Data availability

Surveys EB, Pew and GSS are publicly available and data and details can be found in refs. 27,28,29, respectively. The Fernbach study was published in ref. 9 and the authors made the data available. Lackner survey data are available at: https://doi.org/10.5281/zenodo.7920776.

Code availability

All code used for the analysis is available at: https://doi.org/10.5281/zenodo.7920750.

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Acknowledgements

We thank C. Souto-Mayor, M. West and J. Nolasco for initial extraction and analysis of the EB dataset, members of the SPAC group for valuable discussions, Fernbach et al.9 for making their survey data available and M. Bauer, T. Paixão, M. Entradas and J. Lobo Antunes for critical reading of the manuscript. We also thank L. Hamilton for independently testing the robustness of our metric and confirming some of our findings. This project was partially funded by Welcome DFRH WIIA 60 2011 and ERC-Starting Grant FARE-853566, both to J.G.S. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

Author notes

  1. These authors contributed equally: Simone Lackner, Frederico Francisco, Cristina Mendonça.

Authors and Affiliations

  1. LIP – Laboratório de Instrumentação e Física Experimental de Partículas, Lisboa, Portugal

    Simone Lackner, Cristina Mendonça & Joana Gonçalves-Sá

  2. Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Porto, Portugal

    Frederico Francisco

  3. CICPSI, Faculdade de Psicologia, Universidade de Lisboa, Lisboa, Portugal

    André Mata

  4. Nova School of Business and Economics, Carcavelos, Portugal

    Joana Gonçalves-Sá

Contributions

J.G.S. conceived of this work. All authors contributed to the methodology. S.L., F.F., C.M. and J.G.S were involved in investigation. A.M. and J.G.S. undertook supervision. All authors wrote the manuscript.

Corresponding author

Correspondence to
Joana Gonçalves-Sá.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Human Behaviour thanks Ian Brunton-Smith, Lawrence Hamilton and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Model comparison.

Different expectations of the proportions of correct (yellow), incorrect (purple) and ‘Don’t Know’ (green) answers, per knowledge bin (a, c, e, g, i) or proportion of incorrect (purple) and ‘Don’t Know’ (green) within non-correct answers only, per knowledge bin (b, d, f, h, j) depending on different expectations of the relationship between confidence and knowledge (k). Perfect metacognition (a, b, yellow solid line in k) expects all non-correct answers to be of the ‘Don’t Know’ type. Random answering (c, d, dotted blue line in k) expects a constant and even proportion of ‘Don’t Know’ and incorrect answers regardless of knowledge bin. If overconfidence decreases with knowledge (e,f, green lines in k), the proportion of incorrect answers should decrease as knowledge increases. If overconfidence increases with knowledge (i, j, solid purple line in k), the proportion of incorrect answers should increase as knowledge increases. If respondents only ‘guess’ when they do not know the answer, the distribution of incorrect may vary depending on the baseline knowledge and the fraction of incorrect should grow nonlinearly with knowledge (g, h, large-dash grey line in k).

Extended Data Fig. 2 Knowledge distributions.

Knowledge distributions for EB (a), GSS (b), Pew (c), Lackner (d) and Fernbach (e). Absolute frequencies for the first bin in each dataset were: 1179, 107, 165, 2, 42, respectively. Absolute frequencies for the last bin in each dataset were: 2753, 556, 685, 64, 48, respectively.

Extended Data Fig. 3 Alternative calibration models.

Alternative representation of calibration errors, with different null models. Left axis show the answer proportion with green bars representing observed proportion of ‘Don’t Know’ answers per knowledge bin and purple bars representing observed proportion of incorrect answers per knowledge bin, out of all non-correct answers, for EB (a–d), GSS (e–h), Pew (i–l) and Lackner (m–p). In all plots, solid lines show the expected proportion of incorrect answers (null model) and the dashed line the calibration error calculated as the difference between the observed and the corresponding null. As different null models allow for different expectations please note that the right axis, can vary between 0 and 1 or between -1 and 1. In (a, e, i, m), the null model represents the perfect metacognitive model (yellow lines), in which any incorrect answer represent a calibration error. In (b, f, j, n), the null model represents random guessing (blue lines), such that an equal proportion of incorrect and ‘Don’t Know’ answers is expected, regardless of knowledge level. In (c, g, k, o), the null model expects confidence to increase in tandem with knowledge (purple lines). In (d, h, l, p), the null model is the result of the simulations with 25% guessers (dark-grey lines).

