Illusions of knowledge due to mere repetition

Repeating information increases people ’ s belief that the repeated information is true. This truth effect has been widely researched and is relevant for topics such as fake news and misinformation. Another effect of repetition, which is also relevant to those topics, has not been extensively studied so far: Do people believe they knew something before it was repeated? We used a standard truth effect paradigm in four pre-registered experiments (total N = 773), including a presentation and judgment phase. However, instead of “ true ” / “ false ” judgments, participants indicated whether they knew a given trivia statement before participating in the experiment. Across all experiments, participants judged repeated information as “ known ” more often than novel information. Participants even judged repeated false information to know it to be false. In addition, participants also generated sources of their knowledge. The inability to distinguish recent information from well-established knowledge in memory adds an explanation for the persistence and strength of repetition effects on truth. The truth effect might be so robust because people believe to know the repeatedly presented information as a matter of fact.


Introduction
The last decades brought an unprecedented change in how people access information: An increasing number of people switched from traditional print newspapers to online media such as news websites or social media.In the U.S., social media overtook print newspapers in popularity by the end of 2018 (Shearer, 2018), and by 2021, 48% of U.S. Americans used social media to get news at least sometimes (Walker & Matsa, 2021).However, this development brings its challenges.Social media are vulnerable to the spread of false information, often called fake news.Accordingly, a large body of research has investigated methods to detect fake news (e.g., Mridha, Keya, Hamid, Monowar, & Rahman, 2021) and why people believe and share them (e.g., Pennycook & Rand, 2021).One effect that has regained prominence due to the societal challenges of fake news and misinformation is the repetition-induced truth effect (Hasher, Goldstein, & Toppino, 1977), or more precisely, people's tendency to believe repeated information more than novel information (Dechêne, Stahl, Hansen, & Wänke, 2010;Unkelbach, Koch, Silva, & Garcia-Marques, 2019).As information is shared online due to factors unrelated to the information's veracity (e.g., how funny, surprising, or even how absurd it is), this truth effect might substantially contribute to creating erroneous beliefs.To successfully address the challenges that arise from the effect of repetition on subjective truth, understanding the causes is a prominent research goal.
Here, we investigate a repetition-induced phenomenon that might explain why repetition is such a potent factor in influencing people's beliefs: Illusions of knowledge.Repetition increases a statement's subjective truth but also makes people more likely to claim they have known that statement before the experimental situation (Begg, Robertson, Gruppuso, Anas, & Needham, 1996).These illusions of knowledge may contribute to the robustness of the truth effect.We investigate these illusions of knowledge due to repetition in the following.
We will first outline existing research on the truth effect and introduce two potential underlying processes: increased processing fluency (Reber & Schwarz, 1999) and the formation of referential networks (Unkelbach & Rom, 2017).We will then delineate how repetition may lead to illusions of knowledge and how fluency and the referential model fit as explanations for repetition-induced illusions of knowledge.We will then discuss existing research on illusions of knowledge before describing our own four experiments.We will conclude with a more detailed discussion of our experiments and relate them to existing research in the General Discussion.

The truth effect
The truth effect has been scrutinized in a large body of research over the years (for a meta-analysis, see Dechêne et al., 2010).This research led to several explanations for why repetition increases information's believability.We discuss two prominent accounts.First, the fluency account argues that people rely on the perceived ease of processing information when judging truth (Reber & Schwarz, 1999).People process repeated information more fluently than novel information and thus consider it as more truthful.The fluency-truth link follows if one assumes that repeated information is more often true than non-repeated information; then people would be epistemologically justified to use fluency as a cue for truth (Pillai & Fazio, 2021;Reber & Unkelbach, 2010), and they could learn the fluency-truth contingency in the environment (Unkelbach, 2006(Unkelbach, , 2007)).
Second, a related explanation assumes that repeating a statement instigates a referential network of the concepts provided in that statement (Unkelbach & Rom, 2017).This referential theory assumes that the number of coherently linked references determines the subjective truth of a statement.As presenting (novel) information usually adds new references to existing networks, repeated information has more coherently linked references than new information; consequently, it will appear more true.The fluency explanation and the referential theory are not mutually exclusive, as the more coherently linked references exist, the more fluently the information is processed (see Unkelbach et al., 2019; for a more detailed explanation); however, the referential theory also predicts fluent "false" responses under certain circumstances (see Unkelbach & Rom, 2017).

