ABSTRACT

Previous studies have found a positive link between endorsement of paranormal beliefs and experiencing more “meaningful” coincidences (e.g., thinking of someone and then meeting them unexpectedly) and a stronger repetition avoidance bias. We tested if these effects also apply to pseudoscientific beliefs. Volunteers completed a pseudoscience endorsement scale, reported the frequency and explanations for experienced coincidences, and performed random sequence generation tasks. Higher pseudoscience endorsement was associated with more frequent meaningful coincidences and attributing them to non-chance causes. Believers also avoided consecutive repetitions more often when replicating the tossing of a coin. A regression model suggested that a lower threshold for causally connecting events and a biased representation of randomness independently contribute to pseudoscience endorsement. Our results pave the way for the development of interventions aimed at reducing pseudoscientific beliefs based on improving the interpretation of coincidences and the representation of randomness.

Being able to adequately interpret coincidences between events is of utmost importance for successful adaptation, as it is the basis for establishing reliable causal connections. Nevertheless, it is not obvious how to ascertain whether a given co-occurrence of two events meaningfully indicates a causal relationship between them or if it just reflects a random coincidence.

The general idea behind the present study is that suboptimal interpretation of coincidences might be a cognitive facilitator of pseudoscientific beliefs. The term pseudoscience refers to those disciplines which present themselves as scientific but lack the fundamental requisites to be considered as such (Fasce and Picó 2019). Pseudoscience endorsement, with a prevalence ranging between 24% and 71.3% across different countries (Lee et al. 2022), can have a significant impact on our societies, from individual decisions to public policymaking. For example, preference for health-related pseudoscience can lead to a delay in adopting a life-saving treatment or quitting an ongoing one (Wardle et al. 2014).

Understanding the factors that contribute to pseudoscience endorsement is important because it could set the basis for the design of strategies to help prevent it. Among other social- and individual-level factors, adherence to pseudoscience has been associated with certain cognitive factors such as proneness to false memory generation (Martínez et al. 2024), tendency to jump to conclusions (i.e., lower evidential criteria, or requiring less evidence before reaching a conclusion, Rodríguez-Ferreiro and Barberia 2021) or sensitivity to causal illusions (Torres et al. 2020, 2022). The latter, which is defined as the tendency to perceive a causal connection between two non-contingent events (Matute et al. 2015), is particularly relevant in relation to health-related pseudosciences, as pseudotherapies might appear effective on the basis of coincidences between the supposed treatment (i.e., the potential cause) and relief (i.e., the effect) (Barberia et al. 2019; Matute et al. 2011). For instance, imagine that you frequently have headaches. A friend recommends taking a certain homeopathic pill for pain relief, and you decide to give it a try. The first time you try it, you feel relieved and, given the co-occurrence of the two events, you end up taking the same homeopathic pill most of the times you have a headache. Since you continue experiencing relief on many occasions, you reinforce the impression that the pill is causing the relief, when in fact your headaches would disappear spontaneously without the pill.

Indeed, the variability regarding the importance that different individuals give to coincidences for causal connection has already been associated with other types of beliefs directly related to pseudoscientific ones, that is, paranormal beliefs (Bressan 2002; Brugger et al. 1990). Both are considered, along with conspiracy theories, types of epistemologically unwarranted beliefs (Lobato et al. 2014). The distinction between pseudoscientific beliefs (e.g., the belief in the efficacy of homeopathy) and paranormal ones (e.g., the belief that black cats bring bad luck) is that the latter relates to aspects outside the realm of science and/or does not claim to be considered scientific knowledge (Fasce and Picó 2019). Despite this conceptual disparity, adherence to different types of epistemologically unwarranted beliefs correlates positively, which could suggest that they have, at least in part, a common psychological substrate (Lobato et al. 2014; Torres et al. 2023).

