Paired T Test Power Analysis Calculator

Calculator

Analysis mode

Effect input method

Complete pairs

Cohen dz

Expected mean difference

SD of paired differences

Alpha

Target power

Tail setting

Dropout allowance (%)

Example Data Table

The table shows common planning cases for paired designs.

Case	Mean Difference	Paired SD	Cohen dz	Alpha	Power Target	Tails
Small change	3	12	0.25	0.05	0.80	Two
Moderate change	5	10	0.50	0.05	0.80	Two
Large change	8	10	0.80	0.01	0.90	One

Formula Used

Paired effect size: dz = mean paired difference / standard deviation of paired differences.

Degrees of freedom: df = n - 1.

Noncentrality value: λ = dz × √n.

Power idea: power is the chance that the paired t statistic falls beyond the critical t value under the expected effect.

Dropout adjustment: invited pairs = required complete pairs / (1 - dropout rate).

How To Use This Calculator

Select the analysis mode.
Choose whether to enter Cohen dz or summary data.
Enter complete pairs when the mode needs a fixed sample.
Enter alpha and choose one tailed or two tailed testing.
Enter target power when solving for sample size, effect size, or alpha.
Add a dropout allowance for recruitment planning.
Press the calculate button.
Download the result as CSV or PDF.

Paired Power Planning

A paired t test studies one group twice. It can study matched pairs. Power analysis estimates the chance of detecting a real mean difference. It helps before data collection begins.

Why This Calculator Matters

Matched designs are efficient. Each person acts as their own control. This reduces noise from natural differences between people. Yet weak planning can still miss a useful change. A power calculator gives a clear target for pairs, effect size, and alpha.

Core Study Inputs

The main effect is Cohen's dz. It equals the expected mean of paired differences divided by the standard deviation of those differences. You can enter dz directly. You can also enter the mean difference and standard deviation. The tool then computes dz for you.

G Power Style Use

Alpha controls the false positive risk. A two tailed test is common when change may go either way. A one tailed test is stricter about direction. Target power is often set near 80% or 90%. Higher power needs more complete paired observations.

This page follows a G Power style workflow. You choose the question first. You may solve for achieved power, sample size, minimum effect size, or needed alpha. The calculator then applies paired t test planning logic. It also adjusts the invited sample for dropout.

Reading The Result

The required sample size is the number of complete pairs. A complete pair has both measurements. If dropout is entered, the invited count becomes larger. The noncentrality value shows how strongly the expected effect separates the null and alternative models.

Good Practice Notes

Use realistic pilot data when possible. The standard deviation of differences matters more than separate group spreads. Keep the same measurement method at both times. Predefine the test tail before seeing results. Do not choose a tail after inspecting data.

Export And Report

The download buttons help save the calculation. A CSV file supports spreadsheets. A PDF file gives a compact report. Keep the assumptions with your protocol. Report dz, alpha, tails, power, and complete pairs. Clear records make the final study easier to audit.

Use the output as a planning aid, not a guarantee. Real data quality and missing pairs still matter. Assumption checks shape final evidence strength.

FAQs

What is a paired t test power analysis?

It estimates the chance of detecting a real mean change in matched or repeated measurements. It helps plan pairs before the study starts.

What is Cohen dz?

Cohen dz is the standardized paired mean difference. It equals the expected mean difference divided by the standard deviation of paired differences.

Should I use one tailed or two tailed testing?

Use two tailed testing when change in either direction matters. Use one tailed testing only when a single direction is justified before analysis.

What does complete pairs mean?

A complete pair has both measurements for the same subject or matched unit. Missing one measurement removes that pair from paired analysis.

Why does dropout increase the invited sample?

Dropout reduces complete paired data. The calculator inflates the invitation count so the final complete pairs can still meet the target.

What power target should I choose?

Many studies use 80% or 90%. A higher target reduces missed effects, but it needs more complete pairs or a larger expected effect.

Can I enter raw pilot summary values?

Yes. Enter the expected mean paired difference and the standard deviation of paired differences. The calculator converts them into Cohen dz.

Is this a replacement for final statistical review?

No. It is a planning calculator. Confirm assumptions, design choices, missing data rules, and analysis plans with a qualified statistician.