Illusions of knowledge due to repetition
Why is the effect so robust?The referential theory mentioned above (Unkelbach & Rom, 2017) provides a tentative answer.Repetition might have such a strong influence on belief because repetition is how people indeed acquire knowledge about the world.For example, teachers may tell their students that lead is heavier than gold.This symbolic exposure leads to the subjective knowledge of this fact about the world without ever holding two equally large pieces of lead and gold in one's hands.Using that conceptualization, it follows that symbolic exposure to facts  about the world gradually increases subjective knowledge.Thus, the increase in subjective truth due to repetition may follow from the same process that also contributes to accumulating subjective knowledge about the world.In other words, the process from repetition to truth proposed by the referential theory is structurally similar to how people acquire knowledge.
Fig. 1 illustrates how people may come to judge whether they know information or not based on this theory.Fig. 1 is adapted from Fig. 1a in Unkelbach and Rom (2017), and the theory is delineated from principles outlined by Kunda and Thagard (1996).Please note that Fig. 1 uses a symbolic network model, but one may easily implement it in a subsymbolic framework of coherent references (e.g., Glöckner, Hilbig, & Jekel, 2014).
The well-known fact in Fig. 1's left panel has several references in memory that are coherently linked.Africa is a land, elephants live in Africa, there are many large animals in Africa, and so forth.Thus, people should, correctly or incorrectly, state that they know this fact.The lessknown fact describes two elements that most people will not know, and they will likely also not know whether these are f-block elements.Thus, most people should state that they do not know this fact.The right panel also illustrates that the statements indeed need references in memory that provide meaning.The words "Cerium", "Terbium", and "f-block elements" could be any other label for a layperson, but for chemistry experts, they carry meaning based on references stored in memory: Both Cerium and Terbium are lanthanoid metals that have their 4f electron shell filled.
How does the referential theory now predict that repetition increases people's belief that they know information?Fig. 2 illustrates the assumed process for an example.In a presentation phase, participants see the statement "The flamingo's pink color comes from carotenoid pigments in its food."Most likely, they already have a localized informational network about flamingos, which may already include coherent links between "flamingo", "pink", and "food".After the presentation, "carotenoid pigments" are also included in the network as a coherent reference.In the judgment phase, the statement now activates a referential network with more coherent links.Compared to new information, there are now four references in memory in the test phase with six coherent links.The same statement would have only three references and three coherent links if it were "new" in the test phase.In other words, due to repetition, the repeated information will feel as if participants knew this information, the same way they "know" that African elephants are the largest land animals on Earth (see Fig. 1).Thus, based on the referential theory, we predict that repetition increases people's judgment that they knew this information before.
The theory also allows predicting circumstances when this effect should not occur; for example, when the learning context (e.g., the experiment) is central for the localized referential network.If the presented information is strongly linked to the situation, the effect should not occur.However, in most situations, the learning context for symbolic information is incidental rather than central.This assumption implies that people cannot distinguish between what they have learned before and what they have just learned in the presentation phase of an experiment.

Prior research on illusions of knowledge
Illusions of knowledge are not a novel concept.Begg et al. (1996) first examined what they termed the "illusory knowledge effect" with a design that is similar to typical designs investigating the repetitioninduced truth effect (Bacon, 1979;Garcia-Marques, Silva, Reber, & Unkelbach, 2015).First, participants saw 40 statements in a presentation phase.In the following judgment phase, participants saw the previous 40 statements and 20 novel statements.The last word in each statement was reduced to only the first letter (e.g., "The name of the collarbone is the c______.".Depending on the condition, some participants had to differentiate between statements and only complete the blanks if they had learned them before or within the experiment.Despite being able to differentiate between old (repeated) statements and previously known statements, participants reported 20% more old than new statements when asked to fill in only statements they had known previously.The authors inferred that old statements feel more familiar and people interpret this familiarity feeling as prior knowledge.
There are, however, some limitations to these findings.Westerman (1999) argued that the recollection task made participants disregard other forms of knowledge, such as recognition.Furthermore, participants may have exaggerated their previous knowledge to appear knowledgeable, and because they knew more of the old than the news statements because they were repeated, this might have inflated the difference between old and new statements.The authors consequently extended the experiment by Begg et al. (1996) by adding an alternative dependent variable: Participants should circle all statements they knew before the experiment.This additional DV allows participants to utilize recognition instead of recall and controls for the recall advantage of old statements.They found that the difference between old and new statements was much smaller when participants indicated knowledge by circling (49% vs. 36%) than by recall (48% vs. 13%).The authors interpreted this as evidence that the original study by Begg et al. (1996) could have underestimated the previous knowledge of new statements.
In their second study, the authors introduced false statements: False statements are unlikely to be known beforehand.They replicated the illusions of knowledge effect for false statements (12% vs. 6%), but it was smaller than for true statements (49% vs. 36%).This data pattern replicates the illusions of knowledge effect: People claim to have known statements prior to the experiment more often for old statements than for new statements.This is the case even when they cannot have prior knowledge because all statements are false.
In a related line of research, Marsh (2003) had participants read short stories that contained information about the real world.In the following general knowledge test, participants used the information from the fictional stories to answer the general knowledge questions.Notably, participants claimed that they knew the information in the stories before participating in the experiment.These claims occurred even when the stories contained misinformation, for which participants should not have prior knowledge.
Finally, Jacoby, Kelley, Brown, and Jasechko (1989) showed that participants were more likely to judge a name to be famous when it was presented the day before.Jacoby and colleagues employed (developed) a process-dissociation procedure for this task, thereby ensuring that "becoming famous overnight" depended on familiarity with the names rather than recognition.Similar to how repetition may make people believe a name is famous, repetition may make facts appear to be known.

The present research
Building on this prior research, we aimed to replicate the illusions of knowledge effect and examine its underpinnings across four preregistered experiments.We used a selection of the statements from Jalbert, Newman, and Schwarz (2019).In Experiments 1 and 3, we used only true statements, while in Experiments 2 and 4, we used only false statements from the same source.In this regard, our approach is similar to that of Westerman (1999), but we changed the instructions and dependent variables.
Furthermore, we also included different difficulty levels for the statements.We computed five difficulty levels based on the average percent of "true" judgments provided by Jalbert et al. (2019), which allows for a more fine-grained analysis of difficulty effects on illusions of knowledge than in the previous literature.
Finally, in Experiments 3 and 4, we examined how Illusions of knowledge relate to memory by asking participants about the source of their knowledge.After the judgment phase, where participants indicated for each statement whether they knew it prior to the study, participants F. Speckmann and C. Unkelbach were again presented with all statements they marked as "known" and were asked to specify the source of their knowledge about the statements.This prompt to rethink their previous decision and deliberate about the source of their knowledge could make participants realize their error.However, again, building on the referential model by Unkelbach and Rom (2017), as illustrated in Figs. 1 and 2, we expected participants to generate plausible sources for their reported knowledge (see below).

