An a priori power analysis tells you how many participants you need before you collect data, so that your study has a good chance of detecting a real effect. Enter the expected effect size (Cohen’s d), the significance level and the desired power, and the calculator returns the required sample size per group for an independent samples t test, using the exact noncentral t distribution (the same method as G*Power).
How to use this calculator
- Enter the expected effect size d. Take it from a similar published study or a pilot; if none exists, d = 0.5 (medium) is a common default.
- Choose α (usually .05) and power (usually .80).
- Choose two-tailed unless you have a pre-registered directional hypothesis.
- Click Calculate and report the per-group and total sample size.
Formula
δ = d · √(n / 2) (noncentrality parameter), df = 2n − 2 Power = P(|T′| > t_crit) where T′ follows a noncentral t distribution with δ n is increased until power ≥ target. Normal approximation: n ≈ 2 (z₁₋α/₂ + z₁₋β)² / d²
Step-by-step example
- d = 0.5, α = .05 (two-tailed), power = .80.
- Required n = 64 per group (128 in total).
- For a large effect (d = 0.8) only 26 per group are needed; for a small effect (d = 0.2) you would need 394 per group.
How to interpret the results
The result is the minimum number of participants per group needed to detect the specified effect with the chosen power. If you cannot recruit that many, either justify a larger expected effect from the literature or acknowledge reduced power as a limitation. Add extra participants for expected dropout.
How to report it in APA 7 style
An a priori power analysis for an independent-samples t test (two-tailed, α = .05, power = .80) indicated that a minimum of 64 participants per group (N = 128) was required to detect a medium effect (d = 0.50).
Statistical symbols (t, F, p, r, M, SD, N, d) should be italicised in your thesis.
Assumptions
- The planned analysis is an independent samples t test with two equal-sized groups.
- The expected effect size is a realistic estimate (from prior studies or a pilot).
- For other designs (ANOVA, correlation, regression) a different power calculation is needed.
How to do it in SPSS, R or Excel
G*Power: t tests → Means: Difference between two independent means (two groups) → A priori. R: pwr::pwr.t.test(d = 0.5, power = 0.8). ScholarCalc’s results match statsmodels’ TTestIndPower.
Roman Urdu mein khulasa
Power analysis research shuru karne se pehle batata hai ke aap ko kitne participants chahiyein taake agar asal farq ho to aap ka test use pakar sake. Effect size pichli research se lein; agar na mile to 0.5 (medium) aam choice hai. Alpha 0.05 aur power 0.80 standard hain. Jo number aaye woh har group ke liye hai, total ke liye 2 se multiply karein.
Frequently asked questions
What power should I use?
Power of .80 (an 80% chance of detecting a true effect) is the most common standard. Some funders and journals prefer .90.
Where do I get the effect size from?
Use the effect size reported in similar previous studies or a meta-analysis, or run a small pilot study. If nothing is available, Cohen’s conventions (0.2, 0.5, 0.8) can be used with justification.
Does this match G*Power?
Yes. The calculator uses the noncentral t distribution, the same method as G*Power, and its results were checked against Python’s statsmodels power module.
What is the difference between power analysis and the Cochran sample size formula?
Power analysis is for hypothesis tests that compare groups or test effects. Cochran’s formula is for surveys estimating a proportion with a given margin of error.
Can I do a power analysis after collecting data?
Post hoc (observed) power is widely criticised because it adds no information beyond the p-value. Report confidence intervals and effect sizes instead.
What about ANOVA or regression?
This tool covers the two-group t test. Power analyses for ANOVA, correlation and regression are planned for ScholarCalc; until then G*Power can be used.
Related calculators
- Sample Size Calculator for Thesis
- Cohen’s d Effect Size Calculator
- Independent Samples t Test Calculator
- Not sure which test to use? Try the test chooser
Cite this calculator
If ScholarCalc helped your analysis, you can cite it in APA 7 format:
ScholarCalc. (2026). Power Analysis Calculator [Web application]. https://scholarcalc.com/power-analysis-calculator/
Written and maintained by the ScholarCalc team. Last reviewed: November 2026.
Accuracy: results are computed in your browser and were validated against Python scipy, statsmodels and pingouin on test datasets. See Methodology and accuracy.