In an uncertain environment, individuals utilize not only information from the external world, but also internal states such as confidence, ease of memory retention, and prediction of the likelihood of recall to achieve flexible behavioral control (Hart, 1965; Arbuckle and Cuddy, 1969; Nelson and Louis, 1990). For example, even if there is no external feedback on an action, people can appropriately adjust their behavior by referring to their internal states. This function is called metacognition and often described by two major processes, monitoring and control (Flavell, 1979; Nelson and Louis, 1990).

Commonly known as the “two-process model,” this framework suggests that monitoring entails evaluating and understanding one’s own cognitive states, while control involves modifying behavior or thought processes based on the outcomes of monitoring (Flavell, 1979). For instance, if monitoring indicates that a piece of information is not well retained, an individual might engage in additional study or adopt a more effective learning strategy. This continuous interplay between monitoring and control forms the foundation of adaptive metacognitive functioning, enabling individuals to refine their actions, even without explicit external feedback. By continually assessing and regulating cognitive processes in this manner, people can maximize their performance in uncertain or changing environments and maintain flexible behavioral control (Gourgey, 1998; Egner and Siqi-Liu, 2024).

Recent studies have particularly focused on “metacognitive efficiency” (Maniscalco and Lau, 2012; Fleming and Lau, 2014; Fleming, 2017). Metacognitive efficiency refers to the accuracy of metacognition corrected with perceptual/memory performance, and is considered crucial for real-life applications. For instance, Fischer et al. (2023) reported that individuals with higher metacognitive efficiency are better able to make appropriate judgments about risks, such as vaccinations during the COVID-19 pandemic. Accurate metacognition facilitates flexible, risk-based decision-making; conversely, inaccurate metacognition can result in suboptimal decisions and may aggravate psychiatric symptoms. Notably, impaired metacognitive processes have been associated with various psychiatric conditions, such as schizophrenia and depression, where individuals struggle with accurate self-monitoring and judgment (Wells, 2011; Hasson-Ohayon et al., 2015; Martiadis et al., 2023; Favaretto et al., 2024). These findings indicate that enhancing metacognitive efficiency may promote better mental health outcomes and support adaptive functioning in real-life contexts.

Metacognition can be conceptualized along a temporal dimension, with prospective metacognition focusing on future performance and retrospective metacognition examining past performance (Fleming et al., 2016; Siedlecka et al., 2016). Prospective metacognition is particularly significant for planning, decision-making, and anticipating risks, while retrospective metacognition aids individuals in reflecting on and learning from past outcomes (Fleming and Dolan, 2012; Siedlecka et al., 2016). Despite increasing interest in prospective metacognition (Fleming, 2024; Katyal and Fleming, 2024), most research on metacognitive efficiency has predominantly centered on retrospective processes (Fleming and Dolan, 2010; Goupil and Kouider, 2016; Pereira et al., 2020).

Some comparative studies of prospective and retrospective metacognition have shown that retrospective metacognition has a stronger positive correlation with task performance only after the motor response than prospective metacognition, but not before (Siedlecka et al., 2016, 2019; van den Berg et al., 2016; Qiu et al., 2018). These observations suggest that retrospective metacognition attains greater accuracy by integrating external cues, such as motor information, rather than relying exclusively on internal states. As a result, investigating the efficiency of prospective metacognition offers a meaningful pathway for enhancing our understanding and evaluation of internal-state monitoring accuracy.

Previous research has demonstrated that retrospective metacognition is shaped by factors such as response feedback, priming with task information, and task difficulty (Zohar and Barzilai, 2013; Desender et al., 2017; Carpenter et al., 2019; Luo and Liu, 2023). For instance, Carpenter et al. (2019) investigated whether metacognitive efficiency could be systematically enhanced through adaptive training in a perceptual discrimination task. Their findings revealed that participants who received feedback on their confidence-accuracy relationship demonstrated improvements in metacognitive efficiency without corresponding changes in perceptual or memory performance. Moreover, these benefits were transferred to both trained and untrained recognition memory tasks. However, these effects are minimal and short-lived (Rouy et al., 2022). In a subsequent analysis, Rouy et al. (2022) revisited Carpenter et al.’s study, suggesting that the original findings might have been confounded by inconsistencies in incentives and confidence scales. After replicating the study under more controlled conditions, they found no evidence of genuine metacognitive improvement and concluded that more rigorous experimental designs are required to determine whether metacognitive efficiency can be systematically trained.

