Luck In Action? Belief In Good Luck, Psi-Mediated Instrumental Response, And Games Of Chance

MARLEEN NAGTEGAAL [1]

ABSTRACT: Sixty individuals took part in a study designed to explore connections between belief in good luck (BIGL), performance on a laboratory PMIR (nonintentional psi) task, and expectations of success and actual performance at two games of chance (playing the UK National Lottery and a simple die throwing task). No overall evidence was found of nonintentional psi, t(59) = -.597. A marginally significant positive correlation was found, as predicted, between PMIR and luckiness as measured by the BIGL scale, [r.sub.s] (58) = .210, p = .05, one-tailed. As predicted, BIGL correlated positively with expected lottery success: [r.sub.s] (58) = .438, p [less than] .01, one-tailed, for confidence of winning; [r.sub.s] (58) = .477, p [less than] .01, one-tailed, for expected winnings. With expected die throwing success, [r.sub.s] (58) = .378, p [less than] .01, one-tailed, for confidence of success; [r.sub.s] (58) = .222, p [less than] .01, one-tailed, p [less than] .05, one-tailed for chances of success. Lucky and n ot lucky groups did not differ in terms of actual lottery playing behavior, z = 1.570, p = .116, two-tailed. According to their BIGL responses, lucky participants did no better at the lottery than not lucky participants, z = .695, p = .487, two-tailed. However, those participants who specifically believed their luck could affect their lottery success had significantly greater lottery success than those who did not believe their luck could affect their lottery success, z = 2.472, p = .013, two-tailed. There appeared to be no indication that lucky participants performed better at the die throwing task than not lucky participants.

Rex Stanford (1974, 1977) argues that typical collections of spontaneous paranormal experiences may give a misrepresentative view of the operation of psi in naturalistic situations, because these collections tend to feature cases suggesting a "perceptual-cognitive" model of psi. Such psychic experiences seem to come in the shape of thoughts, feelings, and mental images, albeit degraded ones, that convey some information (e.g., that a loved one is in danger) to the experient. However, there may be another class of spontaneous psi experiences that is largely overlooked--those that feature odd coincidences (e.g., unexpectedly meeting someone who one needed to meet). The experients may be temporarily puzzled, but most are likely to shrug off the coincidence as a happy chance. Stanford's Psi Mediated Instrumental Response (PMIR) model (e.g., Stanford, 1974, 1990) presents a well-elaborated theory suggesting that, in fact, such lucky coincidences represent the operation of nonintentional psi [2] in service of the o rganism's needs. Is nonintentional psi "luck in action"?

Researchers have already begun to explore the connection between luckiness and psi (for a review, see Smith, Wiseman, Machin, Harris, & Joiner, 1997). Most recently, in a study which classified participants as lucky, unlucky or uncertain according to their responses on a Luckiness Questionnaire, Smith et al. (1997) found no difference between lucky and unlucky participants' success on a laboratory computer psi task involving guessing the outcome of pseudo-RNG coin flips. Lucky participants were nonsignificantly more confident of success than unlucky participants. Also, in a finding reminiscent of the "sheep-goat effect" (Palmer, 1972), Smith et al. found a significant positive correlation between predicted psi performance and actual psi performance.

Two postal questionnaire studies have compared perceived luckiness with confidence of a win on the UK National Lottery, actual lottery playing behavior, and actual lottery success, the latter of which may of course be an indicator of psi performance (Smith, Wiseman, and Harris, 1997). These studies found that lucky participants were significantly more confident of winning than unlucky participants. However, there was no difference between lucky and unlucky groups in terms of numbers of tickets bought or actual success.

These studies seem to suggest that there is little difference between lucky and unlucky participants in success at what may be regarded as intentional psi tasks. They do not address the question of luckiness and nonintentional psi, yet here is where one might most reasonably expect to find a relationship between luckiness and psi--you don't try to be lucky; in everyday life good luck just seems to happen. Indeed, Smith, Wiseman, and Harris (1997) conclude that it may be more appropriate to study luckiness in relation to nonintentional psi, as luck may be a form of PMIR.

