Power From Sample Size Calculator

Plan studies with clearer power estimates and assumptions. Adjust sample size, effect, and alpha quickly. Download results for reports, audits, and careful study notes.

Calculator

Example Data Table

Design Sample Size Effect Alpha Direction Approximate Power
Two independent means 64 per group d = 0.50 0.05 Two sided 80.7%
Two independent means 40 per group d = 0.50 0.05 Two sided 60.9%
One sample proportion 150 total p0 = 0.50, p1 = 0.60 0.05 Right sided 80.4%

Formula Used

Power: Power = 1 - beta.

One mean: delta = ((mu1 - mu0) / sigma) x sqrt(n).

Two means: delta = d x sqrt((n1 x n2) / (n1 + n2)).

One proportion: SE0 = sqrt(p0(1 - p0) / n).

Two proportions: SE = sqrt(p1(1 - p1) / n1 + p2(1 - p2) / n2).

Correlation: z = 0.5 x ln((1 + r) / (1 - r)).

Two sided test: Power = P(Z < -zc) + P(Z > zc) under the alternative.

How to Use This Calculator

  1. Select the analysis type that matches your study design.
  2. Choose the test direction and alpha level.
  3. Enter sample size, effect size, or raw planning values.
  4. For two group designs, enter both group sizes.
  5. Press Calculate Power to show results above the form.
  6. Use CSV or PDF export for records and reports.

Why Power Matters

Statistical power tells you how often a study can detect a real effect. It is usually written as one minus beta. A higher value means fewer missed effects. Power planning is useful before data collection. It also helps when reviewers ask why a sample size is defensible.

How Sample Size Changes Power

Sample size affects the standard error. Larger samples make the test statistic more stable. That makes smaller effects easier to detect. This calculator uses normal approximation methods for common planning tasks. You can test means, proportions, and correlations. You can also choose one sided or two sided logic.

Choosing Inputs Carefully

The most important input is the expected effect. For means, this may be a Cohen d value or a raw difference divided by a standard deviation. For proportions, use realistic rates from pilot data or reliable records. For correlation, use a practical expected relationship. Do not choose a large effect only to reduce the planned sample.

Reading The Results

The result shows achieved power, beta, critical value, and an effect statistic. Achieved power near eighty percent is common in many fields. Ninety percent is stronger, but it usually needs more data. Very low power means the design may miss useful findings. It may also produce unstable estimates.

Practical Study Planning

Use the target power field to estimate a required sample size. For two group designs, the tool keeps the allocation pattern you enter. This helps compare balanced and unbalanced studies. Export the result when you need documentation. Save the CSV for spreadsheets. Save the PDF for reports and review notes.

Important Limits

This tool gives planning estimates, not guaranteed outcomes. Exact power can differ when data are small, skewed, clustered, or non normal. A final protocol may need simulation or specialist software. Still, these estimates are helpful for quick design checks and transparent planning discussions.

Good Workflow

Start with the research question. Then define the smallest effect worth detecting. Pick alpha before looking at results. Select the sided test that matches the hypothesis. Enter values, review power, and change one input at a time. This process keeps assumptions visible. It also makes tradeoffs easier to explain to collaborators during early planning meetings and reports.

FAQs

What does statistical power mean?

Power is the chance of detecting a real effect when it truly exists. It equals one minus beta. Higher power reduces missed findings.

What power level should I target?

Many studies target 80% power. Some clinical, safety, or costly studies target 90% or higher. The right value depends on risk and resources.

Can I use Cohen d for means?

Yes. Enter Cohen d in the effect field. You can also enter a raw mean difference and standard deviation for the mean models.

What is a two sided test?

A two sided test checks for effects in both directions. It usually needs more evidence than a one sided test with the same alpha.

Why does sample size increase power?

Larger samples reduce standard error. A smaller standard error makes the test statistic stronger for the same expected effect.

Does this replace specialist software?

No. It gives fast planning estimates. Complex designs, clustering, repeated measures, or very small samples may need simulation or specialist review.

Can I export the result?

Yes. After calculation, use the CSV button for spreadsheets. Use the PDF button for reports, notes, or protocol records.

Why is my power very low?

The effect may be small, the sample may be limited, or alpha may be strict. Increase sample size or reassess design assumptions.

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