Open Science
We report how we determined our sample sizes, all data exclusions (if any), all manipulations, and all measures in the study.The preregistrations, data, analysis code, and materials for all experiments are available at: https://osf.io/7c94q/.

Experiment 1
Experiment 1 established the basic paradigm, consisting of the presentation and judgment phases with judged prior knowledge as the DV, using only true statements.

Materials
Jalbert et al. ( 2019) provided a list of 100 statements of varying topics and difficulty levels, half false and half true.Table 1 shows one example per topic from the list of true statements and one example per topic from the list of false statements.
We selected all true statements, sorted them by trivia category ("science", "geography", "sports", "animals", and "food"), and then arranged them based on the percentage of "true" judgments.This approach yielded five lists (one per category) of 20 statements, each in ascending order of difficulty.From each list, we then selected statements 1, 2, 5, 6, 9, 10, 13, 14, 17, and 18 to create five different difficulty levels, with each containing two statements for a total of 50 statements.In the presentation phase, participants saw a random sample of 25 (five per difficulty level, counterbalanced).In the judgment phase, participants saw all statements, now half new and half old (i.e., repeated).
We used Qualtrics to implement the instructions and manipulations and to collect the dependent variables.

Participants and design
Using previous research from our group as a reference point, we aimed to collect data from 200 participants using Prolific Academic, but 202 participants completed the experiment.As pre-registered, we excluded three participants who responded uniformly to all items and five participants with a self-indicated concentration level below 4 (on a scale of 1 to 6), reducing the sample to 194 (89 male, 104 female, 1 Fig. 2. Illustration of how repetition increases people's belief that they know information.The panels illustrate localized referential networks in the presentation and judgment phases.These panels also correspond to "new" (left) and "repeated" (right) information.As there are more coherently linked references on the right side, the likelihood of an "I knew this" response should be higher for repeated information.preferred not to say; M Age = 33.03,SD Age = 11.07) 1 .There were no between-participant conditions.Participants saw 50 factually true statements, 25 of which (five per difficulty level) were old (i.e., shown in the presentation phase and the judgment phase) and 25 of which were new (i.e., shown only in the judgment phase).

Procedure
From the Prolific Academic website, participants were redirected to our Qualtrics experiment.After reading and signing the informed consent form, participants started the presentation phase.During this phase, the experiment sequentially presented 25 statements, randomly sampled from the pool of 50 statements.Each statement stayed on the screen for three seconds before the experiment automatically advanced to an empty screen and had participants click the continue button to view the next statement.After viewing all 25 statements, participants continued to the judgment phase.In this phase, participants saw the 25 old statements intermixed with 25 new statements.For each statement separately, participants indicated whether they had known the information in this statement before participating in the experiment ("I knew that.")or not ("I did not know that.").After the judgment phase, participants provided demographic information and indicated their concentration level during the experiment before the experiment debriefed and thanked them.

Results
We predicted that participants would more likely report subjective prior knowledge for old compared to new statements because repetition should lead to illusions of knowledge (see Fig. 2).Furthermore, we predicted that participants would indicate more subjective prior knowledge with decreasing item difficulty because participants likely have more genuine prior knowledge for easier items (cf., Jalbert et al., 2019).Finally, we expected that item difficulty interacts with repetition so that the repetition effect decreases with decreasing item difficulty because higher genuine prior knowledge limits how much influence the repetition effect can have.
To test our predictions, we averaged participants' binary decisions for known judgments as a function of repetition (old vs. new) and item difficulty (levels 1 to 5) and submitted them to a repeated measures ANOVA.Fig. 3 shows the repetition effect across difficulty levels.As predicted, there was a significant main effect for repetition, F(1, 192) = 46.24,p < .001,η p 2 = 0.194, with participants overall responding "I knew this" more often to old statements (M = 0.36, SD = 0.24) than to new statements (M = 0.24, SD = 0.16).
Finally, we also expected an interaction of item difficulty and repetition due to ceiling effects (i.e., when everybody knows that Paris is the capital of France, there is no room for a repetition effect anymore).
However, repetition and item difficulty did not interact significantly, F (3.84, 737.72) = 0.75, p = .554,η p 2 = 0.004.This absence of an effect was likely due to overall knowledge levels being substantially lower than anticipated and estimated by Jalbert et al. (2019), thus avoiding the expected ceiling effects.We did not preregister this hypothesis for the following studies.
Based on the literature on the relationship between age and repetition-induced truth, we preregistered an exploratory analysis on the influence of participants' age.We ran a multiple regression analysis with repetition, item difficulty, and age as predictors and percentage of "known" judgments as the criterion, R 2 = 0.1, F(19, 1889) = 11.10,p < .001.Age significantly predicted mean "known" judgments, β = 0.21, p = .003,but did not interact with repetition, β = − 0.10, p = .557.We did not preregister this hypothesis for the following studies.