PMIR may be tested in the laboratory by having participants perform a nonintentional psi task, performance on which will determine their subsequent experience in the session. If they can use their psi appropriately, according to the prearranged experimental contingency, they can avoid an unpleasant situation and instead experience a pleasant situation. This is analogous to how PMIR is thought to occur in daily life--one unintentionally follows an impulse that can lead one to a beneficial outcome. Rammohan & Lakshmi (1993) found a significant positive correlation between self-rated exam luck and performance on a nonintentional psi task. We are aware of only one study, by Watt and Ravenscroft (2000), in which an explicit comparison was made between PMIR and luck. Using Smith, Wiseman, and Harris' (1997) Luckiness Questionnaire, no relationship was found between luckiness and nonintentional psi. However, the primary aim of Watt and Ravenscroft's study was to test some of the fundamental assumptions of the PMIR model. This study used a reciprocal helping design in which each participant had the opportunity to use their psi nonintentionally to help the other avoid an unpleasant condition and instead experience a pleasant condition. To test predictions derived from the model, cost of helping was systematically varied (high cost versus low cost), as was the relationship between participants (friends versus strangers). This design might be more apt for studying "altruistic psi" than the kind of self-benefiting, nonintentional psi that might characterize luck in action.

The present study, conducted at the Koestler Parapsychology Unit at the University of Edinburgh between February and March 1999, attempted to look directly at the relationship between luckiness and nonintentional psi. We used a "straight" PMIR-type task in which an individual could use their psi nonintentionally in order to avoid an unpleasant condition and instead experience a pleasant one. The PMIR model assumes that nonintentional psi operates through triggering behaviors, memories, feelings, and desires that are already in the organism's repertoire (Stanford, 1990, p. 102). We therefore considered that a task measuring aesthetic preference, or liking, could provide a valid vehicle for PMIR For a previous PMIR study, Watt & Ravenscroft (2000) devised a rating task in which participants were asked to indicate their aesthetic preferences for Kanji (Japanese language) characters. A similar task was used for the present study. Luckiness was measured by Darke and Freedman's (1997) Belief in Good Luck Scale (BI GL). This measure has the advantage of systematic psychometric development, plus its relationship with concepts such as belief in bad luck, and measures such as locus of control, self-esteem, optimism, and desire for control, have been reported. We included a questionnaire measure of Desire for Control (DC) (Burger & Cooper, 1979) as part of a wider exploration of the psychology of luck, but hypotheses and results related to this scale will not form part of the present paper.

Finally, we included two questionnaires into confidence of winning at games of chance--the UK National Lottery, and a simple die throwing task. The aim of the lottery questionnaire (Appendix A) was to expand upon the findings of Smith, Wiseman, and Harris (1997). This questionnaire explored whether there were differences between participants' expectations of success at the lottery under two different scenarios: where they chose the numbers personally, and where the numbers were chosen "randomly", with the aim of varying the participants' perceived control at the lottery task. The odds of winning a large sum of money in the UK National Lottery are rather remote; the game is quite impersonal--that is, millions of players take part in each game, and feedback on results is delayed. Milton (1994) has noted that these conditions may not be conducive for the operation of ESP. For these reasons, we wished to examine expectations of success at a more personally involving task with immediate feedback and considerably higher odds of success (though without the promise of any financial gain): throwing a die aiming for a "6" face uppermost. As with the lottery questionnaire, the die throwing questionnaire (Appendix B) explored whether participants' responses would differ across two scenarios--throwing the die personally, and having the experimenter throw the die on the participants' behalf. We only report results on those parts of the lottery and die throwing questionnaires that are most directly relevant to the present paper's emphasis: expected success under the self-chosen lottery numbers and self-thrown die scenarios. Analyses involving perceived control at the games of chance formed part of the wider investigation of the psychology of luck and will be reported elsewhere.

Hypotheses and Exploratory Questions

Hypothesis 1 -- There will be an overall positive nonintentional psi effect (tested by single mean t-test versus MCE, one-tailed).

Hypothesis 2 -- Belief in Good Luck (BIGL) will correlate positively with nonintentional psi (tested by Spearman correlation, one-tailed).

Hypothesis 3 -- BIGL will correlate positively with expected success at lottery playing (Spearman correlation, one-tailed).

Hypothesis 4 -- BIGL will correlate positively with expected success at die throwing (Spearman correlation, one-tailed).