In a fundamental study for the present research, Brugger et al. (1990) investigated whether believers in the paranormal presented a more biased representation of randomness than skeptics, which could influence their interpretation of coincidences. Humans are known to be suboptimal in our understanding of chance (though see Warren et al. 2018), as evidenced, for example, by falling into the gambler’s or hot hand fallacies (e.g., Ayton and Fischer 2004). In their seminal study of the representation of randomness, Kahneman and Tversky (1972) argued that our randomness judgments are based, not on objective probability, but on a representativeness heuristic. Specifically, we tend to expect global characteristics of random sequences to manifest at the local level. Thus, for binary outcome scenarios, subsequences containing equal proportions of each outcome and those with higher outcome alternation rates are more likely considered random than those with unequal proportions of each outcome and those with lower alternation rates, respectively (see also a third criterion termed “lack of internal structure”, which builds upon the previous two, Kahneman and Tversky 1972).

Brugger et al. (1990) showed that, compared to skeptics, believers in the paranormal presented a stronger tendency to avoid repetition (i.e., higher alternation) when generating sequences of purportedly random outcomes (see also Brugger et al. 1995, for a conceptual replication and extension of these findings, but Blackmore and Trościanko 1985, for prior conflicting results). Assuming that humans judge randomness based on a representativeness heuristic, this observation can be interpreted to reflect that believers’ representation of randomness relies (more) on the presence of alternation. Moreover, believers also reported having experienced a greater frequency of personally meaningful coincidences in their daily lives. In the light of these observations, and assuming that believers and skeptics actually experience a similar amount of coincidences, Brugger et al. (1990) argued that biased representation of randomness could be responsible for underestimating the probability that a given pairing of events occurs by chance, leading believers in the paranormal to look for causal (supernatural) explanations to interpret such coincidences (cf. Blackmore 1997).

In a further study, Bressan (2002) replicated the associations between paranormal belief endorsement and both frequency of experienced coincidences (see also Rominger et al. 2011, 2022) and repetition avoidance (also partially by Lesaffre et al. 2018; but not by Mohr et al. 2014). Nevertheless, she did not find evidence for a link between the last two measures (see also Rominger et al. 2011). Bressan suggested that both phenomena could stem from a general tendency for believers to seek meaning. On the one hand, reporting having experienced a higher frequency of meaningful coincidences would naturally result from proneness to seek meaning (i.e., overinterpreting patterns) in sequences of events. This conclusion aligns with the fact that believers among Bressan’s sample tended to attribute non-chance origins to their experienced coincidences to a greater extent than skeptics. On the other hand, oversensitivity to patterns would lead to pattern avoidance when trying to simulate randomness. Bressan’s interpretation is also congruent with studies showing a more pronounced tendency for believers to see meaningful patterns in visual noise (Blackmore and Moore 1994; Brugger et al. 1993) and, generally, to require less evidence before reaching a conclusion (Brugger and Graves 1997), also observed in believers in pseudoscience (Rodríguez-Ferreiro and Barberia 2021).

All in all, whereas Brugger et al. (1990) interpreted believers’ repetition avoidance and heightened perception of coincidences as evidence of probability misjudgments leading to a stronger tendency to attribute non-random causes to paranormal events, Bressan (2002) proposed that both phenomena stem from a broader cognitive tendency to seek meaning. For this study, we presented volunteers ranging on their endorsement of pseudoscientific beliefs with a questionnaire measuring the frequency and attributed cause of experienced meaningful coincidences in their daily lives, as well as random sequence generation tasks. Following Brugger et al. (1990) and Bressan (2002), we expected pseudoscience endorsement to be positively associated with the frequency of meaningful coincidences and non-chance explanations for them. Moreover, we foresaw believers to present an increased repetition avoidance bias. The use of pseudosciences in the current study is especially relevant because the identification of such associations would go against the idea that this tendency is tied to a preference for the supernatural, which does not play a central role in pseudoscientific disciplines, and support alternative explanations, such as those assuming underlying, general, cognitive biases influencing coincidence interpretation.

1 Methods

1.1 Participants

A group of 108 Psychology students of the University of Barcelona took part in the experiment (85 females, 18 males, mean age 22.22, SD 4.36; five participants preferred not to respond to the demographic questions). We gathered informed consent prior to data collection. The study protocols were approved by the university ethics committee (Institutional Review Board IRB00003099).

1.2 Pseudoscience Endorsement Scale

The Pseudoscience Endorsement Scale (Torres et al. 2020) consists of 20 items referring to popular pseudoscientific myths and disciplines. Each item (see Supporting Information) consisted of a statement that the participants are asked to rate on a scale from 1 (i.e., “Totally disagree”) to 7 (i.e., “Totally agree”). Higher scores on this measure indicate greater endorsement of pseudoscientific beliefs. The dependent variable is the mean score obtained in the scale, with values ranging between 1 and 7.

1.3 Questionnaire on Coincidences

Following Bressan (2002), we used the Questionnaire on Coincidences (QC), which is based on a previous survey on coincidence experiences by Henry (1993). The questionnaire consists of different items concerning the frequency of “curious or meaningful” coincidences experienced in general (i.e., the single item used by Brugger et al. 1990) and specifically falling into different categories (items 2 to 8: series of names or numbers, spontaneous associations, “small-world” experiences, perception of something distant in space, perception of something distant in time, unexpected solution of a problem, “guardian angel” experiences). The participants respond using a numerical scale ranging from 1 (“never”) to 5 (“very often”). Finally, the volunteers are asked which they think is/are the cause/s of these coincidences (with the response options “Yes”, “Don’t Know”, “No”) among different options: pure chance, destiny, divine intervention, extra-sensory perception (ESP), intuition, an undiscovered physical principle, and universal connection. The dependent variables are the response to the general question and the mean of the responses to the specific questions, with values ranging between 1 and 5, as well as the causes attributed to the reported coincidences.

We translated the QC into Spanish following a common translation and back-translation procedure. First, a native Spanish speaker of advanced English proficiency, one of the authors, translated the English version into Spanish. Then, an English-native bilingual professional translator back-translated the Spanish version. Finally, the two translators discussed minor differences revealed by comparing the two versions until reaching agreement. The complete Spanish version of the questionnaire and an English version can be found in the Supporting Information.

1.4 Coins

The volunteers viewed 66 pairs of images, one of them showing the head and the other one showing the tail of a 1€ coin. We instructed them to click on one of the two images in each pair. Following Bressan (2002), the participants were instructed to “simulate the tossing of a coin, by selecting the head or the tail randomly, so as to make the resulting sequence as indistinguishable as possible from that of an actually tossed coin.” The dependent variable is the “repetition proportion”, that is, the proportion of consecutive repetitions ([head, head] or [tail, tail]). The actual Spanish wording used in the experiment is presented in the Supporting Information.

1.5 Dice

The participants viewed 66 groups of six images showing the different sides of a die in ascending order. They were asked to click on one of the six images in each group. Following previous studies (Bressan 2002; Brugger et al. 1990), the participants were instructed to “make the resulting sequence as indistinguishable as possible from that of an actually rolled dice.” As in the coins task, the dependent variable is the proportion of consecutive repetitions (e.g., [1, 1]; [2, 2]). The Spanish version of the instructions can be found in the Supporting Information.

1.6 Procedure

The questionnaires and the randomness tasks were presented through Qualtrics. All the participants were in the same room, and they completed the experiment individually from different cloned desktop computers. The PES was presented first to all the volunteers. Then, the two randomness tasks (dice and coins) and the QC were presented in random order.

2 Results

Data for this study is available at https://osf.io/guktm. Results were analyzed with JASP 0.19. Analysis of PES responses, mean = 3.3, SD = 0.97, indicated excellent reliability, ω = 0.92. As for the QC, mean = 2.6, SD = 0.56, ω = 0.7, responses indicated that the different kinds of coincidences were experienced, on average, between “once or twice” and “a few times”. Responses to the general question (i.e., item 1) indicated higher frequency, mean = 3.4, SD = 0.66, t(107) = 13.679, p < 0.001, d = 1.32, between “a few times” and “many times”. Possible causes of the coincidences ordered by selection percentage were: pure chance, 69%; intuition, 57%; destiny, 29%; universal connection, 20%; ESP, 11%; an undiscovered physical principle, 10%; divine intervention, 3%.