Discussion
As predicted, participants judged repeated statements as "known" significantly more often than novel statements, replicating illusions of knowledge due to repetition.Item difficulty linearly decreased the participants' "known" judgments, showing the DV's validity.The repetition main effect did not interact with the difficulty level of the items or with participants' age.
However, one may argue that we are still investigating a mere truth effect.In essence, this statement would be correct.In everyday language, "knowing something" directly implies "knowing that something is true".In addition, Figs. 1 and 2 illustrate that, indeed, increases in subjective truth due to repetition might be so strong because the processes that underlie repetition and knowledge acquisition might be very similar.In short, learning truths about the facts of the world and acquiring knowledge about the facts of the world builds strongly on repeating these facts.
Further, if "Knowing something" might imply "Knowing something to be true", participants might have understood the DV not as "Did you know this?" but as "Is it true?".Thus, the findings may be the typical truth effect with a different dependent variable.
Experiment 2, therefore, aimed to address a prediction with another DV that differentiates judgments of truth and judgments of knowledge: People might also know that something is false.To know that something is false regarding the state of the world (see Kirkham, 1992), one needs to know something about the world.In the terminology of Unkelbach and Rom's (2017) referential theory, one needs references that provide meaning to the elements of a given statement.For example, to know that the statement "London is the capital of France" is false, one needs to know that Paris is the capital of France.By repetition, we may strengthen the subjective experience that people know something about the topic.Experiment 2 thus used "Did you know this to be false."instead of "Did you know this." as the central DV.We expected repetition to increase participants' rate to state that they knew this to be false before the experiment.
Fig. 4 illustrates how one may derive this prediction from the referential theory by Unkelbach and Rom (2017).The necessary additional assumption is that one needs knowledge to know that something is false.Fig. 4 illustrates a case in which a specific reference in memory is likely unknown; however, there are other statements for which additional coherent links might be instigated.For example, while the statement "The electron is the heaviest charged particle found in nature."might only imply the "heaviest charge" to be false, people might not have the link between "particle" and "electron" in memory.Such a case would further strengthen the repetition effect for "I knew this to be false".

Experiment 2
Experiment 2 was similar to Experiment 1 but used a list of trivia statements that were all false (see Table 1 for examples).Most 1 Due to technical errors related to specific web browsers, 16 participants had more than half of the statements in the presentation phase, meaning that for those participants, the proportion of old statements was larger than the proportion of new statements.However, excluding them does not change any of the reported results, and we thus decided to include them. 2 The ANOVAs use the Greenhouse-Geisser correction of degrees of freedom for within-participant factors.
F. Speckmann and C. Unkelbach importantly, Experiment 2 asked participants whether they knew statements to be false before participating in the experiment.By changing the wording in the knowledge judgments to "Did you know this to be false?", the judgments are now distinctly different from typical truth judgments, as the falseness is now inherent in the question, and the question is only about prior knowledge.Thereby, Experiment 2 may provide evidence that the illusions of knowledge effect is not simply the truth effect with another dependent variable.

Materials
We used 50 false statements from Jalbert et al. (2019).Apart from working with the list of false statements, the steps taken to select the 50 statements were the same as in Experiment 1.

Participants and design
Again, we aimed to collect data from 200 participants using Prolific Academic, and 200 participants completed the experiment.As preregistered, we excluded four participants who responded uniformly to all items and five participants with a self-indicated concentration level below 4 (on a scale of 1 to 6).Thus, the sample consisted of 191 (105 male, 85 female, 1 prefer not to say; M Age = 34.72,SD Age = 12.11)3 .The design was identical to that of Experiment 1.

Procedure
The procedure was highly similar to Experiment 1, except that the questions in the judgment phase changed from "Did you know this?" to  Note.The difficulty level is based on the means reported by Jalbert et al. (2019).
Lowest difficulty refers to the five statements per category with the highest average "true" judgments, and highest difficulty refers to the five statements per category with the lowest average "true" judgments.
"Did you know this to be false?".The rest of the procedure was identical to that of Experiment 1.

Results
We again predicted a main effect of repetition.We also again predicted that participants would indicate more subjective prior knowledge with decreasing item difficulty.We did not predict an interaction of repetition and item difficulty, as the response rates in Experiment 1 were far from the expected ceiling effect we hypothesized in Experiment 1.
To test these predictions, we prepared the data in the same way as in Experiment 1 and submitted it to the same 2 (repetition: old vs. new) by 5 (difficulty level: 1 to 5) repeated measures ANOVA.Fig. 5 shows the repetition effect across difficulty levels.As Fig. 5 suggests, there was a significant main effect for repetition, F(1, 188) = 4.66, p = .032,η p 2 = 0.024, with participants responding "I knew this to be false" more often to old statements (M = 0.34, SD = 0.20) than to new statements (M = 0.32, SD = 0.21).
The main effect for difficulty level was also significant, F(3.94,The other polynomial contrasts were also significant but smaller than the linear trend.The interaction between repetition and item difficulty was not significant, F(3.93, 739.59) = 1.75, p = .138,η p 2 = 0.009.