Exploratory Q1 -- BIGL will be compared with actual lottery playing behavior.

Exploratory Q2 -- BIGL will be compared with actual lottery success.

Exploratory Q3 -- BIGL will be compared with actual die throwing success.

METHOD

Participants

Sixty volunteers participated in the study, 19 males and 41 females, ages ranging from 18 to 70 years, mean age 33 years. Participants included undergraduate students, employed and unemployed individuals, and retired individuals, many of whom had previously taken part in parapsychological studies at the Koestler Parapsychology Unit. Participants were recruited byword of mouth or by an initial telephone or email approach by CW, who described the study as one into "personality and luck." There were three experimenters, CW; MN, and VMcG, one of whom was assigned for each session on an ad hoc basis (CW ran 23 sessions, MN 24, and VMcG 13 sessions).

Materials

Consent Form. This records some demographic details including participants' age and sex. It also assures participants of the confidentiality of their individual results, and notes that they are free to terminate the session at any time.

Belief in Good Luck (BIGL) Scale. This is a 12-item scale developed by Darke and Freedman (1997) in order to measure the belief that luck is personal and stable. Low BIGL scores indicate a belief that luck is just random chance. Respondents are required to indicate the extent to which they agree or disagree with each item by ticking one of six boxes (labeled strongly disagree, somewhat disagree, slightly disagree, slightly agree, somewhat agree, strongly agree). Two of the items are reverse scored. The theoretical range of scoring is from 12 to 72. A subset of four items has been identified by Darke and Freedman as indicating a belief in personal good luck. Our formal hypotheses would be tested with overall BIGL scores. As part of our exploratory measures, participants would be divided into personally lucky and personally not lucky groups on the basis of their responses to the subset, enabling comparison between these groups.

Desire for Control (DC) Scale. This is a 20-item scale developed by Burger and Cooper (1979) in order to measure individual differences in motivation to control events in one's life. No further details are given here because DC results will not be reported in the present paper.

The Lottery Questionnaire. This is a 9-item questionnaire constructed by CW for the present study. The first three questions concern actual lottery playing behavior. Questions 4 to 7 concern confidence of winning and expected winnings for numbers to be personally selected and numbers to be randomly selected. Questions 8 and 9 concern participants' general beliefs about whether their luck can influence their lottery success. Questions 8 and 9 were included because, in their lottery studies, Smith, Wiseman, and Harris (1997) felt that it was important to include a question about participants' actual lottery and luck beliefs, in order to allow a valid comparison between luckiness and lottery responses. There are two versions of the lottery questionnaire. In both, the first three questions are identical. Then, the order of presentation of questions about random numbers versus questions about personally chosen numbers alternate. This is to offset any potential order effects (none were found).

Stapled to each lottery questionnaire is an actual betting slip for the UK National Lottery. Participants are asked to answer questions 1 to 9 and then play two boards--to select their lottery numbers personally and to observe the experimenter use the random number function on a calculator to select 6 numbers "randomly."

Die Throwing Questionnaire. This was constructed by CW for the present study, and consists of six items. The first four concern confidence of success, and estimated chances of success, for two scenarios--where the experimenter is to throw aiming for a six, and where the participant is to throw. Questions 5 and 6 concern participants' general beliefs about whether their luck can influence die throwing success. The order of the questions (self throw versus experimenter throw) was alternated, giving two different versions of the questionnaire, to offset any order effects (none were found). A cup and a single die (of the sort used in a casino) were used for actual die throwing. Note that this method of throwing may not rule out deliberate or unintentional bias in throwing, so there will be no attempt to regard the outcome of the throws as possibly evidential of PK.

PMIR Task. This was a rating task in which participants were asked to indicate their aesthetic preferences for Kanji (Japanese language) characters. The Kanji characters were selected on the basis of a previous pilot study with the aim of identifying those characters to which most raters gave relatively neutral ratings (the chosen characters had mean ratings ranging from 3.9 to 4.2, where 4 = neutral), in order to minimize artifact due to some characters being intrinsically more attractive than others. Response booklets were prepared, each consisting of 10 pages with a character and rating scale on each page. Participants were asked to rate the characters in terms of "aesthetic appeal" on a scale that ranged from 0 "Totally Displeasing" through 50 "Neutral" to 99 "Totally Pleasing." The first two pages each contained one dummy character, intended to familiarize participants with the task, and responses which were not included in the analysis. The remaining pages contained the eight experimental characters, in a different random order for each booklet. When doing the rating task, participants were allowed to look through the booklet as they wished and were not permitted to give any tied ratings.

