What is a power analysis in research?

It is a calculation of the sample size needed to detect an expected effect with a given probability (power, usually 80%) at a chosen significance level (usually .05). It is done before data collection to justify the sample size.

What effect size should I use for a power analysis?

Use the effect found in previous similar studies or a pilot study if possible. If none exists, a medium effect (d = 0.5, f = 0.25, r = .30, w = .30) is a common, clearly stated default.

Is this the same as G*Power?

It uses the same noncentral distributions as G*Power for t-tests, ANOVA, and chi-square, so the sample sizes match (for example 64 per group for d = 0.5, α = .05, power = .80). Correlation uses the Fisher z approximation, which can differ by one participant.

Should I use Slovin's formula or a power analysis?

Slovin's and Cochran's formulas estimate a proportion or mean from a population (common in surveys). A power analysis is for hypothesis tests such as t-tests and ANOVA. Many reviewers prefer a power analysis when your research questions are tested statistically.

POWER ANALYSIS CALCULATOR

Power analysis calculator: sample size for t-tests, ANOVA, correlation, and chi-square.

Find the minimum sample size for your study from the effect size, alpha, and desired power, the same a priori analysis G*Power runs, with a power curve and a sentence for your methodology chapter.

A PRIORI POWER ANALYSIS

Independent t-test

BROWSER-ONLY

EFFECT SIZE (COHEN'S D)ALPHA (α)POWER (1 − β)TAILS

Cohen's (1988) benchmarks for Cohen's d:

Power analysis: what it is, how sample size is calculated, and how to report it

What a power analysis tells you

Statistical power is the probability that your study detects an effect that really exists (1 − β). An a priori power analysis, run before data collection, finds the smallest sample that gives the power you want, usually 80%, for an expected effect size and significance level (α = .05). Supervisors and ethics committees ask for it to show that the study is neither underpowered nor wastefully large.

The four linked quantities

Effect size: how big a difference or relationship you expect (Cohen's d, f, r, or w)
Alpha (α): the false-positive rate you accept, usually .05
Power (1 − β): the chance of detecting the effect, usually .80 (.90 for confirmatory studies)
Sample size (N): fix the other three and N follows; smaller effects need much larger samples

How it is calculated

t-test: δ = d·√(n/2) (independent) or d·√n (paired);   ANOVA: λ = f²·N;   chi-square: λ = w²·N;   correlation: z = atanh(r)·√(N − 3)

Power is the probability that the test statistic exceeds its critical value under the noncentral t, F, or chi-square distribution with the noncentrality above. The calculator searches for the smallest N that reaches the target power. Results match G*Power (Faul et al., 2007): d = 0.5, α = .05, power = .80 gives 64 per group; f = 0.25 with 3 groups gives N = 159; w = 0.3 with df = 1 gives N = 88.

Effect size benchmarks (Cohen, 1988)

Cohen's d (t-tests): 0.2 small, 0.5 medium, 0.8 large
Cohen's f (ANOVA): 0.10 small, 0.25 medium, 0.40 large (f = √(η² ÷ (1 − η²)))
Correlation r: 0.10 small, 0.30 medium, 0.50 large
Cohen's w (chi-square): 0.10 small, 0.30 medium, 0.50 large
Prefer an effect size from previous studies or a pilot; use the Effect Size Calculator to convert reported results

How to report it in your methodology

“An a priori power analysis was conducted to determine the required sample size. To detect a medium effect (d = 0.50) with 80% power at α = .05 (two-tailed), an independent-samples t-test requires 64 participants per group (N = 128). Allowing for 20% attrition, 160 participants will be recruited.” Always state the test, effect size and where it came from, α, power, and the resulting N.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175–191.
Lakens, D. (2022). Sample size justification. Collabra: Psychology, 8(1), 33267.
Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159.

Power Analysis Calculator

Justify your sample size the way supervisors expect: choose the test, set the expected effect size, alpha, and power, and get the required N, a power curve, and a methodology sentence.

Justify the sample size in a thesis proposal or ethics application

Find how many participants per group a t-test or ANOVA needs

Check the power of a study with a fixed sample

KEY FUNCTIONS

Independent and paired t-tests, one-way ANOVA, correlation, and chi-squareExact noncentral t, F, and chi-square power (matches G*Power)One- or two-tailed tests and any alpha and powerPower curve and power check for a fixed NMethodology sentence and dropout adjustment

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