowed to play again, or of one’s perceived skill relative to one’s opponent (even in the Winner or Loser groups). Means and standard deviations for these results are summarized in Table 4.
Prior Superstitions
In addition to group assignment, the various behavioral and attitudinal measures were compared with regard to whether or not participants reported having a lucky object (26.4% of participants) or lucky number (43.1% of participants). T-tests re- vealed no main effects for any of our dependent measures (e.g., percentage responses on the active lever, perceived importance of either lever, degree of agreement with statements asking about belief in improved better performance, or in either type of superstitions). However, participants having a lucky number were more likely to re- frain from saying things for fear of jinxing themselves (t (70) = 2.44, p = O.Ol), to select special numbers when playing a lottery (t (70) = 1.70, p = 0.045), to have a higher level of athletic participation (t (70) = 2.86, p = 0.003)) and also to have a lucky charm (t (70) = 2.70, p =0.005). Having a lucky charm was also associated with the degree of athletic involvement (t (70) = 1.64, p = 0.055) (Table 5).
Believing that one could do better if allowed to play the game again was associated with both experimentally-induced superstitious beliefs, Positive correlations were ob- served with the degree of agreement that a specific pattern switching between levers was important (Y (72) = 0.34, p = 0.003) and that the light indicated a change in contingency (r (72) = 0.284, p = 0.016). Belief in improved future performance was also positively correlated with one refraining from saying something for fear of jinxing oneself (r (72) = 0.25, p = 0.037) and with the degree of agreement that one had more skill in the task than one’s partner/opponent (r (48) = 0.307, p = 0.034) (Table 6).
Perceived Skill Relative to One’s Partner/Opponent
Degree of perceived skill relative to one’s opponent was positively associated with belief in improved future performance (see earlier). Furthermore, perceived skill was associated with the degree of agreement that a pattern of switching between levers was important (Y (48) = 0.42, p = 0.003) and that the light signaled a change in the instrumental contingency (r (48) = 0.37 ,p = 0.01).
Degree of Athletic lnvohement and Competitiveness
Participation in athletic competition was not associated with any experimentally controlled superstitious beliefs or behaviors. Moreover, participation in athletics was not associated with perceived skill in the task. However, participation was positively associated with having a lucky number and with having a lucky charm (see earlier). Perceived competitiveness was not associated with any of our variables except for amount of athletic participation (r (72) = 0.47, p < 0.001).
Relationship between Attitudes and Behaviors
People’s behaviors were often correlated with beliefs. For example, people who emitted a greater percentage of overall responding on the active lever were less likely to agree that the inactive lever was necessary for producing points (r (72) =-0.3 1, p = O.Ol), and they agreed less that switching between levers was important (r (72) =-0.35, p = 0.002).
DISCUSSION
Placing people in implied (Pairs) or explicit (Opponent) competitive situations did not significantly increase the degree of agreements with statements indicating the adoption of superstitious beliefs. If anything, people placed in a winning competitive situation were less likely to adopt a superstitious explanation for reinforcement. Fi- nally, reinforcement schedule did not appear to be a major influence on the degree of agreement with or adoption of superstitious behaviors or beliefs,
More participants agreed with statements indicating superstitious beliefs related to a pattern of switching between levers than superstitions related to the importance of the light signaling a change in the instrumental contingency. These two types of supersti- tion are quite different. The first can be thought of as relating to superstitious behavior, while the second can be thought of as a superstition related to the stimulus control of behavior. The current results are similar to those reported by One (1987) who found that 13 of 20 participants responding under fixed- or variable-time schedules devel- oped superstitious response patterns, but only 6 of 20 demonstrated behavior consis- tent with sensory superstitions.
In using a reinforcement schedule similar to the one employed in the current study, Catania & Cutts (1963) explained the maintenance of superstitious behavior in their study as the result of there being close temporal contiguity between a response on the inactive button and a desired outcome following a response on the active (i.e., VI) button. Such an interpretation was strengthened by their inclusion of a change-over delay procedure in which responding on the active button would not produce a sched- uled point if the participant recently switched over from pressing the inactive button. Such a delay necessarily disrupts the temporal contiguity of presses on the inactive lever and reinforcers presented following presses on the active lever. According to Catania & Cutts, a delay of as little as two seconds disrupted the development and maintenance of superstitious behavior in most participants. More recently, the role of temporal contiguity in causality judgements has been stressed in empirical research and theoretical exposition (e.g., Shanks, 1993; Shanks et al., 1989; Wasserman, 1993; Wasserman & Neunaber, 1986). The role of temporal contiguity appears sufficient to explain participants’ agreement that a specific pattern of switching between levers was necessary in the current study.
