knitr::opts_knit$set(root.dir = "~/Documents/GitHub/vanprooijen2018")Replication of Study 2 by van Prooijen et al. (2018, European Journal of Social Psychology)
Introduction
Justification
My research interests lie in how people process and trust information in complex media environments. One phenomenon I am especially interested in is why some individuals find misleading claims compelling. Work demonstrates that illusory pattern perception - the tendency to perceive meaning or structure in randomness - may help explain people’s openness to pseudo-profound statements (Walker et al., 2019). van Prooijen et al. (2018) provide one of the few studies that experimentally manipulate pattern perception itself. In Study 2, the authors induced participants to rely either on intuition and pattern search or on analytic reasoning while evaluating random sequences of coin tosses. Those encouraged to rely on intuition perceived more structure in randomness and, in turn, reported stronger irrational beliefs. I am interested in understanding why some individuals perceive hidden structure or meaning in randomness and how this tendency relates to belief in conspiracy theories and misinformation.
I selected Study 2 particularly because it offers a direct causal test of the relationship between intuitive pattern search and belief formation - an ideal foundation for later work examining how heightened pattern perception might make people more receptive to misinformation or “bullshit” statements. Whereas other paradigms manipulate control or uncertainty to elicit pattern detection indirectly, this study isolates the pattern-perception process itself.
Given that the literature connecting illusory pattern perception to conspiracy beliefs has already produced mixed results, a careful replication of this paradigm can provide valuable clarity about the reliability and boundary conditions in this sphere. This replication contributes not only to my own program of research but also to broader efforts to assess the reproducibility of psychological findings about belief formation and illusory pattern perception.
Stimuli and Procedures
Participants completed a short task involving random coin-toss sequences, followed by ratings of perceived structure and measures of irrational belief.
The key result I hope to replicate is that participants instructed to use intuitive pattern search perceive more structure in random sequences than those instructed to analyze logically, and that higher pattern perception is correlated with stronger endorsement of irrational beliefs (e.g., conspiracy/supernatural).
Pattern-Search Instructions (Manipulation). Participants were randomly assigned to one of two instruction sets: a high pattern-search (intuitive) condition that encouraged relying on “gut feelings” and actively looking for meaningful patterns, or a low pattern-search (analytic) condition that emphasized logical, non-intuitive analysis.
Random Sequence Task (Pattern-Perception Measure). All participants viewed a series of randomly generated coin-toss sequences. After each sequence, they rated how structured or meaningful it appeared on a 1-7 scale (1 = completely random; 7 = clear pattern).
Belief Measures. Participants then completed short conspiracy and supernatural belief scales (Likert ratings of agreement with statements).
For this replication, I will recreate the same structure using Qualtrics and a Prolific participant pool. Primary challenges will be ensuring that the stimuli work reliably online and that participants stay attentive throughout the task.
Links
Methods
Power Analysis
A power analysis to achieve 80% power was conducted using G*Power (using an original effect size of η² = .04 that was converted and rounded to an effect size f = 0.2). This gives a sample size of 200 participants, but the planned sample size is n = 223 to fully replicate the size of the original study.
Planned Sample
223 U.S. adults recruited from Prolific (only pre-screen criteria was an approval rating on Prolific of 95% and above).
Materials
Link to experiment: https://stanforduniversity.qualtrics.com/jfe/form/SV_6DytqtdUq1o5Tgi
Procedure
Procedure from van Prooijen et al. (2018) was followed exactly:
“The study was presented as consisting of two parts. In the first part, participants were asked to play a “coin tossing game”. They saw the outcomes of 10 sequences of 10 coin tosses—these sequences were identical to those used in the pattern perception measure of Study 1. The first of these sequences was presented as an example; the “real” coin tossing game consisted of the remaining nine sequences.