Prospective metacognition has been studied using various measures including judgments of learning (JOL), predictions of future recall performance, and feelings of knowing (FOK), subjective experiences of knowing information that cannot currently be recalled (Hart, 1965; Nelson and Louis, 1990; Koriat, 1997). Despite progress in characterizing prospective metacognition through these measures, our understanding of the factors governing its efficiency remains limited. For example, Koriat (1997) demonstrated that the accuracy of JOLs is sensitive to the inherent difficulty of memory items but not to external factors such as exposure duration or frequency. While the accuracy of metacognition is known to be influenced by actual behavioral performance (Maniscalco and Lau, 2012; Fleming and Lau, 2014), prospective metacognitive research using JOLs and FOKs has often overlooked the impact of memory performance itself on the efficiency of these judgments. This oversight may restrict our understanding of prospective metacognitive efficiency.

In this study, we focus on task instructions in which the internal state was intended to be systematically controlled. Metacognition can be broadly classified into two types based on how it assesses internal states: explicit and implicit metacognition (Nisbett and Wilson, 1977; Hampton, 2001; Persaud et al., 2007; Dienes and Seth, 2010; Yuki et al., 2019; Fleming, 2024). Explicit metacognition is quantified by directly assessing the magnitude of beliefs. It is assumed to require verbal reporting and involves conscious access to one’s internal state. Explicit metacognition depends on working memory and is influenced by cognitive load because it involves verbal reporting (Coutinho et al., 2015; Conte et al., 2023). Implicit metacognition requires an indirect evaluation of beliefs in the form of betting choices. Therefore, it does not require verbal reporting and is often used in animal studies of metacognition (Hampton, 2001; Smith, 2009; Yuki and Okanoya, 2017; Miyamoto et al., 2021).

Furthermore, these two metacognitions are assumed to be functionally distinct. Explicit metacognition is thought to contribute to interindividual decision-making by communicating beliefs through language, whereas implicit metacognition is thought to be important for adaptive behavioral control at the individual level (Frith, 2012; Shea et al., 2014; Heyes et al., 2020). This functional segregation is partially supported by several neuroimaging studies. The medial prefrontal cortex is commonly involved in metacognition with reference to one’s own state (Vaccaro and Fleming, 2018). However, some brain regions such as the lateral prefrontal cortex, which are involved in verbalization processes, are thought to play a role only in explicit metacognition (Fleming and Dolan, 2012). These results suggest that these two metacognitions have distinct functions and that their neural substrates are partially segregated. Considering the expected functional differences that explicit metacognition is involved in interindividual communication and decision-making, while implicit metacognition is involved in adaptive behavioral control at the individual level, it can be predicted that metacognitive efficiency is higher in implicit than in explicit metacognition.

In the current study, we investigated the differences between explicit and implicit prospective metacognition by providing participants with identical behavioral tasks that differed only in the instructions to alter their metacognitive strategies. We extended the auditory delayed match-to-sample task with bet selection developed by Yuki et al. (2019) with a task that asked for prior beliefs about memory in the form of a bet, and a task that asked for prior beliefs about memory directly. We also varied the level of difficulty for the participants to examine the influence of environmental factors on each metacognition. To quantify the efficiency of each type of metacognition, we estimated M-ratio (Maniscalco and Lau, 2012; Fleming, 2017). M-ratio is an index of metacognitive efficiency based on the signal detection theory, which excludes confidence bias and performance-dependent components. Our results show that metacognitive efficiency increased when participants were asked to rate their confidence in making decisions.

