g power sample size calculator - Aaron Graves, PhDude Replica

Statistical test

Effect size (Cohen's d)

Typical benchmarks for d: 0.2 small, 0.5 medium, 0.8 large.

Significance level (alpha)

Desired power (1 - beta)

Tail(s)

Allocation ratio (Group 2 / Group 1)

Use 1 for equal group sizes.

Expected dropout / unusable data (%)

This tool gives a practical approximation to G*Power-style calculations for planning. Final protocol decisions should be checked with your statistician.

What this G*Power sample size calculator does

If you are designing a study, one of the biggest decisions is how many participants you need. This page provides a quick power analysis calculator inspired by the workflow many researchers use in G*Power. You can estimate sample size for three common scenarios: independent-group t tests, one-sample/paired t tests, and correlation analyses.

The calculator is built for speed and clarity. Enter your expected effect size, significance threshold (alpha), desired statistical power, and whether your hypothesis is one-tailed or two-tailed. It then returns the recommended sample size, plus an optional inflation for dropout.

How to use it

1) Pick your test family

Two independent groups: Compare means across two separate groups (e.g., treatment vs control).
One sample / paired: Compare one group to a reference or pre/post repeated measurements.
Correlation: Detect an expected Pearson relationship between two variables.

2) Enter your effect size

For t tests, use Cohen's d. For correlation, use r. Be realistic: overestimating effect size is one of the most common causes of underpowered studies.

3) Set alpha and power

Typical defaults are alpha = 0.05 and power = 0.80. If missing an effect is costly, increase power to 0.90 or higher.

4) Account for attrition

If you expect participants to drop out or data to fail quality checks, add a dropout percentage so your recruitment target remains adequate.

Quick interpretation guide

Small expected effects require larger samples.
Higher power increases required sample size.
Lower alpha (more conservative threshold) increases required sample size.
Two-tailed tests usually need more participants than one-tailed tests.

Formulas used in this calculator

Independent-groups t test (approximation)

For effect size d and allocation ratio k = n₂/n₁, this calculator uses:

n₁ = ((z_alpha + z_power)² × (1 + 1/k)) / d²

and n₂ = k × n₁.

One-sample / paired t test (approximation)

n = ((z_alpha + z_power)²) / d²

Correlation test

Using Fisher's z transform for expected correlation r:

n = ((z_alpha + z_power)²) / (0.5 × ln((1+r)/(1-r)))² + 3

These formulas are widely used for planning and produce close estimates to standard software in many practical cases.

Choosing a defensible effect size

Good sample size determination starts with a justifiable effect size:

Use meta-analysis estimates when available.
Use the smallest effect that would be practically meaningful.
Use pilot data cautiously (pilot studies are noisy).
Pre-register assumptions and sensitivity checks.

Common mistakes to avoid

Confusing one-tailed and two-tailed hypotheses.
Using defaults without domain-specific justification.
Ignoring dropout, missingness, or exclusion rules.
Treating power analysis as a one-time checkbox instead of part of study design.

Final note

This calculator is a practical planning tool for researchers, students, and analysts who need a fast estimate similar to a G*Power workflow. For grant submissions, clinical protocols, or complex models (mixed effects, survival, mediation, multilevel designs), run a full analysis with specialized software and expert review.