power analysis calculator

What this power analysis calculator does

A power analysis helps you estimate how many participants you need before collecting data. This calculator focuses on a common design: two independent groups with equal sample sizes. You provide assumptions (effect size, alpha, and target power), and it returns a recommended sample size per group and total sample size after accounting for dropout.

It can also estimate achieved power if you already have a fixed sample size. That makes it useful both for planning prospective studies and for evaluating practical constraints.

Core concepts in plain language

1) Statistical power

Power is the probability your study detects a real effect. A common target is 0.80 (80%), meaning that if the true effect exists at the assumed size, your study has an 80% chance of finding a statistically significant result.

2) Effect size (Cohen's d)

Cohen's d is a standardized difference between two group means. Typical benchmarks are:

• 0.2 = small effect
• 0.5 = medium effect
• 0.8 = large effect

Smaller expected effects require larger sample sizes.

3) Alpha (Type I error rate)

Alpha is your false-positive threshold. The conventional value is 0.05. Lowering alpha (for stricter evidence) increases required sample size.

4) One-tailed vs two-tailed tests

Two-tailed tests are usually preferred because they allow effects in either direction. One-tailed tests can reduce required sample size but should only be used with a strong, pre-justified directional hypothesis.

Calculation method used

For equal-size independent groups, this calculator uses a normal approximation: n per group = 2 × (zalpha + zbeta)² / d²

• zalpha is based on alpha and tail choice
• zbeta is based on target power
• d is expected Cohen's d

This is ideal for quick planning and educational use. For high-stakes protocols, confirm results with a dedicated power analysis package and your exact model assumptions.

How to use this calculator effectively

• Start with a realistic effect size from prior studies, pilot data, or meta-analysis.
• Keep alpha at 0.05 unless your field requires stricter thresholds.
• Use 0.80 or 0.90 for target power depending on study importance.
• Add attrition to avoid becoming underpowered after exclusions/dropout.
• Run sensitivity checks (e.g., d = 0.35, 0.50, 0.65) to see planning risk.

Common mistakes to avoid

• Overestimating effect size: this makes sample size estimates too small.
• Ignoring attrition: final analyzable sample may fall below target.
• Post-hoc justification only: planning should happen before data collection.
• Blindly using one-tailed tests: only valid with strong directional rationale.

Quick interpretation guide

After calculation, treat the recommended sample as a minimum planning target. If budget allows, recruiting slightly above the minimum improves robustness against missing data, protocol deviations, and real-world noise.

FAQ

Is this only for t-tests?

It is best aligned with two-group mean comparisons and often used as a t-test planning approximation. More complex designs (ANOVA, mixed models, logistic regression, survival analysis) need specialized methods.

Can I use this for unequal group sizes?

This version assumes equal allocation. If you plan unequal groups, use software that allows explicit allocation ratios.

Should I report my power analysis in a paper?

Yes. Report your assumptions (effect size, alpha, power target, test type, and attrition adjustment) so readers can evaluate your study design decisions.