A total of 237 adults participated in this online study through Lancers Inc., a crowdsourcing platform in Japan. Each participant had normal hearing and no history of neurological diseases or absolute pitch. Thirty-three participants (14%) were excluded from the analysis due to either a failure to respond or providing too few responses (exclusion criteria details are in the Analysis section below). The final analysis included 204 participants (83 females, 120 males), aged 19–50 years, with a mean age of 38.5 ± 7.3 years (mean ± SD). All participants provided informed consent before the study. This study was approved by the Doshisha University Ethics Committee for Research Plans Involving Human Subjects (no. 19042 and 23020).

We used tone sequences developed by Yuki et al. (2019) as stimuli to control task difficulty. Each tone sequence had seven distinct tones, each lasting 100 ms and comprising six harmonic components (−6 dB/oct.). The fundamental frequency (F0) of each tone was selected from the following nine frequencies: 440.0, 493.9, 554.4, 622.3, 698.5, 784.0, 880.0, 987.8, and 1108.7 Hz. All sound stimuli were created digitally using MATLAB software (R2014b; MathWorks Inc., Natick, MA, United States) at a 16-kHz sampling rate and 16-bit depth.

To compare explicit and implicit metacognition, we conducted an auditory delayed match-to-sample task with bet selection, extending the study by Yuki et al. (2019). The participants were divided into two groups: confidence and bet (Table 1). As shown in Figure 1, the participants in both groups were presented with two sound stimuli separated by a delay (3.0 s) and asked to judge whether they matched. In the confidence group, the participants were asked to rate their confidence in remembering the first sound. However, in the bet group, participants engaged in bet selection before listening to the second sound to maximize rewards unrelated to money. The bet selection had two options: low-risk/return options, earning one point for a correct answer without any penalty for an incorrect answer, and high-risk/return options, earning two points for a correct answer but losing one point for an incorrect answer. After the match response, the participants evaluated their confidence in their responses on a five-point scale. In short, the pre-rating was evaluated differently across the groups; however, the post-rating was assessed identically for both groups. At the end of each trial, participants received feedback on their responses, with the confidence group receiving information about the correctness of the trial (Correct/Incorrect) and the betting group receiving the points they earned on the trial (Score: ±X point).

The task was conducted over six sessions, each consisting of 12 trials. The level of difficulty varied between the first three sessions and second three sessions of the experiment. In the easy condition, the Pearson correlation between two sounds was 0.1 ≦ r ≦ 0.35, and in the hard condition was 0.7 ≦ r ≦ 0.95. The order of difficulty was counterbalanced among the participants. To avoid fixing pre-ratings (Clifford et al., 2008), the participants were instructed not to fixate on a single option in each session.

To remove outliers from the behavioral data, we first eliminated trials with no response or a response shorter than 100 ms from any one of the three responses. We excluded participants who provided identical responses across all trials within either difficulty condition or had fewer than 18 valid trials in either difficulty condition, accounting for 14% of all participants.

We analyzed accuracy (the rate of correct responses), d’, score (in the confidence group, we emulated a score in the same way as in the bet group), pre-rating, post-rating for each group, and task difficulty level. d’ is sensitivity based on signal detection theory and represents the ability to discriminate between a signal (a sound identical to the sample stimulus) and noise (a sound different from the sample stimulus) so that d’ can eliminate response bias. For statistical analysis, we used JASP 0.19.1.0 and conducted a two-way mixed analysis of variance (ANOVA) to compare behavioral indices across conditions. We calculated the generalized η squared (η²_G) as its effect size, and the significance level was set at α = 0.05. To evaluate the degree of support for the hypothesis, we ran a Bayesian ANOVA, in which the prior distribution was the default Cauchy distribution. Additionally, we conducted frequentist and Bayesian paired t-tests to investigate the relationship between the pre- and post-ratings. We reported BF_incl based on the Bayesian model average and BF₁₀. We adopted the alternative hypothesis if the BF was greater than 3, and the null hypothesis if it was less than 1/3.

We calculated the meta-d’/d’ (M-ratio) to estimate metacognitive efficiency from the betting choice and confidence ratings (Maniscalco and Lau, 2012; Fleming, 2017). Meta-d’ is the sensitivity of metacognition with bias removed based on signal detection theory (SDT), and M-ratio is the metacognitive efficiency, removing the effect of task performance on meta-d’. An M-ratio of one indicates that the participant behaves metacognitively and is perfectly optimal.