The literature on operant superstition has a counterpart in the social psychological construct of the illusion of control. An extensive body of research consistently shows that people frequently claim to possess a degree of control over outcomes which are independent of their behavior (for review see Thompson et al., 1998). For example, Langer (1975) demonstrated that participants who chose their own lottery tickets re- quested more compensation for exchanging it than did participants who were simply assigned tickets. Behavior or beliefs that are independent of the actual contingencies in place are also the hallmark of superstition. While the effects of competition on super- stition have not been systematically examined, several studies have examined the role of competition in the illusion of control. Langer (1975) showed that the illusion of control was higher when participants competed against a confederate who played an unconfident participant than against a confident, attractive opponent. Similarly, Dykstra & Dollinger (1990) reported that participants who observed an incompetent-looking model gave higher estimates of future success at the task than those who observed a competent-looking model.
If one generalized the effects of competition from the illusion of control literature to the current study, one would predict that participants in the Winner condition would have revealed the greatest degree of belief in improved future performance. Further- more, one would predict that the Winner condition would exhibit the highest levels of
superstitious behavior and concomitant beliefs. Curiously, there were no differences across groups in belief in improved future performance, and the Winner group re- vealed the lowest degree of agreement that a specific pattern of responses was neces- sary to produce points. The first finding can be explained by a possible ambiguity in the question “if required to play this game again, how much better do you think you could do?” Although not directly measured, low scores could indicate one of two opposite interpretations: A sense that one is fairly poor at the task, or a sense that one has figured it out and has thus performed optimally. For the second finding, the decreased level of agreement with superstitious belief in the Winner group might result from differences in the use of the term “competition,” or from procedural differ- ences between the current paradigm and the aforementioned illusion of control studies. The variable manipulated in those studies was the projected confidence and compe- tence of an opponent. However, the actual odds of the desired outcome were the same in each condition. In the current study, the probability of the desired outcome was what varied across groups. There actually were winners and losers. In the one prior illusion of control/competition study that also manipulated the favorableness of se- quences of outcomes (hence resulting in winners and losers), Breen & Frank (1994) reported that neither the perceived status of a competitor nor the favorableness of the sequence affected the illusion of control. While Breen & Frank’s experiment does not explain why the “Winners” had lower levels of superstitious beliefs than the other groups, it does help to clear up the apparent contradiction on the effects of competition between the current and the illusion of control studies. It may simply be that being placed in a winning situation makes it more likely that a participant makes contact with the actual contingencies in place. This would result in fewer superstitious beliefs. Finally, it is important to stress a very important procedural difference between the illusion of control literature and the current study. Illusion of control is assessed in circumstances under which there is no actual contingency between behaviors and possible outcomes. In this study, a definite contingency (i.e., RI 30”) between pressing the right-lever and turning on the tone was in place. Competition may produce differ- ent effects under these different circumstances.
While many participants claimed that the inactive lever did nut play much of a role in producing points, all but one continued to occasionally press the lever throughout the session. Indeed, twelve participants who indicated disagreement with the impor- tance of the left lever in producing points (i.e., a score of 4 or less on the Likert-scale) emitted a greater percentage of their responses on that lever. There are several possible explanations for this perseverative behavior. First, the responses may have been a form of adjunctive behavior -behavior that can best be thought of as time-filling. In fact, in a critique of Skinner’s “superstitious pigeon” study, Staddon & Simmelhag (1971) proposed that Skinner’s pigeons weren’t acting superstitiously, but rather engaging is species-typical adjunctive behavior. One can easily imagine that adjunctive behavior in the current procedure would include pressing both levers present in the experimen- tal context. Second, participants may have behaved “superstitiously” without believing that their responses were indeed necessary. In work based on signal detection theory,
Killeen (1977, 198 1) proposed that in the attempt to solve a problem an organism tends to repeat any behavior that may have produced the desired outcome. Killeen suggested that this effect is magnified when effort of response is minimal, as was the case in our current study. Since pressing a lever requires very little effort, pressing a lever considered to be unnecessary might have been maintained “just in case” it played or might come to play a relevant role in producing tones. Not all superstitious behav- iors are strongly believed to be relevant in producing desired outcomes. For example, Bleak & Frederick (1998) report that many athletes engage in superstitious rituals in spite of their self-reports indicating low levels of agreement that such behaviors are effective in influencing sports performance.
