Compute Power of a T-Test Calculator

T-Test Power Calculator

Test design

Input method

Alternative

Alpha

Cohen d

Variance option

Sample size group 1

Sample size group 2

Target power

Maximum n search

Mean A or expected mean

Mean B or null mean

Standard deviation A

Standard deviation B

Example Data Table

Design	Tail	Alpha	Effect d	n1	n2	Expected Use
One sample	Two sided	0.05	0.50	34	Not used	Compare one mean with a target.
Paired sample	Right tailed	0.05	0.40	52	Not used	Compare before and after scores.
Two samples	Two sided	0.05	0.50	64	64	Compare two independent group means.

Formula Used

One sample or paired test: noncentrality = d × √n, with df = n − 1.

Two sample test: noncentrality = d ÷ √(1/n1 + 1/n2), with pooled df = n1 + n2 − 2.

Raw two sample option: standard error = √(sd1²/n1 + sd2²/n2). Noncentrality = mean difference ÷ standard error.

Approximate power: right tail = 1 − Φ(tcrit − noncentrality). Left tail = Φ(−tcrit − noncentrality). Two sided adds both rejection tails.

The critical value uses a t quantile approximation. The final power uses a normal approximation to the noncentral t distribution.

How to Use This Calculator

Select the test design that matches your study.
Choose direct effect size or raw mean inputs.
Enter alpha, sample sizes, and tail direction.
Use positive or negative effect signs carefully.
Press Submit to view power above the form.
Use CSV or PDF buttons to save the result.

Power Planning for T-Tests

A t-test power estimate shows the chance of detecting a real effect. It connects sample size, effect size, alpha, and tail choice. Higher power means a lower risk of missing a meaningful difference.

Why Power Matters

Low power can waste time and money. It can also hide effects that deserve attention. Very high power may need more samples than your budget allows. A balanced plan helps you choose a practical design before data collection starts.

Inputs Used by This Tool

The calculator supports one sample, paired sample, and two independent sample plans. You can enter Cohen’s d directly. You can also enter means and standard deviations. The tool then estimates effect size and noncentrality. Alpha sets the false positive limit. The tail option matches your research question. Two sided tests are common when effects may go either way.

Reading the Result

Power is shown as a percent. Beta is the missed detection risk. The critical t value marks the rejection boundary. Degrees of freedom show the amount of sampling information. The noncentrality value grows when effect size or sample size grows. A larger value usually improves detection.

Improving a Weak Plan

If power is below your target, increase sample size first. Better measurement can also reduce noise. A clearer endpoint may raise the effect size. For two sample tests, balanced groups usually give stronger power. Unequal groups can reduce efficiency when total sample size is fixed.

Using Results Responsibly

This tool gives planning estimates. Real studies may have missing data, unequal variance, nonnormal outcomes, or design limits. Treat the output as a guide. Confirm important plans with statistical software or a statistician. Document your assumptions with the reported power.

Planning Example

Suppose a team expects a medium effect. They choose alpha at 0.05 and a two sided test. The calculator estimates whether the planned sample can detect that effect. If power is near 80 percent, the design may be acceptable for many studies. If it is lower, the team can test a larger sample plan. They can also compare one sided and two sided settings. This makes assumptions clear before results are known. Clear planning reduces guesswork and supports better statistical decisions later for teams.

FAQs

What is t-test power?

It is the chance that a t-test detects a real effect. It depends on effect size, sample size, alpha, variance, and test direction.

What is a good power value?

Many studies use 80% as a planning target. Some regulated or costly studies may need 90% or higher.

Can I use negative effect sizes?

Yes. The sign should match your expected direction. It matters most when using one tailed alternatives.

Should I choose one sided or two sided?

Use two sided when an effect in either direction matters. Use one sided only when the opposite direction is not relevant.

What is beta?

Beta is the risk of missing a true effect. It equals one minus power.

Does this replace statistical software?

No. It gives practical planning estimates. Confirm critical research designs with validated software or a statistician.

Why does larger sample size raise power?

Larger samples reduce standard error. This makes the expected test statistic easier to separate from random noise.

What does the Welch option do?

It adjusts degrees of freedom when two groups have unequal standard deviations. It is useful for raw two sample planning.