Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Foundations of intuitive power analyses in children and adults


Decades of research indicate that some of the epistemic practices that support scientific enquiry emerge as part of intuitive reasoning in early childhood. Here, we ask whether adults and young children can use intuitive statistical reasoning and metacognitive strategies to estimate how much information they might need to solve different discrimination problems, suggesting that they have some of the foundations for ‘intuitive power analyses’. Across five experiments, both adults (N = 290) and children (N = 48, 6–8 years) were able to precisely represent the relative difficulty of discriminating populations and recognized that larger samples were required for populations with greater overlap. Participants were sensitive to the cost of sampling, as well as the perceptual nature of the stimuli. These findings indicate that both young children and adults metacognitively represent their own ability to make discriminations even in the absence of data, and can use this to guide efficient and effective exploration.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Ideal sampling across varied costs.
Fig. 2: Stimuli used in behavioural tasks.
Fig. 3: Adult sampling behavior for each of the ten discriminations (ranging from 51/49 to 95/5) in experiments 1 and 2.
Fig. 4: ‘Measures of adults’ metacognitive awareness before and after sampling in experiments 3a and 3b.
Fig. 5: Adult estimates and sampling behavior using numerical rather than visual proportions.
Fig. 6: Perceptual noise model fits.
Fig. 7: Children’s sampling behavior in experiment 5 and its replication.
Fig. 8: Perceptual noise model fits for Experiment 5 and its replication.

Similar content being viewed by others

Data availability

The data that support the findings of this study are available on the Open Science Foundation project page found at Source data are provided with this paper.

Code availability

Code used for data analysis is available from the corresponding author upon request.


  1. Saffran, J. R., Aslin, R. N. & Newport, E. L. Statistical learning by 8-month-old infants. Science 274, 1926–1928 (1996).

    Article  CAS  PubMed  Google Scholar 

  2. Johnson, M. H., Posner, M. I. & Rothbart, M. K. Components of visual orienting in early infancy: contingency learning, anticipatory looking, and disengaging. J. Cogn. Neurosci. 3, 335–344 (1991).

    Article  CAS  PubMed  Google Scholar 

  3. Marcus, G. F., Vijayan, S., Rao, S. B. & Vishton, P. M. Rule learning by seven-month- old infants. Science 283, 77–80 (1999).

    Article  CAS  PubMed  Google Scholar 

  4. Téglás, E. et al. Pure reasoning in 12-month-old infants as probabilistic inference. Science 332, 1054–1059 (2011).

    Article  PubMed  Google Scholar 

  5. Xu, F. & Denison, S. Statistical inference and sensitivity to sampling in 11-month-old infants. Cognition 112, 97–104 (2009).

    Article  PubMed  Google Scholar 

  6. Kidd, C., Piantadosi, S. T. & Aslin, R. N. The Goldilocks effect: human infants allocate attention to visual sequences that are neither too simple nor too complex. PLoS ONE 7, e36399 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Stahl, A. E. & Feigenson, L. Observing the unexpected enhances infants’ learning and exploration. Science 348, 91–94 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Gweon, H., Tenenbaum, J. B. & Schulz, L. E. Infants consider both the sample and the sampling process in inductive generalization. Proc. Natl Acad. Sci. USA 107, 9066–9071 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Bullock, M., Gelman, R. & Baillargeon, R. in The Developmental Psychology of Time (ed. Friedman, W. J.) 209–254 (Academic Press, 1982).

  10. Saxe, R., Tenenbaum, J. & Carey, S. Secret agents: Inferences about hidden causes by 10-and 12-month-old infants. Psychological Sci. 16, 995–1001 (2005).

    Article  CAS  Google Scholar 

  11. Bonawitz, E. B., van Schijndel, T. J., Friel, D. & Schulz, L. Children balance theories and evidence in exploration, explanation, and learning. Cogn. Psychol. 64, 215–234 (2012).

