Power and Sample Size Calculator

Calculator

Calculation mode

Study design

Test direction

Alpha

Target power

Allocation ratio n2/n1

Null or control mean

Expected treatment mean

SD or paired-difference SD

Treatment SD

Null or control proportion

Expected treatment proportion

Group one sample

Group two sample

Design effect

Dropout percent

Finite population

Example Data Table

Scenario	Design	Alpha	Power	Effect	Typical Output
Mean trial	Two means	0.05	0.80	8 mean units, SD 15	Group sample size
Conversion study	Two proportions	0.05	0.90	0.35 to 0.45	Total enrollment
Pilot review	One mean	0.05	Entered sample	Mean difference	Achieved power

Formula Used

One mean: n = [(Zα + Zβ) × σ / Δ]².

Two means: n1 = (Zα + Zβ)² × σ² × (1 + 1/r) / Δ². Then n2 = r × n1.

One proportion: n = [Zα√p0(1-p0) + Zβ√p1(1-p1)]² / (p1-p0)².

Two proportions: n1 = [Zα√p̄(1-p̄)(1+1/r) + Zβ√{p1(1-p1)+p2(1-p2)/r}]² / (p2-p1)².

Adjustment: adjusted n = raw n × design effect ÷ (1 - dropout). Finite population correction is applied before that adjustment.

The calculator uses normal approximation methods. Use specialist methods for rare events or complex designs.

How to Use This Calculator

Select the calculation mode first. Choose required sample size, achieved power, or minimum detectable effect.

Pick the design that matches your study. Enter alpha, power, effect values, and variability. Use proportions as decimals.

For two group studies, set the allocation ratio. A value of 1 gives equal group sizes.

Add dropout, design effect, and finite population values when needed. Press calculate. Review the result above the form. Download CSV or PDF for records.

Power and Sample Size Planning

Power and sample size planning protects a study from weak evidence. It estimates how many observations are needed before data collection begins. It also shows whether a proposed sample can detect a meaningful effect. A larger sample usually increases power. A smaller alpha usually requires more data. This calculator keeps those tradeoffs visible.

Why Power Matters

Power is the probability of finding a real effect when it exists. Low power can hide important differences. Very high power may waste time and money. Many research plans use eighty percent or ninety percent power. The best value depends on risk, cost, and ethical limits. Clinical, industrial, and academic studies should justify the choice.

Inputs That Drive Results

The main inputs are alpha, desired power, effect size, variability, and allocation ratio. For mean studies, the effect is a mean difference divided by standard deviation. For proportion studies, the effect is the difference between two rates. Dropout, clustering, and finite populations can change the final enrollment target. Use realistic pilot data whenever possible. Guessing too optimistically can create an underpowered design.

Reading the Output

The calculator reports raw and adjusted sample sizes. Raw size reflects the statistical test only. Adjusted size includes design effect and dropout allowance. For two group designs, it separates group one and group two. The power mode estimates achieved power from available sample sizes. The minimum detectable effect mode finds the smallest difference that meets the chosen power.

Good Practice

Treat results as planning estimates. Normal approximation formulas are useful for early design work. Exact, simulation, or specialist methods may be needed for rare events, survival outcomes, repeated measures, or complex surveys. Always document assumptions. Record the alpha level, sidedness, target power, effect definition, and expected loss rate. This makes the study plan easier to review. It also helps others repeat the calculation later. Review assumptions with a statistician when stakes are high. Check whether the effect is practically meaningful, not only statistically detectable. A study can be powerful and still answer the wrong question. Good planning starts with a clear research goal. Compare several scenarios before choosing one. Small changes in dropout or variance can shift enrollment needs. Save reports with the protocol early.

FAQs

What is statistical power?

Power is the chance of detecting a true effect. A common target is 80% or 90%. Higher power usually needs a larger sample.

What alpha should I use?

Many studies use 0.05. A smaller alpha lowers false positive risk. It also increases sample size requirements.

What is effect size?

Effect size is the difference you want to detect. For means, it can be raw or standardized. For proportions, it is the rate difference.

Should I use one-sided or two-sided testing?

Use two-sided tests when effects in either direction matter. Use one-sided tests only when the opposite direction is not scientifically useful.

What is allocation ratio?

Allocation ratio compares group two size with group one size. A ratio of 1 means equal groups. A ratio of 2 means group two is twice as large.

Why add dropout?

Dropout accounts for participants or records lost before analysis. It increases enrollment so the final usable sample remains adequate.

What is design effect?

Design effect inflates sample size for clustering or complex sampling. Use 1 for simple random samples without extra variance.

Can this replace a statistician?

No. It supports planning with normal approximation formulas. Complex trials, rare events, and regulated work need expert review.