Power for Sample Size Calculator

Calculator

Calculation Mode

Test Type

Alternative

Alpha

Target Power

Allocation Ratio Group 2 size divided by group 1 size.

Null or Control Mean

Expected or Treatment Mean

Standard Deviation

Null Proportion

Expected or Group 1 Proportion

Group 2 Proportion

Known Group 1 Sample Size

Known Group 2 Sample Size

Dropout Allowance Percent

Decimal Places

Formula Used

Mean tests: n = ((Zα + Zβ) × σ / Δ)² for one mean. For two means, multiply by (1 + 1 / r), where r is the allocation ratio.

One proportion: n = (Zα√(p0q0) + Zβ√(p1q1))² / (p1 − p0)².

Two proportions: n1 = (Zα√((1 + 1 / r)pq) + Zβ√(p1q1 + p2q2 / r))² / (p1 − p2)². Then n2 = r × n1.

Dropout adjustment: adjusted n = required n / (1 − dropout rate).

How to Use This Calculator

Select whether you need sample size or achieved power.
Choose a mean or proportion test.
Enter alpha, target power, test direction, and allocation.
Enter mean values and standard deviation, or enter proportions.
Add dropout allowance when some data may be lost.
Press Calculate to view the result above the form.
Use CSV or PDF export for records and reports.

Example Data Table

Scenario	Alpha	Power	Effect Inputs	Extra Input
One sample mean	0.05	0.80	Null mean 100, expected mean 108	SD 15
Two independent means	0.05	0.90	Control 50, treatment 55	SD 12, ratio 1
One sample proportion	0.05	0.80	p0 0.50, p1 0.58	Dropout 10%
Two independent proportions	0.01	0.90	p1 0.62, p2 0.50	Ratio 1.5

Understanding Sample Size Power

Power connects design choices with study risk. It estimates the chance of finding a real effect. A larger sample usually gives higher power. A stronger effect also needs fewer observations. This calculator helps you test those links before data collection starts.

Why Power Matters

Low power can miss useful findings. Very high power can waste time and money. A balanced plan protects budgets and improves evidence. Most studies use eighty percent or ninety percent power. The alpha level sets the allowed false positive risk. Common values are 0.05 and 0.01. Direction matters too. A one sided test needs fewer cases than a two sided test.

Choosing Inputs

Start with the test type. Use mean options when your outcome is numeric. Use proportion options when your outcome is a yes or no event. Enter the smallest difference that should matter in practice. Do not choose an effect only because it gives a small sample. Select the standard deviation from pilot data, literature, or a conservative estimate. For two groups, adjust allocation when group sizes will differ.

Reading the Output

The required sample size is rounded upward. That protects the planned power. For two group studies, the result shows each group and the total. The achieved power may be slightly higher because samples must be whole numbers. The calculator also reports z values, effect size, and planning notes. These details help reviewers check the assumptions.

Good Planning Habits

Add an allowance for dropout, missing records, or unusable responses. Keep the practical effect clear. Document where every assumption came from. Run several scenarios. Compare optimistic, expected, and conservative plans. If results change a lot, collect better pilot information. Remember that formulas are approximations. Complex designs may need simulation or specialist software. Cluster samples, repeated measures, nonnormal outcomes, and strict regulatory trials may require extra methods. Share the final assumptions with collaborators before recruitment begins and funding.

Using Results Responsibly

Power planning is not a guarantee. It is a design guide. A well powered study can still find no effect. A small study can still show a result by chance. Treat this calculator as a transparent planning tool. Combine it with sound sampling, clear endpoints, and honest reporting.

FAQs

What is statistical power?

Statistical power is the chance that a test detects a real effect. Higher power lowers the risk of a false negative result.

What power level should I use?

Many studies use 0.80 or 0.90. Use a higher value when missing a real effect would be costly or risky.

What does alpha mean?

Alpha is the chosen false positive risk. A 0.05 alpha means a five percent risk under the null hypothesis.

Should I use one sided or two sided?

Use two sided when effects in either direction matter. Use one sided only when the opposite direction is not relevant.

How do I choose effect size?

Use the smallest difference that has practical value. Pilot data, published studies, or expert judgment can guide this choice.

Why is dropout allowance included?

Dropout allowance increases enrollment targets. It protects the final usable sample after missing data, refusals, or invalid responses.

Can this replace specialist software?

It is useful for planning and checks. Complex designs, clustered data, survival outcomes, and regulatory trials may need specialist tools.

Why are results rounded upward?

Sample sizes must be whole numbers. Rounding upward keeps the planned power from falling below the requested value.