The relationship between participants’ responses related to situational self-efficacy and their degree of superstitious beliefs is arguably the most interesting finding in this study. An individual’s perception that they could do better if allowed to participate again, and their perception of skill in the task relative to their opponent were related to agreement with both types of superstitious beliefs. Such a finding appears to be contra- dictory to previous research revealing a negative relationship between self-efficacy and superstitious belief (Toabcyk & Schrader, 1991). However, prior evidence sug- gesting a positive relationship between self-efficacy and superstition does exist. Buhrmann & Zaugg (1982) found that athletes’ degree of the superstitious behavior is positively related to success at competition. For example, starting basketball players were reportedly more superstitious than non-starters (teams tend to start their best players), and successful teams tended to be more superstitious than teams that won less frequently.
The current finding of a relationship between perceived skill relative to one’s part- ner/opponent and superstition is entirely consistent with traditional explanations of the illusion of control. When Langer (1975) did the first studies on the illusion of control, she explained its occurrence as resulting from the conflation of skill with chance; people believed that their actions have an outcome on the situation despite its random nature. In the present study, participants who reported higher levels of skill (at least relative to their opponents) were also more likely to think they could perform better at the task at a future date- a belief which can easily be interpreted as an illusion of control since the reinforcement schedule remained constant throughout the session.
The current findings also suggest an interesting relationship between optimism and superstition. The illusion of control is often described as implying an unjustified optimism on the part of individuals exhibiting it (e.g., Gollwitzer & Kinney, 1989). Such an optimistic attitude may actually be psychologically adaptive. In a series of experiments, Matute (1994; 1995) exposed participants to aversive tones, and told them that the noise could be eliminated by entering a sequence of key-presses on a computer keyboard. Unknown to the participants, no contingency between key press- ing and noise termination was in effect. When participants received feedback that their responses had no effect on termination of the tone, learned helplessness-a motiva- tional and cognitive deficit characterized by interference in subsequent task perfor- mance and the expectation that their behavior has little effect on the environment-
was observed. However, when failure feedback was eliminated, most participants de- veloped a superstitious pattern of responding on the keys, and also reported some degree of control over the tones. Matute’s results suggest that learned helplessness and superstitious behavior are opposite effects of uncontrollable reinforcement in humans. In the current study the adoption of superstitious beliefs and their relationship to participants’ optimistically thinking they could do better in the future may have been the alternative to a possible experimentally-induced motivational or cognitive deficit. Follow up studies should address whether or not participants demonstrating such be- liefs are more likely to persist at tasks which are usually used to assess learned helplessness.
Superstitious beliefs created in the current experimental procedure appear to be quite different from commonly held superstitions. People who held the more tradi- tional-type superstitions such as having lucky charms or lucky numbers were no more likely to act or think superstitiously than those who did not. However, these traditional (i.e., lucky numbers and charms) were associated with each other. Furthermore, people who reported having a lucky number were also more likely to refrain from saying something for fear of jinxing oneself. This dissociation of results suggests that super- stitious responding which is studied in the laboratory may be quite different from what is typically perceived to be superstition in everyday life. Indeed, in the previously mentioned studies on the relationships between self-efficacy, locus of control, hyp- notic susceptibility, and superstition, the majority of the superstitions dealt with paran- ormal or occult phenomena (e.g., Tobacyk & Milford, 1983; Toabcyk & Schrader, 199 1; Wagner & Ratzenberg , 1987). Further investigations into relationships between common superstitions and those created during the experimental analysis of behavior should address their similarities and differences, as well as their individual relation- ships with other variables, For example, previous studies have identified athletes as traditionally superstitious individuals (Bleak & Frederik, 1998). In the current study, degree of athletic involvement was associated with traditional superstitions such as having a lucky charm or number, but was not associated with any of those generated by the experimental procedure.
In sum, superstitious beliefs in a concurrent two-lever VI EXT task are more closely associated with participants’ belief in improved future performance and relative skill at the task than with specific parameters of the reinforcement schedule, or of type of artificially created competitive situation. The current findings are generally supportive of a link between superstition and the illusion of control, as well as with self-efficacy. Finally, these results suggest that superstitious beliefs that are experimentally induced may be qualitatively different from more traditionally thought of superstitions.
NOTES
Accepted for publication: 17 February 2000. Address correspondence to: Jeffrey Rudski, Muhlenberg College, Department of Psychology, 2400
Bleak, J.L. & Frederick, C.M. (1998). Superstitious behavior in sport: Levels of effectiveness and determi- nants of use in three collegiate sports. Journal of Sport Behavior, 21, 1-15.
Breen, R.B. & Frank, M.L. (1993). The effects of statistical fluctuations and perceived status of a competi- tor on the illusion of control in experienced gamblers. Jouranl of Gambling Studies, 9, 265-276.
Catania, A.C. & Cutts, D. (1963). Experimental control of superstitious responding in humans. Journal uf the Experimental Analysis of Behavior, 6, 203-208.
Dykstra, S.P. & Dollinger, S.J. (1990). Model competence and the illusion of control. BuEletin of the Psychonomic Society, 28,235-238.
Gollwitzer, P.M. & Kinney, R.F. (1989). Effect of deliberative and implemental mind-sets on illusion of control. Journal of Personality and Social Psychology, X,53 l-542.
Killeen, P.R. (1977). Superstition: A matter of bias, not detectability. Science, 199, 88-90. Killeen, P.R. (1982). Learning as causal inference. In M.L. Commons and J.A. Nevin (eds.) Quantitative
analyses of behavior: Discriminative properties of reinforcement schedules, (pp. 89-112), Cambridge, MA: Ballinger .
Langer, E.J. (1975). The Illusion of control. Journal of Personality and S&al Psychology, 32, 3 1 l-328. Matute, H. (1994). Learned helplessness and superstitious behavior as opposite effects of uncontrollable
reinforcement in humans. Learning and Motivation, 25, 2 16-232. Matute, H. (1995). Human reactions to uncontrollable outcomes: Further evidence for superstitions rather
than helplessness. Quarterly JournaE of Experimental Psycholugy, 488, 142-l 57 _ Morse, W.H. & Skinner, B.F. (1957). A second type of superstition in the pigeon. American Journal of
Psychology, 70, 308-3 11. One, K. (1987). Superstitious behavior in humans. Journal of the Experimental Analysis of Behavior, 47,
261-271 Rudski, J.M., Lischner, M.I. & Albert, L.M. (1999). Superstitious rule generation is affected by probability
and type of outcome. The Psychological Record, 49,245-260 _ Shanks, D.R. ( 1993). Human instrumental learning: A critical review of data and theory. British Journal of
Psychology, 84,319. Shanks, D.R., Pearson, S .M. & Dickinson, A. ( 1989). Temporal contiguity and the judgment of causality
by human subjects. The Quarterly Journal of Experimental Psychology, 41 B(2), 139- 159. Skinner, B .F. (1948). Superstition in the Pigeon. Journal of Experimental Psychology, 38, 168-l 72. Staddon, J.E.R. & Simmelhag, V.L. (1971). The “superstition” experiment: A reexamination of its implica-
tions for the principles of adaptive behavior. Psychological Review, 78, 343. Starr, B.C. & Staddon, J.E.R. (1982). Sensory superstition on multiple interval schedules. Journal of the
Experimental Analysis of Behaviur, 37, 267-280. Thompson, S.C ., Armstrong, W. & Thomas, C. (1998). Illusions of control, underestimations, and accu-
racy: A control heuristic explanation. Psychological Bulletin, 123, 143-161. Tobacyk, J .J. & Milford, G. ( 1983). Belief in paranormal phenomena: Assessment instrument development
and implications for personality functioning. Journal of Personality and Social Psychology, 44, 1029- 1037.
Tobacyk, J.J. & Shrader, D. (1991). Superstition and self-efficacy. Psychological Reports, 68, 1387-1388. Vyse, S.A. (1991). Behavioral variability and rule generation: General, restricted, and superstitious contin-
gency statements. Psychological Record, 41,487-506. Vyse, S.A. (1997). Believing in Magic. New York, NY: Oxford University Press. Wagner, M.W. & Morris, E.K. (1987). “Superstitious” behavior in children. The Psycholugical Record, 37,
Reports, 60, 1069-1070. Wasserman, E.A. (1990). Detecting response-outcome relations: Towards an understanding of the causal
texture of the environment. In G.H. Bower (Ed.), The Psychology of Learning and Motivation, 26, (pp. 27-82). New York” Academic Press.
Wasserman, E.A. & Neunaber, D.J. (1986). College students’ responding to and rating of contingency relations: The role of temporal contiguity. Juumal of the Experimental Analysis of Behavior, 46, 15-35.