Given that the responses to the different possible causes were not mutually exclusive (i.e., the questionnaire allowed participants to respond “Yes” to all the possible explanations presented), we assessed response patterns by means of a series of χ2 analyses exploring possible links between responses to the chance question and to all the other questions suggesting other explanations. We obtained significant results for all of them, χ2 < 13.304, ps ≤ 0.01, except for ESP, χ2 = 6.031, p = 0.197, and intuition, χ2 = 3.303, p = 0.508. The identified associations showed a general tendency for those who respond “Yes” to the chance question to respond “No” to the other causes. Moreover, the amount of non-chance responses selected by the participants, mean = 1.3, SD = 1.36, positively correlated with their frequency of reported coincidences, r = 0.282, p = 0.017.

With regards to the randomness representation tasks, our participants showed evidence of a repetition avoidance bias, as indicated by significant differences between repetition proportions expected by chance and mean observed repetition proportions (coins: expected = 0.5, mean = 0.44, SD = 0.14, t(107) = −4.385, p < 0.001, d = −0.42; dice: expected = 0.17, mean = 0.12, SD = 0.15; t(107) = −3.380, p = 0.001, d = −0.33; repetition proportions in the two tasks correlated at r = 0.610, p < 0.001).

As for the associations between the responses to the different tasks, PES scores positively correlated with mean QC scores, r = 0.282, p = 0.003 (r = 0.264, p = 0.006, for the general question), indicating that individuals with stronger endorsement of pseudoscientific beliefs were also more prone to report a higher frequency of meaningful coincidences in their daily lives (i.e., an average of the responses to the seven types of coincidences). Moreover, the amount of non-chance explanations selected (i.e., “Yes” response) on the qualitative questions regarding possible causes of such coincidences also correlated with pseudoscience endorsement, r = 0.437, p < 0.001 (see Figure 1). Neither the frequency of reported coincidences (mean QC scores) nor the amount of non-chance explanations correlated with repetition proportions in the coin task, r ≤ 0.119, p ≥ 0.221. The association between repetition proportions in the dice task and frequency of coincidences barely reached the significance threshold, r = −0.195, p = 0.043, but that with the amount of non-chance explanations did not, r = 0.097, p = 0.318.

Scatterplot showing the association between frequency of experienced coincidences (mean responses to the specific QC questions), amount of non-chance explanations selected in the qualitative questions and pseudoscientific belief endorsement (mean PES scores).

In a similar vein, an ANOVA with PES scores as the dependent variable and the response given to the chance question of the cause questionnaire as the independent variable indicated significant differences in the level of endorsement of pseudoscientific beliefs of the volunteers depending on their response (“Yes”, “Don’t know”, or “No”), F(2, 105) = 7.340, p < 0.001. Tukey-corrected post hoc comparisons indicated significant differences between those responding “Yes” and both “No”, p = 0.002, and “Don’t Know”, p = 0.011; but not between these last two groups, p = 0.723 (see Figure 2). The relationship with PES scores went in the opposite direction for the rest of the possible causes, ps ≤ 0.002, except for intuition, which generated no significant differences, p = 0.135. Note, however, that the distributions of volunteers choosing each of the response options changed drastically between questions, ranging from a distribution of 91% of “No” responses, 6% of “Don’t Know” responses, and 3% of “Yes” responses for the divine intervention question to 13% of “No” responses, 18% of “Don’t Know” responses, and 69% of “Yes” responses for the pure chance question.

Bar plot showing means and standard errors of Pseudoscience Endorsement Scale scores for each type of response to the qualitative questions, as well as percentages of respondents selecting them.

The correlation between PES scores and repetition proportions in the dice task was not significant, r = −0.091, p = 0.351. In contrast, PES scores were negatively correlated with repetition proportions in the coins task, r = −0.22, p = 0.022 (see Figure 3). Differences between the results obtained with regards to the two sequence generation tasks could be due to a floor effect on the dice task, in which the repetition proportions were very low (with 25th and 75th percentiles being 0.05 and 0.14, respectively), compared to the coins task, in which the repetition proportions were much higher (with 25th and 75th percentiles being 0.37 and 0.48, respectively). The restricted number of repetitions observed in the dice task, which might stem naturally from the greater number of alternative outcomes in a die compared to a coin (6 instead of 2), might have hindered our capacity to detect a significant association with scores on the pseudoscience scale.