Discussion
Repetition increased the percentage of "known to be false" judgments, albeit less so than "known" judgments in Experiment 1.This reduction is likely due to Experiment 2's more conservative test of illusions of knowledge.Similarly to the argument by Westerman (1999) in response to the original work by Begg et al. (1996), participants in Experiment 1 may have used any form of knowledge as the basis for a "known" judgment.This includes recognition but also more vague forms of familiarity.In addition, the DV "knowing something to be false" is more complex and thus more error-prone and less reliable than the DV "knowing something (to be true)".Participants may only claim to know a statement to be false if they believe they know something about the true state of the world.Finally, one may derive the reduction directly from the assumed processes presented in Figs. 2 and 4. In Fig. 2, the difference for the true flamingo statement would be three vs. six coherent links, which provides a much stronger localized network.In Fig. 4, the difference hinges on the strengthening of existing links (rather than new ones) and the potential inclusion of new references in the network (e.g., "electrons" -"particles").However, we did not delineate this prediction a priori, but after observing the data and it is therefore a post-hoc interpretation.Together, these points potentially explain the observed reduction of illusions of knowledge in Experiment 2. Importantly, Experiment 2 shows that the illusion of knowledge effect is not simply a variant of the truth effect.If participants had judged old statements more likely to be true, this should have led to fewer "known to be false" judgments for old statements than for new statements.However, although reduced in comparison to Experiment 1, the observed effect in Experiment 2 is the opposite: Participants judged repeated statements more as "known to be false".
Similar to Experiment 1, the significant linear trend for statement difficulty suggests that the difficulty levels worked as intended, but the difficulty level again did not influence the illusions of knowledge.
In Experiment 3, we implemented another way to distinguish Fig. 4. Illustration of how repetition increases people's belief that they know information to be false.The panels illustrate localized referential networks in the presentation and judgment phases.These panels also correspond to "new" (left) and "repeated" (right) information.The "Did you know this to be false."framing questions the coherence of the newly instigated links.However, as repetition strengthens the coherent links between references on the right side, the likelihood of an "I know this to be false."response should increase.
F. Speckmann and C. Unkelbach knowledge from truth and asked participants to indicate the source of their knowledge about a given statement.As the effect was substantially reduced in Experiment 2, we returned to the original DV.

Experiment 3
Experiment 3 aimed to extend the previously observed subjective knowledge judgments by adding a source indication phase in which participants indicated a source for all statements they previously judged as "known".There are two potential outcomes.First, once participants start thinking about sources, they may notice that they cannot recall the source, leading them to revoke their initial "known" judgmentan option that we offered.If this is the case, these corrections should be more prevalent for repeated statements.
Second, building on the referential model by Unkelbach and Rom (2017), we expected participants to generate plausible sources or report sources that fit into related reference networks.This prediction follows because the referential networks provide meaning to the concepts in a given statement.For example, the statement "The flamingo's pink color comes from carotenoid pigments in its food" needs a reference (among others) for the concept of "flamingo" to have meaning.Consequently, participants should generate sources for the statement that derive from their information in memory about flamingos.
The generation of plausible sources also follows from a fluency perspective, albeit with necessary additional assumptions: If fluency leads to an illusion of knowledge, we would need to assume that people aim to justify that knowledge by providing a plausible source.However, the source would not follow from the associated networks but could be freely generated (cf., "Telling more than we can know" Nisbett & Wilson, 1977).
As outlined below, when prompting participants for the source of their knowledge, we also offer the response option "I do not remember how I know this." to avoid an artificial increase through a forced response format.

Materials
We used the same materials as in Experiment 1.

Participants and design
We again aimed to collect data from 200 participants using Prolific Academic; 201 participants completed the experiment.As preregistered, we excluded two participants who responded uniformly to all items and two participants with a self-indicated concentration level Fig. 5. Average percentage of "Known to be false" judgments as a function of repetition ("old" vs. "new"), separated by difficulty levels ("lowest" to "highest") in Experiment 2. Note.Error bars represent standard errors of the means.The black dots represent the means, the black horizontal lines represent the medians, the boxes represent the 25% quartiles, and the whiskers extend to the highest (lowest) point within the interquartile range (distance between first and third quartile).
F. Speckmann and C. Unkelbach below 4 (on a scale of 1 to 6), reducing the sample to 197 (81 male, 114 female, 2 other; M Age = 39.90, SD Age = 14.13)4 .The design was the same as in Experiments 1 and 2.

Procedure
The procedure was similar to Experiment 1 until the end of the judgment phase, after which participants entered the source indication phase.The experiment then presented the statements judged as "known" in the judgment phase and asked participants to indicate how they knew each statement.Specifically, the question read: "You indicated that you knew this before taking part in this study.How do you know this?" with the response options "I read it in a book; I read it in a newspaper/ magazine; I heard it on the radio; I saw it on television; I read it / saw it on the internet; I heard it from someone; Other; I do not remember how I know this; I did not know that after all".After participants responded to all statements previously judged as "known", the experiment continued with the demographics and debriefing parts as in Experiment 1.