Extended Data Fig. 4 Demographic analyses for the EB and Lackner surveys.

(a–d) EB data, (e–g) Lackner data. (a, e) Box plot shows the fraction of female (orange) and male (blue) respondents that never say ‘Don’t know’ across (a) 31 territories or (e) 3 countries. Data was negatively tested for normality using scipy’s stats module’s normaltest function (α = 0.001) and for similarity (two-tailed Mann-Whitney U test) in both datasets. Three black asterisks indicate statistical significance with p < 0.001 in (a) and in (e) no significant difference was found. (b, f) Box plot shows the fraction of different age group bins that never say ‘Don’t know’ across all (b) 31 territories or (f) 3 Lackner-surveyed countries. Diamond indicates an outlier (values in the panel). A two-tailed Kruskal-Wallis H-test and all pairwise comparisons were found to be significant with post hoc Tukey’s tests except for (b) 25-39 vs. 40-49 and 40-49 vs. 55+ and no evidence of significance in (f) (p = 0.042). (c, g) Box plot shows the fractions of different bins of age at time of completing their education that never say ‘Don’t know’ across all (c) 31 territories or (g) 3 Lackner-surveyed countries. Diamonds mark outliers (values in the panel). A two-tailed Kruskal-Wallis H-test and all pairwise comparisons were found to be significant with post hoc Tukey’s tests, except for ‘Up to 15’ vs. ‘Still studying’ and ‘16-19’ vs. ‘20 + ’, in (c) and no evidence of significance in (g) (p = 0.036). (d) Scatter plot shows for each territory the fraction of respondents that never say ‘Don’t know’ sorted according to latitude of the territory. Black line shows the linear regression with low correlation represented R2 = 0.21. (h). Table with values for all whiskers (low, 3rd column and high, 7th column) and quartiles (Q1, Median and Q3).

Extended Data Fig. 5 Answer distributions to the ‘How Informed’ questions and calibration errors.

(a, c, e, g, i) Stacked bar plots showing fraction of respondents who answered ‘Poorly’ (yellow), ‘Moderately well’ (light blue) and ‘Very well’ (dark green) when questioned how informed they were about (a) new inventions and technologies, (c) new medical discoveries, (e) new scientific discoveries, (g) politics and (i) sports news, per knowledge level. In all panels, black solid lines with squares indicate mean fraction of respondents who answered ‘Moderately well’ or ‘Very well’ per quartile, while solid grey line shows average knowledge rank per quartile. (b, d, f, h, j) Plot showing the difference between average fraction of respondents who answered ‘Moderately well’ or ‘Very well’ per quartile and average knowledge rank per quartile, each represented by a circle marking the average and a vertical line marking the variation in average between bins of the same quartile.

Extended Data Fig. 6 EB attitudinal data.

(a, c, e, g, i, k, m) show stacked bar plots with fractions of Agree (orange), Neutral (yellow) and Disagree (red) answers in response to 7 EB attitude questions. Order of stacked bars is inverted in (e, k) as, in those two items, a negative attitude could be revealed by the Agree answer, while the reverse might be true for (a, g, m). (c) and (i) show a more nuanced response. Figures in (b, d, f, h, j, l, n) show the mean fractions across 34 EU territories with standard error of the mean.

Extended Data Table 1 Knowledge questions
Extended Data Table 2 Attitude questions

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Lackner, S., Francisco, F., Mendonça, C. et al. Intermediate levels of scientific knowledge are associated with overconfidence and negative attitudes towards science.
Nat Hum Behav (2023). https://doi.org/10.1038/s41562-023-01677-8

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