T-Test Sample Size Calculator

Calculator Form

Test design

Tail setting

Effect size input

Alpha

Power

Cohen d

Group 1 mean

Group 2 or target mean

Group 1 standard deviation

Group 2 standard deviation

Expected difference

Standard deviation for one or paired design

Allocation ratio, group 2 / group 1

Expected dropout percentage

Design effect

Formula Used

One-sample or paired design:

n = ((t critical + z power) / d)² × design effect

Two independent groups:

n₁ = ((1 + 1 / r) × (t critical + z power)² / d²) × design effect

n₂ = n₁ × r

Dropout adjustment:

Recruitment sample = analyzable sample / (1 - dropout rate)

The calculator uses a normal starting estimate, then refines the result with an approximate critical t value.

How to Use This Calculator

Select the t-test design that matches your study.
Choose one-tailed or two-tailed testing.
Enter alpha and desired power.
Use Cohen d directly, or calculate it from means.
Add allocation ratio for two independent groups.
Add dropout and design effect when needed.
Press the calculate button and review the result above the form.
Download the result as CSV or PDF after calculation.

Example Data Table

Scenario	Design	Alpha	Power	Effect Size	Dropout	Use Case
Clinical comparison	Two independent groups	0.05	0.80	0.50	10%	Compare treatment means
Before and after scores	Paired test	0.05	0.90	0.40	15%	Measure within-person change
Quality target check	One-sample test	0.01	0.80	0.60	5%	Compare mean with standard

Understanding T-Test Sample Size

A t-test compares means. It helps decide whether an observed difference is likely meaningful. Sample size controls how well that decision works. Too few observations can hide a real effect. Too many observations can waste time, money, and participants.

Key Planning Ideas

Power is the chance of detecting a true effect. Many studies use 80% or 90% power. Alpha is the false alarm risk. A two-tailed test splits alpha across both directions. A one-tailed test uses one direction, so it often needs fewer observations. Effect size is the expected difference measured in standard deviation units. Larger effects need fewer samples. Smaller effects need more samples.

One-Sample And Paired Tests

A one-sample test compares one mean with a target value. A paired test compares matched measurements, such as before and after scores. Both designs need one final sample count. For paired designs, use the standard deviation of paired differences. That choice is important. It reflects within-person change, not raw score spread.

Two Independent Groups

A two-sample test compares separate groups. The calculator supports unequal allocation. This is useful when one group is harder to recruit, more expensive, or ethically limited. The ratio tells how many people go into group two for each person in group one. A balanced ratio is often efficient. Still, real studies may need different ratios.

Practical Adjustments

Dropout changes recruitment targets. If some participants may leave, recruit more at the start. Design effect handles clustering or repeated sampling loss. A design effect above one increases the needed sample. Use conservative values when planning important work.

Interpreting Results

The result gives analyzable sample size first. That is the number needed after exclusions. The recruitment target includes dropout. Review both values before budgeting. Also review the achieved power estimate. It is approximate, because exact noncentral t methods can differ slightly. For final trials, confirm the plan with a statistician.

Good Use

Use realistic effects from earlier studies. Avoid choosing an effect only because it gives a small sample. Document every assumption. Clear planning improves ethics, reporting, and confidence in the final conclusion. Check sensitivity by testing several effect values. This shows how fragile the plan may be. Keep notes for transparent peer review and audits.

FAQs

1. What is a t-test sample size?

It is the number of observations needed to detect an expected mean difference with chosen alpha and power. The result depends heavily on effect size and design.

2. What does power mean?

Power is the chance of finding a real effect when it truly exists. Common choices are 80% and 90%, but stronger studies may need higher power.

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

Use two-tailed testing when differences in either direction matter. Use one-tailed testing only when the opposite direction is not scientifically useful.

4. What is Cohen d?

Cohen d is a standardized mean difference. It divides the expected difference by a standard deviation, making effects easier to compare across studies.

5. Why does dropout increase recruitment size?

Dropout means some recruited participants may not provide analyzable data. The calculator raises the recruitment target so the final usable sample stays adequate.

6. What is allocation ratio?

Allocation ratio controls group balance in two independent group tests. A ratio of 1 means equal groups. A ratio of 2 means group two is twice as large.

7. What is design effect?

Design effect adjusts sample size for clustering, complex sampling, or reduced independence. Use 1 for a simple independent design with no extra inflation.

8. Are these results exact?

The results are planning estimates using t critical refinement. For regulated trials or complex designs, confirm assumptions with a qualified statistician before recruitment.