We estimated M-ratio using a hierarchical Bayesian model. Bayesian analysis offers a robust framework for making inferences from limited data by integrating prior knowledge (Fleming, 2017). Hierarchical Bayesian models utilize the hierarchical structure to “pool” information across participants, allowing for reliable estimation even when the number of trials per individual is limited (Gelman et al., 1995). This pooling mechanism enables stable estimation by leveraging information from other participants, which is a particularly advantageous when within-participant data are sparse. In addition, we extended the model used in previous studies to apply a two-way mixed ANOVA.

For estimating M-ratio, Markov chain Monte Carlo methods (MCMC) used three chains with 10,000 iterations, 1,000 burn-ins and the rest being the default parameters of JAGS (Just Another Gibbs Sampler) v4.3.1. We confirmed that R-hat was <1.001, and tail effective sample size (tail-ESS) was sufficient for the parameters of interest in all models. For the statistical tests, we reported the medians, 95% highest density intervals (HDI), and the probability of direction (pd) to test for the presence or absence of the effect of parameters (Makowski et al., 2019). We accepted the alternative hypothesis if the 95% HDI did not include 0 and the pd. was greater than 95%.

We first conducted a two-way mixed ANOVA for accuracy, d’, and score in task instruction and difficulty (Table 2). As expected, the average accuracy was higher in the easy condition (Figure 2A, p < 0.001, BF_incl > 100), but there was no difference between the task instructions and their interaction (p > 0.1, BF_incl < 1/3). The d’ and total scores also increased in the easy condition (d’ (Figure 2B) and total score (Figure 2C); p < 0.001, BF_incl > 100), but were not influenced by the task instruction (p > 0.1, BF_incl < 1/3).

Next, we examined the effects of instruction and difficulty on the pre- and post-ratings. A two-way mixed ANOVA revealed that the average pre-rating was not affected by task difficulty, instruction, or interaction (Figure 2D, p > 0.1, BF_incl < 1/3). Average post-confidence was higher in the easy condition (Figure 2E, difficulty: p < 0.001; BF_incl = 52.161; instruction and interaction: p > 0.1, BF_incl < 1/3).

We investigated whether the task instructions influenced metacognitive efficiency. Therefore, we calculated the effect of metacognitive efficiency (M-ratio) on task instruction and difficulty by applying hierarchical Bayesian modeling to the pre- and post-rating data (Table 3). As shown in Figure 3A, the pre-M-ratio increased at the betting instruction (median = −8.755, 95% HDI = [−17.725, −3.827], pd. = 1.000), but there was no main effect of difficulty and their interaction (difficulty: median = −2.922, 95% HDI = [−12.872, 3.460], pd. = 0.643; interaction: median = −3.438, 95% HDI = [−24.914, 1.781], pd. = 0.782). Despite the lack of manipulation in the “post-rating” phase, the post-M-ratio was influenced by task instruction, and difficulty (Figure 3B, instruction: median = −0.366, 95% HDI = [−1.075, −0.110], pd. = 0.992; difficulty: median = −8.924, 95% HDI = [−15.655, −1.314], pd. = 1.000; interaction: median = −1.920, 95% HDI = [−8.351, 1.956], pd. = 0.778). Specifically, the post-M-ratio was higher in the betting instruction and easy conditions. As shown in Figures 3A,B right, the pre- and post-M ratios were <1.

We wondered why the instruction manipulated only prospective metacognition, but also showed effects on retrospective metacognition. It was postulated that information derived from the pre-rating stage may have been carried over to the post-rating stage. Consequently, a paired t-test was conducted on the post- and pre-rating. The analysis showed that the pre-rating corresponded to the post-rating, that is, if the pre-rating was high, the post-rating was also high [Figure 4, t(203) = −8.574, p < 0.001, Cohen’s d = −0.600, BF₁₀ = 2.256 × 10¹²].