For each sequence, participants’ task was to guess what the next coin outcome would be (Heads or Tails). Within this context, we manipulated intuitive pattern search. In the high pattern search condition, participants received the following instruction before starting the game: “Try to see if you can find a pattern in each sequence. Do NOT try to calculate this—use your intuition. Ask yourself: ‘Do I see a pattern here—and based on that, what next coin outcome would make most sense?’” In the low pattern search condition, participants received the following instruction: “These are random sequences, generated by the website http://random.org. In a particular sequence there may be more Heads or Tails; this is to be expected when a sequence is random. Each coin toss is independent and has an exact probability of 50% of being a Head or a Tail.” After completing the game, we assessed participants’ pattern perception with the following item: “To what extent were the coin flip sequences random, or showed a pattern?” (1 = they were totally random, 7 = they totally showed a pattern). Furthermore, we assessed participants’ current mood on a slider ranging from 1 (very negative) to 100 (very positive) as a filler task and also as a means to test whether the effects of the intuitive pattern search manipulation are attributable to mood effects.
Participants then started the second part of the study, in which they responded to a series of statements. Here, we measured belief in existing conspiracy theories (α = .84), belief in fictitious conspiracy theories (α = .86), and supernatural beliefs (α = .94) with the same scales as in Study 1. Upon completion of the questionnaire, participants were thanked and debriefed.”
Analysis Plan
The key analysis found in Study 2 is as follows:
“An ANOVA on the pattern perception measure revealed a significant effect of the intuitive pattern search manipulation, F(1, 179) = 8.26, p = .005; η2 = .04. Participants in the high pattern search condition detected clearer patterns in the random sequences (M = 4.03, SD = 1.64) than participants in the low pattern search condition (M = 3.32, SD = 1.71). These findings indicate that the manipulation successfully influenced the extent to which participants perceived patterns in the coin toss sequences.”
Additional analyses from Study 2 will be analyzed as well:
“A MANOVA on the three dependent variables yielded no significant multivariate or univariate effects, all Fs < 1. Contrary to predictions, the intuitive pattern search manipulation did not exert a direct effect on the dependent variables.
As noted above, however, the manipulation did influence the extent to which participants perceived patterns in the coin toss outcomes. Furthermore, consistent with Study 1, we found that the pattern perception measure was significantly correlated with belief in existing conspiracy theories (r = .23, p = .002), belief in fictitious conspiracy theories (r = .29, p < .001), and magical ideation (r = .32, p < .001). Given that we predicted the manipulation to influence irrational beliefs because of its effects on people’s tendency to see patterns in the sequences, we tested the indirect effect of the intuitive pattern search manipulation (effect‐coded: 1 high pattern search, −1 low pattern search) on irrational beliefs through pattern perception. As indicated by the fact that 0 was not in the 95% confidence interval, bootstrapping analyses (5000 samples) utilizing the “MEDIATE” macro by Hayes and Preacher (2014) revealed a significant indirect effect on all three dependent variables: for belief in existing conspiracy theories, (B = 0.04, SE = 0.02) CI95%[0.01; 0.09], for belief in fictitious conspiracy theories (B = 0.05, SE = 0.02) CI95%[0.02; 0.11], and for supernatural beliefs (B = 0.05, SE = 0.02) CI95%[0.01; 0.10]. These findings suggest that whereas the intuitive pattern search manipulation did not exert a direct effect on irrational beliefs, it did exert an indirect effect on all three dependent variables through pattern perception.
Although the lack of a direct effect precludes conclusions about causality, the findings of the present study suggest that intuitively searching for patterns in the coin toss sequences increases pattern perception, which in turn predicts irrational beliefs. As such, the indirect effect that we observed in Study 2 further supports a role for pattern perception in belief in conspiracy theories and supernatural beliefs.”
“The intuitive pattern search manipulation did not influence participants’ mood, F < 1. Hence, the results relating to irrational beliefs are not attributable to variations in participants’ mood.”
Differences from Original Study
The original paper uses a sample run online through the Crowdflower forum on a U.S. sample, while this study recruits participants from Prolific. The original paper also dropped 42 participants for the main analysis (unclear as to why since this is not clarified anywhere).
Methods Addendum (Post Data Collection)
Actual Sample
n = 223 U.S. adults recruited from Prolific.
No participants were excluded. The sample was broadly distributed across age (with the largest proportions aged 25–34 and 35–44), sex (52.9% female; 45.8% male), and was politically diverse, with 47.1% identifying as Democrats, 32.2% as Republicans, and 18.9% as Independents.