    Article  PubMed  Google Scholar 

  12. Legare, C. H. Exploring explanation: explaining inconsistent evidence informs exploratory, hypothesis-testing behavior in young children. Child Dev. 83, 173–185 (2012).

    Article  PubMed  Google Scholar 

  13. Cook, C., Goodman, N. D. & Schulz, L. E. Where science starts: spontaneous experiments in preschoolers’ exploratory play. Cognition 120, 341–349 (2011).

    Article  PubMed  Google Scholar 

  14. Sobel, D. M., Tenenbaum, J. B. & Gopnik, A. Children’s causal inferences from indirect evidence: backwards blocking and Bayesian reasoning in preschoolers. Cogn. Sci. 28, 303–333 (2004).

    Google Scholar 

  15. Sobel, D. M. & Kushnir, T. Knowledge matters: how children evaluate the reliability of testimony as a process of rational inference. Psychological Rev. 120, 779 (2013).

    Article  Google Scholar 

  16. Marazita, J. M. & Merriman, W. E. Young children’s judgment of whether they know names for objects: the metalinguistic ability it reflects and the processes it involves. J. Mem. Lang. 51, 458–472 (2004).

    Article  Google Scholar 

  17. Patterson, C. J., Cosgrove, J. M. & O’Brien, R. G. Nonverbal indicants of comprehension and noncomprehension in children. Developmental Psychol. 16, 38 (1980).

    Article  Google Scholar 

  18. Balcomb, F. K. & Gerken, L. Three-year-old children can access their own memory to guide responses on a visual matching task. Developmental Sci. 11, 750–760 (2008).

    Article  Google Scholar 

  19. Lyons, K. E. & Ghetti, S. I don’t want to pick! Introspection on uncertainty supports early strategic behavior. Child Dev. 84, 726–736 (2013).

    Article  PubMed  Google Scholar 

  20. Hembacher, E. & Ghetti, S. Don’t look at my answer: subjective uncertainty underlies preschoolers’ exclusion of their least accurate memories. Psychological Sci. 25, 1768–1776 (2014).

    Article  Google Scholar 

  21. Kim, S., Paulus, M., Sodian, B. & Proust, J. Young children’s sensitivity to their own ignorance in informing others. PLoS ONE 11, e0152595 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  22. Ghetti, S., Hembacher, E. & Coughlin, C. A. Feeling uncertain and acting on it during the preschool years: a metacognitive approach. Child Dev. Perspect. 7, 160–165 (2013).

    Article  Google Scholar 

  23. Coughlin, C., Hembacher, E., Lyons, K. E. & Ghetti, S. Introspection on uncertainty and judicious help-seeking during the preschool years. Developmental Sci. 18, 957–971 (2015).

    Article  Google Scholar 

  24. Lyons, K. E. & Ghetti, S. The development of uncertainty monitoring in early childhood. Child Dev. 82, 1778–1787 (2011).

    Article  PubMed  Google Scholar 

  25. Paulus, M., Proust, J. & Sodian, B. Examining implicit metacognition in 3.5-year-old children: an eye-tracking and pupillometric study. Front. Psychol. 4, 145 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  26. Call, J. & Carpenter, M. Do apes and children know what they have seen? Anim. Cognition 3, 207–220 (2001).

    Article  Google Scholar 

  27. Chouinard M. M. Children’s questions: a mechanism for cognitive development. Monogr. Soc. Res. Child Dev. (2007).

  28. Whitebread, D. et al. The development of two observational tools for assessing meta-cognition and self-regulated learning in young children. Metacognition Learn. 4, 63–85 (2009).

    Article  Google Scholar 

  29. Destan, N., Hembacher, E., Ghetti, S. & Roebers, C. M. Early metacognitive abilities: the interplay of monitoring and control processes in 5-to 7-year-old children. J. Exp. Child Psychol. 126, 213–228 (2014).

    Article  PubMed  Google Scholar 

  30. Flavell, J. H., Friedrichs, A. G. & Hoyt, J. D. Developmental changes in memorization processes. Cogn. Psychol. 1, 324–340 (1970).