Results
We again predicted a main effect of repetition (i.e., higher subjective knowledge for old statements compared to new statements).We also predicted an equal percentage of source indications for old and new statements because participants should not realize their "known" judgments were only due to repetition.We split the tests of our predictions into two paragraphs.
Percentage of "Known" judgments.We prepared the data in the same way as in Experiment 1 and submitted it to the same 2 (repetition: old vs. new) by 5 (difficulty level: 1 to 5) repeated measures ANOVA.Fig. 6 shows the repetition effect across difficulty levels.As Fig. 6 suggests, there was a significant main effect for repetition, F(1, 192) = 37.30, p < .001,η p 2 = 0.163, with participants responding "I knew this." more often to old statements (M = 0.37, SD = 0.23) than to new statements (M = 0.26, SD = 0.18).The main effect for difficulty level was also significant, F(3.88, 744.62) = 52.29,p < .001,η p 2 = 0.214.As the percentages of "known" judgments across all difficulty levels in Table 2 suggest, the linear trend was again significant, t(192) = − 12.55, p < .001,d = − 1.81, 95% CI [− 2.15, − 1.47].The other polynomial contrasts were also significant but smaller than the linear trend.The interaction between repetition and item difficulty was not significant, F(3.71, 713.24) = 0.43, p = .774,η p 2 = 0.002.Indicated sources.Participants provided more "known" judgments for repeated statements compared to new statements.As the statements are randomized, these "known" judgments follow from repetition, and a higher percentage must be erroneous.Thus, if participants notice this error when asked about the source of their knowledge, they should show a higher percentage of times noticing the error for repeated statements.In contrast, if repetition indeed leads to illusions of knowledge, there should be no difference in this percentage between repeated and new statements.
To analyze the differences in source indications for old and new statements, we first coded the option "I did not know that after all" option as "1" and all other response options for sources as "0".After averaging, this coding provides the percentage of times when participants revoked their initial "known" judgment, suggesting that they noticed their erroneous "known" judgment and tried to rectify it.On average, participants corrected their judgment ("I did not know that after all.") for less than one statement (i.e., 1.43%, SD = 6.60%).For old statements, the percentage of "I did not know that after all."judgments was slightly higher (M = 2.08%, SD = 8.55) than for new statements (M = 0.77%, SD = 4.65), indicating that participants, at least descriptively, noticed the error due to repetition.
To test whether the differences between these percentages were equivalent, we ran a pre-registered equivalence test.An a-prior power analysis using the TOSTER package in R (Lakens, 2017) showed that for our planned sample size of 200, we could test for equivalence using the smallest effect size of interest of |d z | = 0.233 at α = 0.05 and 90% power.
Fig. 7 shows the distribution of different knowledge sources that participants indicated during the source indication phase.It suggests that books are the most frequently named source of knowledge.In addition, the distribution suggests that the sources are plausible.For example, most science "knowledge" stems from books, while most sports "knowledge" stems from television, and most food "knowledge" stems from the internet.

Discussion
Experiment 3 replicated the illusion of knowledge due to repetition.Repetition led to more "known" judgments, and increasing item difficulty led to less "known" judgments, while both effects did not interact.In addition, Experiment 3 showed that participants generated plausible sources for their reported knowledge.This source generation may follow from true knowledge, referential networks, and processing fluency (with additional assumptions; see above).Importantly, participants only corrected their initial "known" judgment by indicating "I did not know that after all" in the source indication phase 1.43% of the time.The difference in corrections between old and new statements was significant, indicating that participants could, in principle, correct the illusion of knowledge due to repetition.However, numerically, the correction was minor.People indicated prior knowledge for 16 statements (out of 50), and the difference between old and new statements was thus less than one statement.The data thus suggests that participants, in principle, may notice their erroneous "known" judgment due to repetition and correct it, but it is a rare outcome.
The overall low correction rate provides further evidence for robust illusions of knowledge.However, one may apply the same conceptual problem as for Experiment 1 to Experiment 3: Because all trivia statements were factually true, participants likely had some knowledge, an assumption we also built into Figs. 1, 2, and 4. While all statements were randomly sampled to control factual prior knowledge and repetition did not interact with how often participants judged statements as "known", a more conservative test would exclude true knowledge entirely.Thus, Experiment 4 again used false statements.

Experiment 4
Experiment 4 replicated Experiment 3 with one difference.By using the same factually false statements as in Experiment 2, we aimed to exclude potential actual knowledge as an influence on "known" judgments and the generation of sources, similar to the research by Westerman (1999).
As we argued, to know something to be false, people need to know something, and it might not be clear to what our question refers to.Thus, we asked them "Did you know this before?"Although most people will understand "Did you know this before?"as "Did you know this to be true?", this ambiguity was by choice.We did not deceive our participants by asking them to judge false information as "known to be true", and we avoided the "Did you know this to be false?",which provides challenges for the following question.However, asking "Did you know this before?"makes the follow-up question of "How do you know this?" easy to answer.

Materials
The materials were similar to Experiment 2.

Participants and design
We again aimed to collect data from 200 participants using Prolific Academic; 200 participants completed the experiment.As preregistered, we excluded nine participants who responded uniformly to all items, reducing the sample to 191 (85 male, 103 female, 3 diverse; M Age = 40.78,SD Age = 14.08)5 .The design was identical to the previous experiments.

Procedure
The procedure was highly similar to Experiment 3, with some changes regarding the wording of the questions.As all statements were factually wrong, we wanted to avoid confirming participants' illusions of knowledge by asking for a source for the "knowledge".Instead, the question read: "You indicated that you knew this before taking part in this study.Where have you heard/seen this before?"with the adapted response options "I read it in a book; I read it in a newspaper/magazine; I heard it on the radio; I saw it on television; I read it / saw it on the internet; I heard it from someone; Other; I do not remember where I have seen/heard this; I have not seen/heard that before after all".

