Power Analysis for the t-test
Statistical Power Analysis for the t-test · Also known as: t-test power analysis, sample size calculation for t-test, Güç Analizi — t-Testi
Power analysis for the t-test is a sample size planning procedure that determines how many participants are required to detect a mean difference of a given magnitude with acceptable probability. Formalised by Jacob Cohen in his 1969 and 1988 editions of Statistical Power Analysis for the Behavioral Sciences, it links four quantities — effect size (Cohen's d), significance level (α), statistical power (1 − β), and sample size — so that fixing any three allows calculation of the fourth.
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When to use it
Use this procedure when planning any study that will be analysed with an independent-samples or paired t-test. The two key assumptions are that you can estimate Cohen's d from prior literature or a pilot study, and that you have fixed your significance level in advance (typically 0.05). No normality requirement is imposed on the power calculation itself, though the t-test it plans for does require approximately normal data or a sufficiently large sample.
Strengths & limitations
- Provides a principled, quantitative justification for sample size decisions before data collection.
- Directly reduces the risk of underpowered studies, which are a major source of non-replicable findings.
- Sensitivity analysis across a range of plausible d values takes only seconds and reveals how robust the design is to effect-size uncertainty.
- Widely accepted by ethics boards, grant agencies, and journal editors as a methodological prerequisite.
- The result is only as accurate as the effect-size estimate; an unrealistic d yields a misleading sample size.
- Does not account for attrition, missing data, or complex designs — the calculated n is a minimum for the simple two-group case.
- Post-hoc power computed from the observed effect size is circular and should not be used to interpret a non-significant result.
Frequently asked
What value of Cohen's d should I use?
Use the smallest effect you consider practically meaningful, derived from prior literature or a well-conducted pilot study. Cohen's conventional benchmarks (d = 0.2 small, 0.5 medium, 0.8 large) are starting points only; the most defensible approach is to justify the chosen d from domain knowledge.
Why is 0.80 the conventional power target?
Cohen (1988) proposed 0.80 as a pragmatic balance between sample cost and the risk of a false negative, noting that it implies a 4:1 ratio of β to α errors. It is a convention, not a law — high-stakes applications routinely require 0.90 or 0.95.
Can I run power analysis after collecting data?
Post-hoc power computed from the observed effect size is circular and uninformative: a non-significant result will always appear to have low power, adding no new information. For interpreting a non-significant result, report a confidence interval and consider equivalence testing instead.
Does this apply to both independent and paired t-tests?
Yes. For the paired t-test, d is computed from the mean difference and the standard deviation of differences, and only one sample size is needed rather than two. The statwise tool covers both variants.
Sources
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates. ISBN: 978-0805802832
How to cite this page
ScholarGate. (2026, June 1). Statistical Power Analysis for the t-test. ScholarGate. https://scholargate.app/en/statistics/power-analysis-ttest
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Independent t-testStatistics↔ compare
- Paired t-testStatistics↔ compare
- Power Analysis for ANOVAStatistics↔ compare
- Power Analysis for RegressionStatistics↔ compare
- Welch t-testStatistics↔ compare