Post-Experiment Questionnaire. This is a five item questionnaire, intended as a check on the validity of the nonintentional psi task. Items one to four ask participants to rate for pleasantness whichever of the post-PMIR options they did (tracking, computer game, relaxing music, leave early). The rating was on a seven point scale from 0 (not at all pleasant) through 3 (neutral) to 6 (very pleasant). Item five asked participants to note if they had any ideas as to what the study was about, in addition to what they had already been told by the experimenters (recall that the true nature of the nonintentional psi task was supposed to be unknown to participants). Only one participant, a parapsychologist, gave any indication on the Post-experiment questionnaire that he guessed there was a nonintentional psi task involved in the experiment.

Procedure

Target Selection and Security. The key Kanji character for each trial was randomly selected in advance of the whole experiment by a person otherwise uninvolved in the study. The randomizer used a calculator random number function in order to select an entry point into the RAND tables (Rand Corporation, 1955). Once the entry point had been identified, the randomizer read the table one row at a time, selecting one of the eight target numbers for each trial. For each target, the randomizer folded a piece of paper containing the designated Kanji character, and its number, and sealed the folded paper in a numbered manilla envelope. Thus, envelope 1 was intended for trial 1, envelope 2 for trial 2, and so on. The randomizer kept a separate written record of his selected target sequence in a location outside the department that was unknown to the experimenters, for the purpose of later cross-checking (no discrepancies were found). Once all target envelopes were sealed, the randomizer passed these to CW and she kept them in a locked filing cabinet in her office, which was also locked when unoccupied. Shortly prior to each session, CW or MN accessed the filing cabinet and removed the appropriate target envelope. This was then kept on their person, or passed to VMcC who would also keep the envelope on her person, until the appropriate moment during the experimental session when the target identity was able to be revealed.

Session Procedure. The experimenter met the participants and took them to the testing room, a large windowless room in the basement of the psychology department. The experimenter described the study as one into "personality and luck," and outlined the general procedure. After answering any questions, the experimenter directed the participant to complete the consent form, the BIGL and the DC questionnaires. The participant then completed the lottery and die questionnaires. For the lottery questionnaire, participants were informed that, although no bet would be placed on the selected numbers, the two boards would be compared with the next lottery draw, either a Saturday or a Wednesday, whichever was soonest. Once participants had completed the die questionnaire, the participant and experimenter each threw the die once, by shaking it in the cup and throwing the die against a wall below which was a table on which the die could bounce freely. The experimenter recorded the outcome of each throw on the die question naire.

Participants then did the nonintentional psi task. No indication was given that there was a psi component to this task; the implication was that it was just another of the psychological measures. Once the participant had completed their ratings, the experimenter checked for tied ratings and, if any were found, asked the participant to rerate to break the tie. The experimenter then opened the envelope revealing the identity of the key Kanji character. If a participant gave their highest rating to the key Kanji, they were directed to do a pleasant task. This was a choice of three options; the ability to choose was itself regarded as a positive feature of the pleasant task. The choice was either to leave the experiment early, to listen to a relaxing audio tape over headphones in a comfortable chair, or to play an "asteroids" style computer game. These options were intended to be relatively pleasant even for participants with quite varying individual preferences. If a participant did not give their highest ratin g to the key Kanji, they were directed to an unpleasant task. This was a tedious and rather tiring task using the computer mouse to track a slowly moving target on the computer screen. If the mouse drifted off target, an auditory tone was heard. Apart from the physical and mental strain of this task, there were other ways in which the task was unpleasant: there was no choice (unless the participant opted to abort the session altogether); and the participant was not informed about how long the task would take (10 minutes).

Finally, the participant was asked to complete the post-experiment questionnaire, was thanked, and shown out of the department. Most participants were given no debriefing information about the nature of the rating task at the completion of the session. On a few occasions, when a participant was particularly curious, the experimenter gave further information about the PMIR nature of the rating task; in these cases, the participant was requested not to reveal the further information to any potential participants. Typically, a session took 40 minutes to complete. GW checked each participant's two lottery boards against the next lottery draw, and noted how many matches occurred. Following completion of the study and analysis of the results, each participant was sent an individual feedback letter that gave details of the experiment's hypotheses and results and that invited participants to contact GW or MN if any further information was desired.

RESULTS AND DISCUSSION

The Dependent Variable: Measure of Nonintentional Psi

For each trial, a Kanji character was randomly selected (see Procedure section) as the "key" or target Kanji. The psi measure was a standardized rating score calculated for each participant's session from the difference between the participant's rating on the key Kanji and their mean rating for all eight Kanji, divided by the SD of all eight ratings. Thus, positive standardized rating scores indicated higher than average preference for the key Kanji, even if this Kanji did not receive the highest preference rating overall. Therefore, if participants' ratings were unrelated to the identity of the key Kanji, their standardized scores would not deviate from MCE. For the analyses reported below, in cases where exact p-values were not available (because p-values were too small to be found on relevant tables or were too small for the three decimal places output of statistical software packages, a conservative value of p[less than].01 is reported).

Hypothesis 1- Nonintentional Psi. The mean standardized rating score for all 60 participants was -.066 (SD= 0.86); this did not differ significantly from chance, t(59)= -.597, p= .553, two-tailed; effect size, Cohen's d = .16. Therefore, there was no support for the prediction of an overall positive nonintentional psi effect.

All five participants who scored a hit opted for the computer game as the post-PMIR task. The mean pleasantness rating given to the game on the post-experiment questionnaire was 4.6 (SD = 0.89), where 3 is neutral and 6 is very pleasant, suggesting that participants did indeed find the game a pleasant experience. The remaining 55 participants, who did not score a direct hit, did the computer tracking task. This was given a mean rating of 2 (SD= 1.33) on the post-experiment questionnaire, where 0 is not at all pleasant and 3 is neutral, suggesting that the task was unpleasant for participants, but not strongly so. No attempt is made to test the significance of the difference between the mean pleasantness ratings due to the large difference in N between the two groups, which would limit the usefulness of any statistical test.

Hypothesis 2 - BIGL and Nonintentional Psi. Mean BIGL score was 40.7 (SD = 9.523). There was a marginally significant positive correlation between total scores on the BIGL questionnaire and performance on the nonintentional psi task, [r.sub.s] (58) = .210, p = .05, one-tailed. This provides some weak support for the prediction that luckiness and PMIR would be positively related, but clearly further replication is needed to support the postulated luckiness-PMIR link.

Belief in Personal Good Luck

In order to explore further the relationship between BIGL and PMIR and between BIGL and the games of chance, participants were divided into two groups on the basis of their responses to the four BIGL questions concerning belief in personal good luck. In terms of face validity, responses to these questions might be particularly likely to relate to PMIR and expectations and performance on the lottery and die throwing tasks: some of the other BIGL questions are general rather than personal. For instance, BIGL Q2 ("Some people are consistently lucky, and others are unlucky") is asking about general beliefs about luckiness, not about the participants' belief in their own luckiness. There was a correlation of [r.sub.s] (58) = .773, between scoring on the subset of four items about personal good luck and the full BIGL scale.

Mean personal luck score was 13.33 (SD = 3.676). In order to balance as far as possible the number of participants in each group, those who scored 13 or under were assigned "personally not lucky," N = 27, and those who scored 14 or over were designated "personally lucky," N = 33. Mean scores of these two groups are given in Table 1. Note that we used the term "not lucky" rather than "unlucky" because in developing BIGL, Darke and Freedman (1997) reported that in an initial version of the questionnaire, answers to the question "I consider myself to be an unlucky person" correlated only .05 with total BIGL scores, N = 214. Darke and Freedman concluded that beliefs about personal good luck and personal bad luck should not be regarded as opposite ends of a single continuum.

The personally lucky group had a mean nonintentional psi score of 0.006 (SD = .760) and the personally not lucky group had a mean nonintentional psi score of -0.156 (SD = .981). Therefore, the lucky group scored at chance and the not lucky group tended to score negatively. The difference in scoring between these groups was not statistically significant, t(58) = 0.720, p = .474, two-tailed.

BIGL and Expected Success at Lottery and Die Games

Table 1 gives results of the planned one-tailed Spearman correlations between total BIGL scores and expected success. For each game of chance, there are two measures of expected success: confidence of winning at the lottery (lottery Q4) and expected winnings at the lottery (Q5); confidence of success at die throwing (die throwing Q1) and estimated chances of success at die throwing (Q2). For additional information, the table includes two-tailed Spearman correlation for BIGL and lottery Q8, as this is a question about the participants' belief that their luck can affect their lottery success, and two-tailed Spearman correlation for BIGL and die throwing Q5, which asks about the participants' belief that their luck can affect their die throwing success.

Hypothesis 3 -- BIGL and Expected Lottery Success. The mean confidence of winning was 2.6 (SD = 1.64), where 1 = not at all confident and 7 = extremely confident; therefore, overall, participants were not confident of winning. There was, however, a significant positive correlation between BIGL and confidence of winning, [r.sub.s] (58) = .438, p [less than] .01, one-tailed, in the predicted direction. The mean expected winnings was 1.9 (SD = 1.22), where 1 = nothing and 2 = [pound]10, so on average, participants reported expecting to win around [pounds]10. There was a significant positive correlation between BIGL and expected winnings, [r.sub.s] (58) = .477, p [less than] .01, one-tailed, in the predicted direction. Both these results support Hypothesis 3.

Table 1 provides additional information on how personally lucky and personally not lucky participants responded to the questions on expected lottery success; the difference between the groups is tested using Mann-Whitney statistics. For both questions, lucky participants tend to have greater expectations of success than not lucky participants. This is almost significant for confidence of winnings, z = 1.874, p = .061, two-tailed, and is significant for expected winnings, z = 2.623, p = .009, two-tailed.

For the more general question of the relationship between participants' BIGL and their beliefs that their luck can affect their lottery success, a positive correlation was found, [r.sub.s] (58) = .652, P[less than].01, two-tailed. Table 1 also shows that personally lucky participants reported a greater belief that their luck could affect their lottery success than personally not lucky participants, z = 4.081, P[less than].01, two-tailed, on a Mann-Whitney test. However, it is interesting to note that even for this more general question, lucky participants' mean response was 4.3 (4 = neutral). Rather than lucky participants having particularly positive beliefs that their luck can affect their lottery success, the pattern seems to be that not lucky participants have relatively negative beliefs that their luck can affect their lottery success.

Hypothesis 4--BIGL and Expected Die Throwing Success. The mean confidence of die throwing success was 3.5 (SD = 1.36, where 1 = not at all confident and 4 = neutral); therefore, participants were not particularly confident of success. A statistically significant positive correlation was found, as predicted, between confidence of success and BIGL [r.sub.s] (58) = .378, p [less than] .01, one-tailed. The second measure of expected success was participants' indications of their approximate chances of throwing a six. For this question, participants were asked to check one of 7 boxes, labeled 0%, 17%, 33%, 50%, 67%, 83%, and 100%. The mean score for all participants was 30.1 (SD = 17.41), indicating an average estimation of the chances of success at approximately 30%. This is an over estimation of the actual chances of success (17%, or 1/6). A significant positive correlation was found, as predicted, between BIGL and expected chances of success, [r.sub.s] (58) = .222, p [less than].05, one-tailed. Both these find ings support Hypothesis 4.

Further information is provided in Table 1 of the results for expected die throwing success, broken down between personally lucky and personally not lucky participants. It can be seen that the lucky participants have a tendency toward greater confidence of success than not lucky participants, but that both rate their confidence as less than neutral. The lucky group tend to exaggerate their chances of success compared to not lucky participants, but neither group gives objectively accurate estimations of success on average. Table 1 shows that the differences between lucky and not lucky participants in confidence of success are not significant according to a Mann-Whitney test.

For the more general question of the relationship between BIGL and participants' beliefs that their luck can affect their die throwing success, a positive correlation was found [r.sub.s] (58)= .697, p [less than].01, two-tailed. Table 1 also shows that personally lucky participants had a significantly greater mean belief that their luck could affect their die throwing success (M = 4.1, where 4 = neutral) than personally not lucky participants (M = 2.2), z = 3.860, p [less than] .01, two-tailed. As with the lottery playing question, it seems that lucky participants are relatively neutral on the question of their beliefs in their luck at die throwing, while not lucky participants have relatively low belief in their luck at die throwing.

Comparing expected success for the lottery and die throwing, Table 1 suggests that there is a stronger relationship between belief in good luck and lottery playing, than between belief in good luck and die throwing (we can use [r.sub.s] as an estimate of effect size because the Nis 60 throughout). However, both lucky and not lucky participants were more confident of success at die throwing than at lottery playing. This latter trend may reflect participants' appreciation of the more favorable odds of success for the die task compared to the lottery task. This impression is confirmed by a Wilcoxon test of the difference between lottery confidence (lottery Q4) and die throwing confidence (die Q1), which showed a significant effect, z = 4.202, p [less than] .01, two-tailed.

Actual Lottery Playing Behavior

According to their responses on the lottery questionnaire, 29 participants said they did not play the UK National Lottery. Of the 31 who did play the lottery, the mean frequency of playing was approximately fortnightly (4.1, SD = 1.69), and the mean amount spent per week was approximately [pound]1.50 (2.4, SD = 0.84).

Exploratory Q1- BIGL and Actual Lottery Playing Behavior. The mean BIGL score for those who played the lottery was 42.2 (SD = 9.369), which did not significantly differ from the mean BIGL score of 39.1 (SD = 9.582) for those who did not play the lottery, according to a Mann-Whitney test, z = 1.570, p = .116, two-tailed. For the 31 players, no correlation was found between BIGL and reported frequency of playing, [r.sub.s] (29) = -.087, and between BIGL and reported amount spent on the lottery, [r.sub.s] (29) = .084. Looking at beliefs in personal good luck, 19 out of 33 lucky participants played the lottery (57.6%), compared to 12 out of 27 not lucky participants (44%). This distribution does not differ from chance [X.sup.2](1) = 0.311.

In sum, we have found that BIGL is significantly positively correlated with expectations of success at playing the UK National Lottery, but there is no relationship between BIGL and actual playing behavior. These findings replicate those of the two postal questionnaire studies by Smith, Wiseman, and Harris (1997). Given that we used a different measure of luckiness, and a different kind of lottery task and methodology, the fact that we nevertheless replicated Smith et al.'s findings suggests that these findings reflect a robust effect.

Actual Lottery Success

Exploratory Q2 -- BIOL and Actual Lottery Success. It was decided that a correlation would not be informative for this analysis due to the large number of tied scores. A comparison between personally lucky and personally not lucky groups was conducted on the number of matches between participants' personally selected lottery numbers and the results of the lottery draws. Table 2 gives the mean number of lottery matches for lucky and not lucky participants. The difference between the groups was not significant according to a Mann-Whitney test, z = 0.695, p = .487, two-tailed.

Smith, Wiseman, and Harris (1997) recommended evaluating lottery success specifically for those participants who claimed they believed their luck would affect their lottery success. For this reason, we divided participants into three groups on the basis of their answers to Q8 of the lottery questionnaire: "Do you think your luck can affect how well you do in the lottery with personally selected numbers?" Those who answered 1, 2, or 3 (where 1 = definitely no) were categorised as not lucky, N = 33; those who answered 4 were categorized as neutral, N = 6; those who answered 5, 6, or 7 (where 7 = definitely yes) were categorised as lucky, N = 21. Table 2 gives the descriptive statistics for the lucky and not lucky participants. Participants who felt their luck could influence their lottery performance had a significantly higher number of matches than those who did not feel their luck could influence their lottery performance, z = 2.472, p = .013, two-tailed. This finding is contrary to that of the second study by Smith, Wiseman, and Harris (1997), who found no relationship between participants' beliefs that their luck could affect their lottery success and actual success (Smith et al.'s first study did not ask this question). However, our finding does mirror that of Smith, Wiseman, Machin, Harris, and Joiner's (1997) study which found a significant correlation between predicted success at a computer psi task and actual success at the task.