Results
We again predicted a main effect of repetition (i.e., higher subjective knowledge for old statements compared to new statements) and an equal percentage of source indications for old and new statements.We split the tests of our predictions into two paragraphs.
Percentage of "Known" judgments.We prepared the data in the same way as in Experiment 1 and submitted it to the same 2 (repetition: old vs. new) by 5 (difficulty level: 1 to 5) repeated measures ANOVA.Fig. 8 shows the repetition effect across difficulty levels.As it suggests, there was a significant main effect for repetition, F(1, 188) = 43.32,p < .001,η p 2 = 0.184, with participants responding "I knew this" more often to old statements (M = 0.26, SD = 0.22) than to new statements (M = 0.16, SD = 0.13).
Note.Error bars represent standard errors of the means.The black dots represent the means, the black horizontal lines represent the medians, the boxes represent the 25% quartiles, and the whiskers extend to the highest (lowest) point within the interquartile range (distance between first and third quartile).
The main effect for difficulty level was also significant, F(3.53, 663.18) = 127.05,p < .001,η p 2 = 0.403.As the percentages of "known" judgments across all difficulty levels in Table 2 suggest, the linear trend 6.Average percentage of "Known" judgments as a function of repetition ("old" vs. "new"), separated by difficulty levels ("lowest" to "highest") in Experiment 3. Note.Error bars represent standard errors of the means.The black dots represent the means, the black horizontal lines represent the medians, the boxes represent the 25% quartiles, and the whiskers extend to the highest (lowest) point within the interquartile range (distance between first and third quartile).
While we replicated the predicted repetition effect, Table 2 shows another interesting aspect of Experiment 4's data.The "I knew this before" rate is lower than in all other experiments, notably compared to Experiment 2, which employed the same statements.One potential reason is that for the factually false statements, the absence of knowledge should contribute to "I knew this to be false" rates, while the same absence should obstruct "I knew this before" responses.Such an explanation follows from our overall reasoning, although this is a post-hoc explanation.
Indicated sources.We used the same data preparations and analyses as in Experiment 3 to compare the percentages of error corrections for old and new statements.For old statements, the percentage of "I have not seen/heard that before after all" judgments was slightly higher (M = 4.28%, SD = 16.03)than for new statements (M = 2.37%, SD = 10.26).The equivalence test was not significant, t(177) = 1.60, p = .056,g = 0.11, 90% CI [− 0.04, 0.27], and the Welch test was also not significant, t (169) = − 1.31, p = .194,d = − 0.14, 95% CI [− 0.35, 0.06], indicating that there is no clear evidence for a difference nor equivalence.
Fig. 9 shows the distribution of different knowledge sources that participants indicated during the source indication phase.Although the distributions deviate somewhat from Fig. 6, books are still the most frequently named source of knowledge and the sources are again plausible in regards to their "knowledge" category.
Note. "Mistaken" refers to the "I did not know that after all" response option.

Discussion
Experiment 4 replicated the pattern of the previous experiments: Repetition increased "known" judgments, and increasing item difficulty decreased "known" judgments, but both effects did not interact.Of note, Experiment 4 delivers the most straightforward pattern so far.This indicates that if one aims to show the illusions of knowledge effect, precluding other knowledge sources is an important design feature.
The overall percentage of corrections was again low (3.33%), and with people on average indicating prior knowledge for ten statements, participants corrected less than one statement on average.
Different from Experiment 3, for the corrections, neither the equivalence test nor the Welch test was significant.This result further supports that the difference in corrections between old and new statements is indeed minor.The result is in line with an illusion of knowledge, however it may be supported by other causes.For example, people have a general tendency to confirm what they believe to know (i.e., a confirmation bias; see Oeberst & Imhoff, 2023) and a bias to continue the status quo (Samuelson & Zeckhauser, 1988), which takes many shapes and forms (e.g., the endowment effect; Kahneman, Knetsch, & Thaler, 1990).Besides this tendency, it is cognitively more effortful and emotionally challenging to update and shift beliefs about the world, and people in these two experiments might simply be reluctant to admit an error or a failure (see Eskreis-Winkler & Fishbach, 2022, for a review).
Experiment 4 nevertheless provides clearer evidence for the "illusions of knowledge" effect.Participants thought they knew statements from before participating in the experiment merely due to them being repeated, and they barely corrected their initial judgments when further probed about the source of their knowledge, instead indicating likely (but necessarily false) sources.Fig. 7. Sums of all response options for knowledge sources by statement category in Experiment 3. Note."Mistaken" refers to the "I did not know that after all" response option.