Differences from pre-data collection methods plan
None.
Results
Data preparation
### data preparation
library(tidyverse)Warning: package 'tibble' was built under R version 4.3.3── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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✔ lubridate 1.9.2 ✔ tidyr 1.3.0
✔ purrr 1.0.2
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(mediation)Loading required package: MASS
Attaching package: 'MASS'
The following object is masked from 'package:dplyr':
select
Loading required package: Matrix
Attaching package: 'Matrix'
The following objects are masked from 'package:tidyr':
expand, pack, unpack
Loading required package: mvtnorm
Loading required package: sandwich
mediation: Causal Mediation Analysis
Version: 4.5.0df <- read.csv("data/PSYCH 251 Replication_December 5, 2025_11.32-anon.csv")
### data exclusion / filtering
names(df) <- make.names(names(df))
stopifnot(all(c("Finished","QID1185","Q11","Q32","Q52_1") %in% names(df)))
#### existing conspiracy belief items: Q147_1–Q147_9
exist_cols <- paste0("Q147_", 1:9)
#### fictitious conspiracy belief items: Q61_1–Q61_9
fict_cols <- paste0("Q61_", 1:9)
#### supernatural belief items: Q62_1–Q62_30
super_cols <- paste0("Q62_", 1:30)
d <- df %>%
filter(as.logical(Finished) == TRUE) %>%
filter(tolower(trimws(QID1185)) %in% c("yes","y","true","1"))
#### drop the data from friends in pilots
drop_ids <- c("R_1liTJPYAoikbwhU", "R_1Qmr1xstM6JpSYb", "R_64w2157Kz9bsjqa",
"R_6FR4OAFpcZdyD3k", "R_3SeQxLORbYzjQN4","R_7kL1ACZPfz9rbcs",
"R_3AFX4LwXrljWHIZ", "R_7mOfv2ExW0w7sCB", "R_6JL50stmvNPPtuy",
"R_7JpQKNTqNFrnklj", "R_5FfHfOV3nyFznaB", "R_3xvtrU0slmNfzkl",
"R_6oHJj6XoQTL8tjI", "R_3DkUBNSwPjJYXCx", "R_6sT1jlx2gMUSAsZ",
"R_3xQdnhEeqHBgurg", "R_5EMFymcxI6cP46X", "R_6pSYCAZ6T51Ew0x",
"R_1nVDozRCmfZm7r7", "R_1kCaOpobkDyCjk4", "R_7ypvG8EQ4odXSfc",
"R_1ekQ49CnQzZoEZh", "R_5tbN9M9sPl8C6Fr", "R_12okXl4lCtnUlUD")
d <- d %>%
filter(!ResponseId %in% drop_ids)
d <- d %>%
mutate(Condition = case_when(tolower(trimws(condition)) == "high" ~ "High pattern search",
tolower(trimws(condition)) == "low" ~ "Low pattern search",
TRUE ~ NA_character_),
Condition = factor(Condition,
levels = c("Low pattern search", "High pattern search")),
# 0/1 coding for mediation
HPS_num = ifelse(Condition == "High pattern search", 1, -1)) %>%
filter(!is.na(Condition))
#### pattern perception measure (main DV)
d <- d %>%
mutate(PatternPerception = (as.numeric(Q52_1)))
#### coding irrational belief scales
lkrt_map <- c("definitely not true" = 1,
"probably not true" = 2,
"unsure" = 3,
"probably true" = 4,
"definitely true" = 5)
recode_belief <- function(x) {
x_chr <- tolower(trimws(as.character(x)))
as.numeric(unname(lkrt_map[x_chr]))}
d <- d %>%
mutate(across(all_of(c(exist_cols, fict_cols, super_cols)), recode_belief),
# existing conspiracy beliefs (Q147_* scale)
ExistingConspiracyBeliefs =
rowMeans(across(all_of(exist_cols)), na.rm = TRUE),
# fictitious conspiracy beliefs (Q61_* scale)
FictitiousConspiracyBeliefs =
rowMeans(across(all_of(fict_cols)), na.rm = TRUE),
# supernatural beliefs (Q62_* scale)
SupernaturalBeliefs =
rowMeans(across(all_of(super_cols)), na.rm = TRUE))### demographics
d$sex <- d$QID1158
d$age <- d$QID1157
d$race <- d$QID1154
d$education <- d$QID1155
