Given Power Minimum Sample Size Calculator

Calculator inputs

Study design

Target power (%)

Alpha level

Test tails

Expected mean difference

Standard deviation

Null proportion p0

Expected proportion or group 1

Group 2 proportion

Allocation ratio n2 / n1

Expected dropout (%)

Design effect

Example data table

Design	Power	Alpha	Effect	Dropout	Estimated total
Two means	80%	0.05	Difference 5, SD 12	10%	202
One proportion	90%	0.05	p0 0.30, p1 0.42	5%	172
Two proportions	80%	0.05	0.42 versus 0.30	10%	556

Formula used

One mean: n = [(zα + zβ) × σ / Δ]^2.

Two means: n1 = (1 + 1/r) × (zα + zβ)^2 × σ^2 / Δ^2. Then n2 = r × n1.

One proportion: n = [zα√p0(1-p0) + zβ√p1(1-p1)]^2 / (p1-p0)^2.

Two proportions: n1 uses pooled pbar for alpha and separate rates for power. Then n2 = r × n1.

Inflation: final n = ceiling(raw n × design effect / (1 - dropout rate)).

How to use this calculator

Select the study design that matches your outcome.
Enter target power as a percent, such as 80 or 90.
Enter alpha and choose one-tailed or two-tailed testing.
For means, enter the expected difference and standard deviation.
For proportions, enter rates as decimals between 0 and 1.
Use allocation ratio when group sizes are not equal.
Add dropout and design effect when needed.
Press the calculate button to show results above the form.

Minimum sample size from given power

Power planning turns a research goal into a required sample. The target power states how often a study should detect a real effect. Many teams use eighty percent or ninety percent. Higher power needs more observations. Lower alpha also needs more observations. This calculator joins these choices in one clear workflow.

Why power matters

A study with weak power may miss a useful difference. That can waste time, money, and effort. A study with too many participants can also waste resources. Good planning balances sensitivity and cost. It also records assumptions before data collection starts. That record supports review, budgeting, and protocol writing.

Supported study designs

The tool supports one mean, two independent means, one proportion, and two independent proportions. Mean designs use the expected difference and standard deviation. Proportion designs use expected rates. Two group designs can use unequal allocation. For example, a two to one allocation may place twice as many participants in the treatment group.

Key assumptions

Every sample size result depends on assumptions. Enter a realistic effect size. Use pilot data when possible. Use published estimates when pilot data are missing. The standard deviation should match the outcome scale. Proportions should be entered as decimals. A value of zero point thirty means thirty percent.

How results are rounded

The calculator first estimates the mathematical sample size. It then applies the design effect. Next, it inflates the value for expected dropout. Finally, it rounds up to a whole participant. This conservative rounding helps protect the planned power. Group designs round each group separately, then report the total.

Interpreting the answer

The final sample size is a planning target. It is not a guarantee. Real power can change if variability, response rates, or dropout differ from assumptions. Treat the result as a decision aid. Review it with a statistician for clinical trials, regulatory studies, or high cost experiments.

Practical notes

Choose one sided testing only when the research question justifies it. Do not choose it only to reduce sample size. Check that the minimum detectable effect is meaningful. Small effects often need large studies. Save the exported file with your protocol notes. It keeps assumptions visible for later review and updates now.

FAQs

What does given power mean?

Given power means the desired chance of detecting a true effect. A power of 80% means the study aims to detect the assumed effect in 80 of 100 similar studies.

What power value should I use?

Many studies use 80% or 90% power. Higher power is safer but requires more participants. Choose a value that fits your risk, budget, and study importance.

What is alpha in sample size planning?

Alpha is the Type I error rate. It is the chance of claiming an effect when no real effect exists. A common value is 0.05.

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

Use two-tailed testing when effects in either direction matter. Use one-tailed testing only when the protocol and research question justify one direction before data collection.

What is allocation ratio?

Allocation ratio is n2 divided by n1. A value of 1 means equal groups. A value of 2 means group two has twice as many participants.

Why include dropout?

Dropout reduces the final analyzable sample. Adding dropout inflation helps preserve power after missing data, withdrawals, nonresponse, or incomplete follow-up.

What is design effect?

Design effect inflates sample size for complex designs. It is often used for cluster sampling, repeated field sites, or other designs with extra correlation.

Can this replace a statistician?

No. It is a planning aid. Complex trials, survival outcomes, repeated measures, and regulatory work should be reviewed by a qualified statistician.