    Article  Google Scholar 

  31. Koriat, A., Sheffer, L. & Ma’ayan, H. Comparing objective and subjective learning curves: judgments of learning exhibit increased underconfidence with practice. J. Exp. Psychol.: Gen. 131, 147 (2002).

    Article  Google Scholar 

  32. Metcalfe, J. & Finn, B. Metacognition and control of study choice in children. Metacognition Learn. 8, 19–46 (2013).

    Article  Google Scholar 

  33. Hofer, B. K. & Pintrich, P. R. The development of epistemological theories: beliefs about knowledge and knowing and their relation to learning. Rev. Educ. Res. 67, 88–140 (1997).

    Article  Google Scholar 

  34. Lockl, K. & Schneider, W. The effects of incentives and instructions on children’s allocation of study time. Eur. J. Developmental Psychol. 1, 153–169 (2004).

    Article  Google Scholar 

  35. Roebers, C. M. & Howie, P. Confidence judgments in event recall: developmental progression in the impact of question format. J. Exp. Child Psychol. 85, 352–371 (2003).

    Article  PubMed  Google Scholar 

  36. Schneider, W. & Pressley, M. Memory Development Between Two and Twenty (Psychology Press, 2013).

  37. Veenman, M. V., Van Hout-Wolters, B. H. & Afflerbach, P. Metacognition and learning: conceptual and methodological considerations. Metacognition Learn. 1, 3–14 (2006).

    Article  Google Scholar 

  38. Siegel, M. H., Magid, R. W., Pelz, M., Tenenbaum, J. B. & Schulz, L. E. Children’s exploratory play tracks the discriminability of hypotheses. Nat. Commun. 12, 3598 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. Xu, F. & Garcia, V. Intuitive statistics by 8-month-old infants. Proc. Natl Acad. Sci. USA 105, 5012–5015 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Vul, E., Goodman, N., Griffiths, T. L. & Tenenbaum, J. B. One and done? Optimal decisions from very few samples. Cogn. Sci. 38, 599–637 (2014).

    Article  PubMed  Google Scholar 

  41. Zhang, H. & Maloney, L. T. Ubiquitous log odds: a common representation of probability and frequency distortion in perception, action, and cognition. Front. Neuroscience (2012).

  42. Tversky, A. & Kahneman, D. Belief in the law of small numbers. Psychological Bull. 76, 105–110 (1971).

    Article  Google Scholar 

  43. Tversky, A. & Kahneman, D. Judgment under uncertainty: heuristics and biases. Science 185, 1124–1131 (1974).

    Article  CAS  PubMed  Google Scholar 

  44. Jones, P. R. et al. Efficient visual information sampling develops late in childhood. J. Exp. Psychol.: Gen. 148, 1138–1152 (2019).

    Article  Google Scholar 

Download references


Thank you to the Boston Children’s Museum and the families who participated in this research. This material is based on work supported by the National Science Foundation Graduate Research Fellowship under grant no. 1745302 to M.C.P., and National Science Foundation grant no. 1231216 to L.E.S. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

Authors and Affiliations



M.C.P. and L.E.S. conceived and designed the behavioural studies. K.R.A. and J.B.T. contributed the computational modelling. The manuscript was written primarily by M.C.P. and L.E.S. with input and comments from K.R.A.

Corresponding author

Correspondence to Laura E. Schulz.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Human Behaviour thanks Yingying Yang, Matteo Lisi 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.

Supplementary information

Source data

Source Data Fig. 1

Model output data.

Source Data Fig. 3

Statistical source data.

Source Data Fig. 4

Statistical source data.

Source Data Fig. 5

Statistical source data.

Source Data Fig. 6

Statistical source data.

Source Data Fig. 7

Statistical source data.

Source Data Fig. 8

Statistical source data.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pelz, M.C., Allen, K.R., Tenenbaum, J.B. et al. Foundations of intuitive power analyses in children and adults. Nat Hum Behav 6, 1557–1568 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing