power analysis sample size calculator - Aaron Graves, PhDude Replica

Power Analysis & Sample Size Tool

Estimate required sample size before running a study. Choose your design, set alpha and power, then enter effect assumptions.

Study Design

Hypothesis Type

Significance Level (alpha)

Desired Power (1 - beta)

Allocation Ratio (n2 / n1)

Use 1 for equal group sizes.

Standardized Effect Size (Cohen's d)

Typical benchmarks: 0.2 (small), 0.5 (medium), 0.8 (large).

Standardized Effect Size (dz)

For one-sample or paired designs, dz = mean change / SD of change.

Expected Proportion in Group 1 (p1)

Expected Proportion in Group 2 (p2)

Example: conversion rates in A/B testing or event rates in treatment vs control.

Why a power analysis sample size calculator matters

A power analysis sample size calculator helps you answer one of the most important design questions in research: How many observations do I need? If your sample is too small, you may miss a real effect. If it is too large, you may spend unnecessary time and money. Planning sample size in advance creates more reliable, ethical, and interpretable studies.

Core concepts behind sample size estimation

1) Alpha (Type I error)

Alpha is the probability of a false positive: rejecting the null hypothesis when it is actually true. Common choices are 0.05 or 0.01.

2) Power (1 - beta)

Power is the probability of detecting a real effect of the size you care about. Many studies target 80% or 90% power. Higher power generally requires a larger sample.

3) Effect size

Effect size is the minimum practically meaningful difference you want to detect. Smaller target effects require bigger samples. In this calculator, effect size is entered as:

Cohen's d for means-based designs (difference in means divided by standard deviation).
p1 and p2 for two-proportion designs (such as conversion rates).

How to use this calculator

Select the study design (two means, one/paired mean, or two proportions).
Choose one-sided or two-sided hypothesis testing.
Enter alpha and desired power.
Provide effect assumptions (d, dz, or p1/p2).
Click Calculate Sample Size and use the rounded-up group counts.

Practical guidance for setting assumptions

Use prior evidence when possible

The best inputs come from pilot data, meta-analyses, domain benchmarks, or previous experiments in the same population. Guessing effect sizes without evidence often leads to underpowered studies.

Run sensitivity scenarios

Don't rely on one guess. Try optimistic, realistic, and conservative effect sizes. If sample size changes dramatically, your plan is sensitive and should be discussed in your protocol.

Account for dropout

If you expect attrition, inflate planned enrollment. Example: if required n = 200 and dropout is 15%, recruit approximately 200 / (1 - 0.15) = 236 participants.

Interpretation tips

The output is the minimum target sample size under the assumptions entered.
Results are based on normal-approximation formulas commonly used for planning.
For complex models (mixed effects, survival, non-inferiority, cluster trials), use specialized methods.

Common mistakes to avoid

Choosing effect sizes that are unrealistically large to force smaller sample requirements.
Ignoring one-sided vs two-sided testing differences.
Forgetting unequal allocation when one group is harder to recruit.
Not documenting assumptions in a preregistration or analysis plan.

Final note

This power analysis sample size calculator is a practical planning aid for common study designs. It is excellent for fast decisions, proposal drafts, and first-pass planning. For regulatory work, high-stakes trials, or advanced designs, confirm with a statistician and software tailored to your exact endpoint and model.