Scatterplot showing the association between pseudoscientific belief endorsement and repetition proportions on the coins and dice tasks.

An additional regression model over PES scores, including mean QC frequency scores and the amount of non-chance causes selected, as well as repetition proportions in each randomness task as predictors, R2 = 0.295, showed main contributions of QC non-chance causes, β = 0.421, p < 0.001; and coin repetition, β = −0.303, p = 0.005, along with a smaller effect of mean QC frequencies, β = 0.178, p = 0.046, and no effect of dice repetition, β = 0.092, p = 0.388.

3 Discussion

Following previous studies addressing possible cognitive facilitators of paranormal beliefs, we assessed whether greater endorsement of pseudoscience is associated with reporting greater amounts of meaningful coincidences in daily life and/or a stronger repetition avoidance when generating random sequences.

As for reports of meaningful coincidences, we extended previous observations (Bressan 2002; Brugger et al. 1990; Rominger et al. 2011, 2022) to the field of pseudoscientific beliefs by confirming a positive association between belief endorsement and reported frequency of experienced meaningful coincidences. The effect was observed both with regard to responses to a question generally asking about these kinds of coincidences (Brugger et al. 1990) and to averaged responses to questions referring to specific examples (Bressan 2002).

Moreover, when asked to select possible causes of such coincidences, participants considering chance a plausible cause for the coincidences appeared to be more skeptical than those uncertain or the ones rejecting this possibility. The opposite pattern was generally observed with regard to destiny, divine intervention, ESP, an undiscovered physical principle, and universal connection, as those who selected these as plausible causes for the coincidences endorsed pseudoscience to a greater extent. In contrast, no differences were observed in relation to intuition. The absence of differences regarding this last explanation might be related to the lack of a shared definition of the concept of intuition among participants. For instance, different individuals might understand it as some sort of spiritual force, as a feeling-based hunch, or as the result of associative learning. Importantly, the amount of non-chance causes selected on the coincidences questionnaire was strongly associated not only with the frequency of reported coincidences but also with pseudoscience endorsement.

Hence, the observed results corroborate that believers in pseudoscience tend to attribute supernatural explanations to curious coincidences such as “thinking of someone and running unexpectedly into that person afterwards” or “worrying about a person at the exact time in which that person is having an accident”. In the study by Bressan (2002), the association between such kinds of explanations and paranormal beliefs could be argued to be a tautological finding, in the sense that it shows that believers in the paranormal are those who believe that certain events have paranormal causes (such as precognitive or ESP abilities in the aforementioned examples). Nevertheless, in our view, the fact that this pattern of results already described with paranormal beliefs is replicated with regards to pseudoscientific ones reinforces the idea that the observed association could be indicative of a general cognitive tendency, rather than a domain-specific preference for supernatural explanations.

We also observed an association between randomness representation and pseudoscientific beliefs, as volunteers with a stronger endorsement of pseudoscience also presented a stronger repetition avoidance bias in a random sequence generation task. These results corroborate previous observations with regard to paranormal beliefs (Bressan 2002; Brugger et al. 1990; Lesaffre et al. 2018) and suggest a link between the tendency to accept pseudoscience and a biased understanding of chance.

Crucially, when entered simultaneously into a regression model, the amount of non-chance causes attributed to meaningful coincidences in the QC and the outcome alternation produced on the coins task appeared to be the main contributors to pseudoscientific belief endorsement, suggesting that proneness to seek meaning and biased representation of randomness could represent two independent contributors to pseudoscience.

Brugger et al. (1990) suggested that an underestimation of the probability of cooccurrences between events in some individuals could be influencing the interpretation of certain coincidences as meaningful, thus prompting them to come up with alternative (i.e., non-chance) explanations for their observations. Bressan then suggested that both a higher number of coincidences and a stronger repetition avoidance bias in believers could stem from an increased tendency to seek meaning in given information. Thus, believers would be more inclined to identify meaning/patterns in observed data, leading them to more easily establish causal connections between events and then look for putative explanations (other than pure chance). As previously stated, this could stem from a more liberal decision criteria or a tendency to jump to conclusions (see also Rodríguez-Ferreiro and Barberia 2021). In addition, this increased sensitivity to pattern identification would also lead them to avoid repetition when attempting to generate a supposedly random sequence.

In contrast, given that, in our study, the amount of non-chance explanations and repetition avoidance appeared to independently predict belief endorsement, we propose that they could be representing separate sources of influence to belief generation. First, more frequent reports of experienced coincidences and, crucially, an increased tendency to attribute non-chance explanations to those coincidences could be reflecting a stronger tendency to seek meaning. Going back to the example of the homeopathic pill presented in the introduction, in order to adequately assess whether the pill is actually effective, we should try to ascertain whether the probability of relief after intake is higher than the probability of relief without intake (i.e., higher than spontaneous recovery by chance). Nevertheless, it might be the case that some individuals are more prone to look for a non-chance cause when encountering relevant cooccurrences of events (i.e., coincidences between pill intake and relief in our example, or “cell A” information in the words of Arkes and Harkness 1983).

Second, a biased representation of chance (i.e., overreliance on alternation at the local level to assess randomness) could be influencing pseudoscience endorsement through differential relevance given to the order of outcome occurrences in a sequence. For instance, when assessing whether the homeopathic pill is effective, and assuming a certain degree of spontaneous remission, some individuals could be more inclined to perceive a causal link after being exposed to healing outcomes appearing in a row than when they appear intermixed with non-healing (even when the total proportion of healing outcomes is maintained equal).

As for the limitations of the present study, it is worth mentioning that participants were not hinted about any specific interpretation of the term “curious and meaningful coincidences” before answering the QC (Bressan 2002). Moreover, the QC might be considered to some extent circular as a tool to evaluate experienced meaningful coincidences. This is due to the two-steps nature of the test, in which participants initially recall the amount of experienced meaningful coincidences and they are subsequently asked to interpret the extent to which these coincidences are meaningful (i.e., by indicating the reasons for such coincidences, and including “pure chance” as an option). To this respect, it is not clear how the two steps might be combined (e.g., a person who indicates having experienced “curious or meaningful coincidences” very often, but then attributes those frequent experiences only to pure chance). Future studies might consider refining the questionnaire, first, clarifying the relevant terms and, second, integrating (instead of separately considering) both recalling and interpretation of coincidences.

Moreover, given the characteristics of our convenience sample of western Psychology students, any generalization of our results to other populations should be done with caution. Future studies could try to extend our findings to other contexts, especially considering the differences between cognitive contributors to unwarranted beliefs among individuals from different cultures observed in the past (Majima et al. 2022).

All in all, our study extends previously observed associations between belief in the paranormal, increased experience of coincidences, and repetition avoidance to the field of pseudoscientific beliefs. Interestingly, our results pave the way for the development of interventions aimed at reducing pseudoscientific beliefs based on improving the interpretation of coincidences (e.g., advising against jumping to conclusions after being exposed to single pairings of events) and the representation of randomness (e.g., preventing the use of outcome repetition as a reliable cue to assess lack of randomness).

Author Contributions

Javier Rodríguez-Ferreiro: conceptualization, methodology, software, data curation, supervision, resources, project administration, formal analysis, validation, investigation, funding acquisition, visualization, writing – review and editing, writing – original draft. Nia Pangani: writing – original draft, formal analysis, data curation. Itxaso Barberia: conceptualization, writing – review and editing, funding acquisition.

Acknowledgments

The study was supported by grant PID2022-138016NB-I00, funded by MICIU/AEI/10.13039/501100011033, FEDER/UE, and grant 2021 SGR 01102 funded by AGAUR.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data generated for this study is accessible at https://osf.io/guktm/?view_only=4f5d32ae38294fc4ba139e4c25f7c567.

References