Article Figures & Data
Figures
- Figure 1.
A, Task. B, Example trial with both continuous report (CR+) and first-order 2AFC response. On each 5 s trial, two stimuli pairs appeared serially in four consecutive intervals. Participants pressed one of two keys for the entire duration of the trial, tracking the visual presentation (continuous report). Following stimulus offset, participants reported which of the two stimuli had the longest duration overall. B, Experimental design. Each trial was one of the four possible conditions resulting from a combination of first-order 2ACF response and continuous report (CR+R+; CR+R−; CR−R+; or CR−R−). Participants rated their confidence in all conditions. Thus, the task demanded that participants make a first-order 2AFC judgment in every trial, but the corresponding overt action was only present in R+ conditions.
- Figure 2.
A, Differences in confidence judgments between conditions. A 2 × 2 ANOVA on mean confidence judgments revealed that trials with continuous report (CR+) were associated with higher confidence. B, Relationship between first-order reaction times and confidence judgments. Linear mixed-effects regressions revealed that, as expected, confidence judgments had a strong negative relationship with first-order reaction times on a trial-wise level. This relationship was present in all R+ trials (R− trials were not included in this analysis) but was stronger in the subset of correct trials. Regression lines and confidence intervals around them represent the model fit. The model took continuous reaction times as input. For illustrative purposes, we plot open circles and error bars that represent mean ± 95% CI over participants after rounding reaction times and subtracting 0.5 s.
- Figure 3.
Differences in metacognitive performance between conditions. A, Metacognitive sensitivity quantified with a regression model on accuracy versus confidence. Estimated regression curves from the proxy for first-order 2AFC response (left) and overt first-order 2AFC response (right). The presence of a first-order 2AFC response did not affect the relationship between confidence and the first-order accuracy of the proxy. Open circles and error bars represent the mean ± 95% CI over participants after rounding confidence ratings. B, Metacognitive efficiency quantified with M-ratio. As in A, we found no evidence that either giving an overt first-order response (left) or pairing an action to perceptual input (right) improved metacognitive efficiency. The insets above the panels highlight (in gray) which trials were used for each of the analyses.
- Figure 4.
Power simulations. A, Data simulation strategy. We considered two conditions (in this case, CR+R+ and CR+R−) expected to differ in M-ratio. For each 1 of 250 experiments, we simulated 80 trials per condition, drawing three values for each of the “real” internal signal (top left row, i), a noisy confidence estimate (internal signal + metacognitive noise for each of two conditions; middle row, ii) and a value for the noisy proxy (bottom left row, iii). We fed the simulated trials into a logistic regression model, and determined the power of our analysis [i.e., the proportion of “experiments” in which the interaction term (representing a difference in metacognitive sensitivity between conditions) was significant (right)]. B, C, Results: power estimations for the analysis based on actual responses (B) and for proxy-based responses (C). D, The power difference between B and C. There are no differences in power when differences in M-ratios between two conditions are large (regions away from the diagonal), whereas there are small decreases in power for the proxy-based analysis for combinations of M-ratios that are closer to the diagonal.
Tables
Data structure Type of test Power/effect size Statistic a: Performance in first-order task (CR+R+ vs CR− R+) Mean per subject (continuous) Bayesian t test d = −0.02 BF10 = 0.22 b: Mean perceptual evidence (CR+R+ vs CR−R+) Mean per subject (continuous) Bayesian t test d = 0.36 BF10 = 0.54 c: interaction between overt first-order (R+/R−) and continuous report (CR+/CR−) on mean confidence (all trials) Single-trial confidence ratings (continuous) Bayesian mixed-effects linear regression Mean = −0.02 ± 0.01 Evidence ratio = 0.10 d: Main effect of CR+ on confidence (all trials) Single-trial confidence ratings (continuous) Bayesian mixed-effects linear regression Mean = 0.04 ± 0.02 Evidence ratio = 75.92 e: Main effect of first-order RT on confidence (R+ trials) Single-trial response times (continuous) Bayesian mixed-effects linear regression Mean = −0.15 ± 0.02 Evidence ratio > 4000), f: Interaction between condition (CR+R+/CR+R−) and confidence on proxy accuracy Single-trial accuracy (binomial) Bayesian mixed-effects logistic regression Mean = −0.11 ± 0.39 Evidence ratio = 1.57 g: Main effect of confidence on proxy accuracy (CR+ trials) Single-trial confidence ratings (continuous) Bayesian mixed-effects linear regression Mean = 0.82 ± 0.32 Evidence ratio = 116.65 h: M-ratio between conditions (CR+R+ vs CR+R−) Posterior probability distributions (continuous) Differences between Highest density intervals HDI = [−1.42, 0.89] NA NA, Not applicable.
Extended Data
Supplementary Experimental codes, raw data, analysis, and simulation files. Download Extended Data, ZIP file.
In this issue