Exploratory Q3-BIGL and Actual Die Throwing Success. The outcome of participants' die throws was noted (they were aiming for a "6" face uppermost). Table 3 gives the descriptive statistics for the die throwing outcomes of personally lucky and personally not lucky participants (according to BIGL). One participant did not do the die throwing task due to an oversight by the experimenter, so the total N is 59. The numbers are too small to permit a reliable statistical test, but eyeballing the data it is clear that there is no tendency for lucky participants to throw more 6s than not lucky participants, even for those participants who indicate they feel their luck can influence their die throwing.

CONCLUSION

This study asked whether PMIR might be a form of "luck in action," on the basis of the argument that if luckiness is a form of psi, it would most likely operate nonintentionally, since everyday lucky events seem to occur quite spontaneously. We found no overall evidence of nonintentional psi as measured by a PMIR-type task. There was, however, marginal support for the hypothesized positive relationship between belief in good luck and nonintentional psi. The weak luck-PMIR relationship clearly needs further replication.

Considering replication and further systematic exploration of the luck-PMIR relationship, it is important to get an effective measure of PMIR. This depends, in part, on the validity of the nonintentional psi task. The post-experiment questionnaire indicates that the psi task remained unintentional. However, participants did not find the tracking task to be strongly unpleasant, and this raises a question mark over the validity of that aspect of the PMIR task. Is the task sufficiently aversive to warrant the use of nonintentional psi to avoid it? It will surely be difficult to answer this question empirically. In their previous PMIR study, Watt and Ravenscroft (2000) used the same tracking task, but the duration was 15 minutes rather than 10 minutes. The forty participants who did the tracking task in that study gave the task a mean rating of 1.3 (compared to a mean rating of 2 in the present study), which indicates that the longer task was more strongly unpleasant in the first study.

Another question concerns our method of allocating participants to the pleasant or unpleasant conditions. This was done using a binary "hit or miss" decision. However, our principal psi measure was deliberately chosen as a continuous measure, because Stanford (1976, p. 174) has suggested this might be a more sensitive measure of a disposition towards PMIR than a direct hits measure. We might also have operationalized PMIR by calculating participants' standardized rating at the time of testing and directing them to the pleasant or unpleasant task depending on this rating--so that even if they did not score a direct hit they could avoid the unpleasant task by giving a higher than average rating to the key Kanji. This method could be explored in a future study.

Future studies will have to look more systematically at the question of what makes a good PMIR task, including a comparison of different kinds and degrees of aversive experiences (within the strictures of good ethical practice) to see if the amount of nonintentional psi covaries accordingly.

We found that on two games of chance--lottery playing and die throwing--lucky participants had greater confidence of success than participants who did not consider themselves lucky, confirming the two formal hypotheses on this question. There was no difference between the personally lucky and the personally not lucky group in actual lottery playing behavior and there was no indication that lucky participants did better than not lucky participants in die throwing. However, those participants who believed that their luck could influence their lottery success did indeed have greater success at the lottery than those who did not believe their luck could influence their lottery success.

Our findings indicate that lucky participants may be more optimistic or confident of success than not lucky participants (perhaps justifiably so, given that we found signs of greater lottery success for those who believed their luck could influence their lottery success). However, the fact that lucky participants' actual mean confidence ratings were quite "neutral" on the lottery and die throwing questionnaires indicates that lucky participants are certainly not being wildly optimistic of their chances of success. Indeed, in developing the BIGL scale, Darke and Freedman (1997) found BIGL to be unrelated to measures of optimism and self-esteem. It is quite likely that confidence of success will vary depending on the nature of the task in question. We found a tendency for higher confidence with the die throwing task than with the lottery task, which may reflect an appreciation of the higher odds of success with die throwing. However, motivation for success will also be an important factor--the large monetary p rizes on offer with the UK National Lottery are likely to affect motivation. It would be interesting to see if "superstitious behavior" could be manipulated, or elicited, by varying the odds and rewards of success. There is clearly scope for further investigation of the psychology and parapsychology of luck.

(1.) An earlier version of this paper was presented at the 1999 Parapsychological Association Convention. We are very grateful to Valerie McGregor for assisting as experimenter during this study and for helping to double-cheek scoring. Thanks also to Ricardo Eppinger for randomly selecting targets and to our anonymous referees for their helpful suggestions.

(2.) Throughout this paper, we will use the terms PMIR and nonintentional psi interchangeably.

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