Statistical power

Last updated on Feb 18, 2026
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Definition: Statistical power is the long-run probability that a statistical test correctly rejects the null hypothesis if the alternative hypothesis is true. It ranges from 0 to 1, but is often expressed as a percentage. Power can be estimated using the significance criterion (alpha), effect size, and sample size used for a specific analysis technique. There are two main applications of statistical power. A priori power where the researcher asks the question “given an effect size, how many participants would I need for X% power?”. Sensitivity power asks the question “given a known sample size, what effect size could I detect with X% power?”.

Related terms: Effect Size, Meta-analysis, Null Hypothesis Significance Testing (NHST), Power Analysis, Positive Predictive Value, Quantitative research, Sample size, Significance criterion (alpha), Type I error, Type II error **Related terms to alternative definition:** Type II Error

References:

  • Carter, A., Tilling, K., & Munafo, M. R. (2021). Considerations of sample size and power calculations given a range of analytical scenarios. https://doi.org/10.31234/osf.io/tcqrn
  • Cohen, J. (1962). The statistical power of abnormal-social psychological research: A review. The Journal of Abnormal and Social Psychology, 65(3), 145–153. https://doi.org/10.1037/h0045186
  • Cohen, J. (1969). Statistical power analysis for the behavioral sciences. Academic Press.
  • Dienes, Z. (2008). Understanding psychology as a science: An introduction to scientific and statistical inference. Macmillan International Higher Education.
  • Giner-Sorolla, R., Aberson, C. L., Bostyn, D. H., Carpenter, T., Conrique, B. G., Lewis, N. A., & Soderberg, C. (2019). Power to detect what? Considerations for planning and evaluating sample size. Retrieved from https://osf.io/jnmya/
  • Ioannidis, J. P. (2005). Why most published research findings are false. PLoS Medicine, 2(8), e124. https://doi.org/10.1371/journal.pmed.0020124
  • Lakens, D. (2021). Sample Size Justification. https://doi.org/10.31234/osf.io/9d3yf

Originally drafted by: Thomas Rhys Evans

Reviewed by: James E. Bartlett, Jamie P. Cockcroft, Adrien Fillon, Emma Henderson, Tamara Kalandadze, William Ngiam, Catia M. Oliveira, Charlotte R. Pennington, Graham Reid, Martin Vasilev, Qinyu Xiao, FlĂĄvio Azevedo