d$income <- d$QID1156
d$polparty <- d$QID1215065339
d$repstrength <- d$QID1215065340
d$demstrength <- d$QID1215065341
d$independent <- d$QID1215065342
#### age summary
age_dist <- d %>%
count(age) %>%
mutate(percent = 100 * n / sum(n))
age_dist age n percent
1 18-24 years old 5 2.202643
2 25-34 years old 53 23.348018
3 35-44 years old 53 23.348018
4 45-54 years old 49 21.585903
5 55-64 years old 37 16.299559
6 65+ years old 30 13.215859#### sex summary
d %>%
count(sex) %>%
mutate(percent = 100 * n / sum(n)) sex n percent
1 Female 120 52.8634361
2 Male 104 45.8149780
3 Non-binary / third gender 2 0.8810573
4 Prefer not to say 1 0.4405286#### party summary
d %>%
count(polparty) %>%
mutate(percent = 100 * n / sum(n)) polparty n percent
1 Democrat 107 47.136564
2 Independent 43 18.942731
3 No preference 4 1.762115
4 Republican 73 32.158590Confirmatory analysis
### main analysis
#### condition on pattern perception (ANOVA and manual calculation of effect size)
print(summary(aov(PatternPerception ~ Condition, data = d))) Df Sum Sq Mean Sq F value Pr(>F)
Condition 1 55.6 55.60 15.34 0.000119 ***
Residuals 225 815.6 3.62
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(t.test(PatternPerception ~ Condition, data = d, var.equal = TRUE))
Two Sample t-test
data: PatternPerception by Condition
t = -3.9165, df = 225, p-value = 0.0001192
alternative hypothesis: true difference in means between group Low pattern search and group High pattern search is not equal to 0
95 percent confidence interval:
-1.4878641 -0.4917974
sample estimates:
mean in group Low pattern search mean in group High pattern search
3.159292 4.149123 a <- aov(PatternPerception ~ Condition, data = d)
ss <- summary(a)[[1]][,"Sum Sq"]
eta_partial <- ss[1] / (ss[1] + ss[2])
eta_partial[1] 0.06382082d %>%
group_by(Condition) %>%
summarise(
n = n(),
mean = mean(PatternPerception, na.rm = TRUE),
sd = sd(PatternPerception, na.rm = TRUE)
)# A tibble: 2 × 4
Condition n mean sd
<fct> <int> <dbl> <dbl>
1 Low pattern search 113 3.16 2.09
2 High pattern search 114 4.15 1.69# main plot (effect of condition on pattern perception)
mean_se <- function(x) {
n <- length(x)
mean <- mean(x)
se <- sd(x) / sqrt(n)
return(c(y = mean, ymin = mean - se, ymax = mean + se))
}
d %>%
ggplot(aes(Condition, PatternPerception)) +
stat_summary(fun = mean, geom = "point") +
stat_summary(fun.data = mean_se, geom = "errorbar", width = 0.1) + labs(y = "Pattern Perception (1-7)", x = "Instruction Condition", color = "Condition", title = "Pattern Perception by Condition", subtitle = "SE Bars") + theme_bw()
An ANOVA on the pattern perception measure revealed a significant effect of the intuitive pattern search manipulation, F(1, 225) = 15.34, p < .001, η² = .064. Participants in the high pattern search condition detected clearer patterns in the random sequences (M = 4.15, SD = 1.69) than participants in the low pattern search condition (M = 3.16, SD = 2.09). These findings replicate and extend the original effect reported by van Prooijen et al. (2018), who found a significant but smaller effect of the same manipulation, F(1, 179) = 8.26, p = .005, η² = .04, with higher pattern perception in the high pattern search condition (M = 4.03, SD = 1.64) than in the low pattern search condition (M = 3.32, SD = 1.71).
Exploratory analyses
### exploratory analyses
#### correlations (between pattern perception and diff. belief scales)
print(cor.test(d$PatternPerception, d$ExistingConspiracyBeliefs,
use = "pairwise.complete.obs"))
Pearson's product-moment correlation
data: d$PatternPerception and d$ExistingConspiracyBeliefs
t = 1.1001, df = 225, p-value = 0.2725
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.05761759 0.20143686
sample estimates:
cor
0.07314327 print(summary(lm(ExistingConspiracyBeliefs ~ PatternPerception, data = d)))
Call:
lm(formula = ExistingConspiracyBeliefs ~ PatternPerception, data = d)
Residuals:
Min 1Q Median 3Q Max
-1.7121 -0.5700 0.1096 0.4739 2.0295
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.49505 0.11691 21.34 <2e-16 ***
PatternPerception 0.03101 0.02818 1.10 0.272
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.8319 on 225 degrees of freedom
Multiple R-squared: 0.00535, Adjusted R-squared: 0.0009293
F-statistic: 1.21 on 1 and 225 DF, p-value: 0.2725print(cor.test(d$PatternPerception, d$FictitiousConspiracyBeliefs,
use = "pairwise.complete.obs"))
Pearson's product-moment correlation
data: d$PatternPerception and d$FictitiousConspiracyBeliefs
t = 2.4135, df = 225, p-value = 0.0166
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.02925253 0.28321324
sample estimates:
cor
0.1588595 print(summary(lm(FictitiousConspiracyBeliefs ~ PatternPerception, data = d)))
Call:
lm(formula = FictitiousConspiracyBeliefs ~ PatternPerception,
data = d)
Residuals:
Min 1Q Median 3Q Max
-1.54157 -0.52307 -0.07245 0.58188 2.70532
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.23295 0.10608 21.049 <2e-16 ***
PatternPerception 0.06172 0.02557 2.414 0.0166 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.7548 on 225 degrees of freedom
Multiple R-squared: 0.02524, Adjusted R-squared: 0.0209
F-statistic: 5.825 on 1 and 225 DF, p-value: 0.0166print(cor.test(d$PatternPerception, d$SupernaturalBeliefs,
use = "pairwise.complete.obs"))
Pearson's product-moment correlation
data: d$PatternPerception and d$SupernaturalBeliefs
t = 1.5937, df = 225, p-value = 0.1124
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.0249019 0.2326641
sample estimates:
cor
0.1056528 print(summary(lm(SupernaturalBeliefs ~ PatternPerception, data = d)))
Call:
lm(formula = SupernaturalBeliefs ~ PatternPerception, data = d)
Residuals:
Min 1Q Median 3Q Max
-1.3530 -0.3390 -0.1121 0.2717 1.9878
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.14978 0.07558 28.444 <2e-16 ***
PatternPerception 0.02904 0.01822 1.594 0.112
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.5378 on 225 degrees of freedom
Multiple R-squared: 0.01116, Adjusted R-squared: 0.006768
F-statistic: 2.54 on 1 and 225 DF, p-value: 0.1124#### mediations: indirect effect of the intuitive pattern search manipulation (effect-coded: 1 high pattern search, 1 low pattern search) on irrational beliefs through pattern perception
#### a-path (same mediator model for all three)
m.mod <- lm(PatternPerception ~ HPS_num, data = d)
set.seed(251)
#### (a) Existing conspiracy beliefs
y.exist <- lm(ExistingConspiracyBeliefs ~ HPS_num + PatternPerception, data = d)
med.exist <- mediate(
m.mod, y.exist,
treat = "HPS_num",
mediator = "PatternPerception",
boot = TRUE, sims = 5000
)Running nonparametric bootstrap print(summary(med.exist))
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals with the Percentile Method
Estimate 95% CI Lower 95% CI Upper p-value
ACME 0.01874 -0.00877 0.05 0.20
ADE -0.05324 -0.16254 0.06 0.33
Total Effect -0.03450 -0.14154 0.07 0.54
Prop. Mediated -0.54333 -5.00987 5.41 0.64
Sample Size Used: 227
Simulations: 5000 #### (b) Fictitious conspiracy beliefs
y.fict <- lm(FictitiousConspiracyBeliefs ~ HPS_num + PatternPerception, data = d)
med.fict <- mediate(
m.mod, y.fict,
treat = "HPS_num",
mediator = "PatternPerception",
boot = TRUE, sims = 5000
)Running nonparametric bootstrap print(summary(med.fict))
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals with the Percentile Method
Estimate 95% CI Lower 95% CI Upper p-value
ACME 0.03634 0.00949 0.07 0.0056 **
ADE -0.09073 -0.18767 0.01 0.0648 .
Total Effect -0.05440 -0.15164 0.05 0.2808
Prop. Mediated -0.66805 -7.27777 7.35 0.2864
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Sample Size Used: 227
Simulations: 5000 #### (c) Supernatural beliefs
y.super <- lm(SupernaturalBeliefs ~ HPS_num + PatternPerception, data = d)
med.super <- mediate(
m.mod, y.super,
treat = "HPS_num",
mediator = "PatternPerception",
boot = TRUE, sims = 5000
)Running nonparametric bootstrap print(summary(med.super))
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals with the Percentile Method
Estimate 95% CI Lower 95% CI Upper p-value
ACME 0.01642 -0.00107 0.04 0.072 .
ADE -0.03208 -0.10411 0.04 0.358
Total Effect -0.01567 -0.08522 0.06 0.656
Prop. Mediated -1.04809 -7.82130 6.36 0.698
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Sample Size Used: 227
Simulations: 5000 #### MANOVA (testing multivariate direct effect of manipulation on the diff. belief scales)
mv.mod <- manova(
cbind(
ExistingConspiracyBeliefs,
FictitiousConspiracyBeliefs,
SupernaturalBeliefs
) ~ Condition,
data = d
)
print(summary(mv.mod, test = "Wilks")) Df Wilks approx F num Df den Df Pr(>F)
Condition 1 0.99489 0.38215 3 223 0.766
Residuals 225 print(summary.aov(mv.mod)) Response ExistingConspiracyBeliefs :
Df Sum Sq Mean Sq F value Pr(>F)
Condition 1 0.27 0.27013 0.3889 0.5335
Residuals 225 156.28 0.69458
Response FictitiousConspiracyBeliefs :
Df Sum Sq Mean Sq F value Pr(>F)
Condition 1 0.672 0.67165 1.1549 0.2837
Residuals 225 130.851 0.58156
Response SupernaturalBeliefs :
Df Sum Sq Mean Sq F value Pr(>F)
Condition 1 0.056 0.055705 0.1906 0.6628
Residuals 225 65.750 0.292224 #### plots (relationship of pattern perception w diff. belief scales)
ggplot(d, aes(PatternPerception, ExistingConspiracyBeliefs, color = Condition)) +
geom_point(alpha = .7) +
geom_smooth(method = "lm", se = TRUE) +
labs(title = "Relation between pattern perception and existing conspiracy beliefs",
x = "Pattern perception (1–7)",
y = "Existing conspiracy beliefs (1–5)",
color = "Condition") +
theme_minimal()`geom_smooth()` using formula = 'y ~ x'
ggplot(d, aes(PatternPerception, FictitiousConspiracyBeliefs, color = Condition)) +
geom_point(alpha = .7) +
geom_smooth(method = "lm", se = TRUE) +
labs(title = "Relation between pattern perception and fictitious conspiracy beliefs",
x = "Pattern perception (1–7)",
y = "Existing conspiracy beliefs (1–5)",
color = "Condition") +
theme_minimal()`geom_smooth()` using formula = 'y ~ x'
ggplot(d, aes(PatternPerception, SupernaturalBeliefs, color = Condition)) +
geom_point(alpha = .7) +
geom_smooth(method = "lm", se = TRUE) +
labs(title = "Relation between pattern perception and supernatural conspiracy beliefs",
x = "Pattern perception (1–7)",
y = "Existing conspiracy beliefs (1–5)",
color = "Condition") +
theme_minimal()`geom_smooth()` using formula = 'y ~ x'
A MANOVA on the three belief measures yielded no significant multivariate or univariate effects, with all Fs < 1.2. Consistent with the original study, the intuitive pattern search manipulation therefore did not exert a direct effect on participants’ belief endorsement. As in the original study, however, the manipulation reliably influenced participants’ tendency to perceive patterns in the coin toss sequences. We therefore examined whether perceived pattern structure was associated with belief endorsement and whether the manipulation exerted an indirect effect on beliefs via pattern perception.