General discussion
Across four pre-registered experiments, we found evidence for illusions of knowledge.Experiment 1 replicated the original work by Begg et al. (1996) and Westerman (1999).Experiment 2 provided evidence that the illusions of knowledge effect is not simply the truth effect with an alternative dependent variable.Experiments 3 and 4 extended the paradigm with a source indication phase and found that participants readily provided sources for the statements they claimed to have known.It seems that participants provide plausible but false sources for their assumed knowledge.Whereas both, the fluency account and the referential network can explain this result, we argue that it fits better with the referential model because the fluency account needs the added assumption that participants spontaneously generate sources to attribute increased fluency to (see introduction of Experiment 3).
Experiments 3 and 4 also provide insight into how participants generated plausible sources.The questions from Jalbert et al. (2019) consist of five categories: animals, food, geography, science, and sports.For categories like geography or science, there is a high probability that people learned the information from books (e.g., in school).However, this does not explain the popularity of books as a knowledge source in Experiment 4 when all statements were false.Prior research found that when asked to report a source they have forgotten, people report a source that fits the related content (Bayen, Nakamura, Dupuis, & Yang, 2000;Kuhlmann, Bayen, Meuser, & Kornadt, 2016).This typicality-fit is visible in Figs. 4 and 6, where books served primarily as an indicated source for science and geography statements, whereas television served primarily as an indicated source for sports statements.
This pattern fits with the referential theory (Unkelbach & Rom, 2017) that we delineated in Figs. 1, 2, and 4. When asked about the source of their knowledge, participants may retrieve a supposed source that should be coherent with an existing localized information network.To provide another example, the statement "Neptune is part of the Kuiper belt" (false) should form a network containing the nodes "Neptune" and "Kuiper belt".This would constitute a coherent network because Neptune and the Kuiper belt are both in space.For this network, "book" as a potential source follows because to understand the statement, people need to know that the word Neptune references a planet in the solar system and that the words "Kuiper belt" refer to a large group of objects in the solar system.This knowledge about astronomy is often a school subject taught with the help of books.
Another possible explanation related to the referential theory lies in the relatedness of different informational networks.When hearing the statement "The flamingo's pink color comes from carotenoid pigments in its food", participants might recall established networks containing the reference "flamingo".In those existing networks, a source for the statement could also be a coherent reference.Participants have likely heard something about flamingos before.If they can recall the source of their existing flamingo knowledge, they thus become more likely to indicate this source, regardless of whether they integrate multiple networks containing the reference "flamingo" or if they form a new one specifically for the presented statement.Although we did not assess truth judgments and thus cannot examine the relationship between illusions of knowledge and illusions of truth directly, we postulate that illusions of knowledge might contribute to the robustness of the repetition-induced truth effect.This assumption is supported by related research on repetition.For example, Hertwig, Gigerenzer, and Hoffrage (1997) found that repetition also contributes to the hindsight bias (Hertwig et al., 1997), and although the authors investigated participants' confidence rather than "I knew this"-responses, their model fits well with our results.Similarly, Arkes et al. (1991) found that participants who dissociate the source of a statement (i.e., think they have known it prior to the experiment) show a greater truth effect.Finally, as mentioned in the introduction, Marsh (2003) had participants read fictional stories that contained information that helped them answer later questions.Although participants correctly stated that the stories had helped them answer the questions, they also reported higher levels of prior knowledge after reading the stories.This was unlikely, however, because the authors also introduced misinformation into the stories that people most likely did not possess prior to the experiment (c.f., Experiments 2 and 4).Thus, the illusion of knowledge may contribute to the truth effect because participants believe that they knew it beforehand and even where they knew it from.
The creation of plausible but false sources in Experiments 3 and 4 is noteworthy because people tend to forget the actual sources behind information (Begg, Anas, & Farinacci, 1992;Jacoby et al., 1989) as well as the context they learned a statement in (Skurnik, Yoon, Park, & Schwarz, 2005), whereas the fluency advantage through repetition lasts longer (Garcia-Marques et al., 2015).Note that this applies mainly to fluency, not actual item recognition, which decays at the same rate as source recognition (Bornstein & Lecompte, 1995).This could lead to scenarios in which people read a false statement online from a nonreputable source and initially doubt the statement because of its source.However, over time, they forget the source, and if confronted with the statement again, they judge it as more truthful because they forgot the initial source (and its implications), but the increased fluency from previous exposures remains.Critically, when subsequently asked about the source of their knowledge, people may now infer a plausible source for their assumed knowledge that is different from the original source, further bolstering judged truth.This process could be accelerated by the nature of online information.Most statements we read online should become part of semantic memory rather than episodic memory.However, because source information is less easily retrievable in semantic than in episodic memory (Schacter, Harbluk, & McLachlan, 1984), the source substitution might start relatively early after the first exposure.This would explain why people believe statements from lying sources (Begg et al., 1992) and statements with questionable content (Pennycook et al., 2018).
Although the statements we used as materials were not political or topical, our results can also be interpreted in the context of fake news.For example, after reading a (false) statement on social media from dubious sources, people might realize that the statement is not trustworthy.However, they might eventually forget information about the source and substitute a different one, leading to illusory knowledge about the statement.Thus, forgetting, in combination with the truth effect, could lead people to believe statements despite initially identifying them as untrustworthy.
In closing, our data show illusions of knowledge effect due to repetition.Further, it also suggests which -measures and amelioration interventions for repetition-induced truth effects will likely work or fail.For example, information about sources should only work if they are integral to the informational network of a given statement, but not if the source is incidental.Most importantly, we believe the present illusions of knowledge explain why the truth effect is so robust: Though artificial, the presentation phase in a truth experiment might not be so different from how people acquire knowledge about the world in real life.9. Sums of all response options for knowledge sources by statement category in Experiment 4.

Fig. 1 .
Fig. 1.Illustration of how people judge whether they know information.The panels illustrate localized referential networks for a well-known and a less-known fact about the world.The light grey lines indicate the incoming information.The grey circles indicate existing references in memory that give meaning to the statement.White circles indicate information that has no references in memory.Solid lines indicate existing links between references.Dotted lines indicate links that are instigated by the presentation.A "+" sign indicates a coherent link, and a "-"would indicate an incoherent link (not depicted).Line thickness indicates link strength.

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.Speckmann and C. Unkelbach

Fig. 3 .
Fig. 3. Average percentage of "Known" judgments as a function of repetition ("old" vs. "new"), separated by difficulty levels ("lowest" to "highest") in Experiment 1. Note.Error bars represent standard errors of the means.The black dots represent the means, the black horizontal lines represent the medians, the boxes represent the 25% quartiles, and the whiskers extend to the highest (lowest) point within the interquartile range (distance between first and third quartile).

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.Speckmann and C. Unkelbach

Table 1 Example
Jalbert et al. (2019)t et al. (2019)with one statement per topic and truth status (i.e., true vs. false)."Mayonnaise is usually made with raw egg whites."Geography "The Zulu are the single largest ethnic group in South Africa.""Taboga Island is in Nicaragua."Science "Many of the genes in baker's yeast are also present in humans.""The electron is the heaviest charged particle found in nature."Sports "The steeplechase, in athletics, is a footrace over an obstacle course.""Golf was originally called mintonette."F. Speckmann and C. Unkelbach

Table 2
Percentage of "known" judgments as a function of item difficulty for Experiments 1-4.Standard deviations in parentheses.