Pattern perception was not significantly correlated with belief in existing conspiracy theories (r = .073, p = .272) or with supernatural beliefs (r = .106, p = .112), but it was significantly correlated with belief in fictitious conspiracy theories (r = .159, p = .017). To test whether intuitive pattern search influenced beliefs indirectly through pattern perception, we conducted bootstrapped mediation analyses (5,000 samples) using effect-coded condition assignment (−1 = low pattern search, +1 = high pattern search). For existing conspiracy beliefs, the indirect effect was not significant (B = 0.019, 95% CI [−0.009, 0.05], p = .20). In contrast, a significant indirect effect emerged for fictitious conspiracy beliefs (B = 0.036, 95% CI [0.009, 0.07], p = .006). The indirect effect for supernatural beliefs was not significant (B = 0.016, 95% CI [−0.001, 0.04], p = .072).
Taken together, these findings partially replicate the original pattern. Although the intuitive pattern search manipulation did not exert a direct effect on belief endorsement, it indirectly influenced belief in fictitious conspiracy theories via increased pattern perception. However, unlike the original study, this indirect effect did not generalize to existing conspiracy beliefs or supernatural beliefs, suggesting that the downstream consequences of illusory pattern perception may be domain-specific rather than broadly applicable across belief systems.
Discussion
Summary of Replication Attempt
The present replication successfully reproduced the primary experimental effect reported in the original study: participants instructed to look for patterns in the random coin tosses perceived significantly more patterns than participants in the low pattern search. The magnitude of this effect was comparable to - and somewhat larger than - that reported by van Prooijen et al. (2018), indicating a robust and replicable influence of intuitive processing (or this particular manipulation) on illusory pattern perception.
In contrast, downstream effects on belief endorsement showed only partial replication. As in the original study, a MANOVA revealed no direct effects of the manipulation on belief measures. However, whereas the original study reported significant correlations and indirect effects via pattern perception for all three belief domains (existing conspiracy beliefs, fictitious conspiracy beliefs, and supernatural beliefs), the present replication found evidence for a significant indirect effect only in the case of fictitious conspiracy beliefs. Associations between pattern perception and existing conspiracy beliefs and supernatural beliefs were weaker and not statistically significant. Overall, the replication supports the reliability of the manipulation and the proximal cognitive mechanism, but provides only partial support for its broader downstream consequences for belief endorsement.
Commentary
Several insights emerge from follow-up analyses and comparison with the original findings. First, the strongest and most reliable downstream effects were observed for fictitious conspiracy beliefs - beliefs that are novel, implausible, and weakly embedded in participants’ prior ideological or identity-based commitments. This pattern suggests that illusory pattern perception may be most consequential for belief formation when individuals lack strong prior attitudes, rather than for entrenched or culturally salient beliefs such as existing conspiracy theories or supernatural worldviews.
Second, differences between the original and replication samples plausibly moderate the observed effects. The present study employed a larger and perhaps more heterogeneous Prolific sample, which may yield more conservative estimates of belief associations. The original paper did not clearly document exclusion criteria despite discrepancies between reported sample size and analytic degrees of freedom, limiting the precision with which the original analyses can be reconstructed. The weaker correlations and indirect effects observed here are consistent with the possibility that the original downstream effects were overestimated or context-dependent, rather than spurious. However, endorsement of existing conspiracy theories (e.g., 9/11 or JFK) is likely shaped by motivated reasoning, ideological commitments, and broader trust or distrust in institutions. As a result, momentary increases in pattern perception may be insufficient to shift these beliefs, which likely require sustained motivational or contextual influences rather than a transient cognitive manipulation. Future research should examine whether the effects of illusory pattern perception depend on the type of belief being evaluated.