Sample Size T Test Calculator

Calculator

T test design

Tail setting

Input mode

Expected mean difference

Standard deviation 1

Standard deviation 2

Effect size d

Alpha

Power

Allocation ratio n2/n1

Dropout percentage

Finite population size

Round target to multiple

Example Data Table

Scenario	Design	Difference	SD 1	SD 2	Alpha	Power	Dropout
Clinical mean change	Paired	4	8	8	0.05	0.80	10%
Two education groups	Independent	5	10	12	0.05	0.90	15%
Quality target check	One sample	3	7	7	0.01	0.80	5%

Formula Used

For one sample or paired planning, the calculator uses this approximation:

n = (z_alpha + z_power)^2 / d^2

For two independent groups with raw standard deviations, it uses:

n1 = (z_alpha + z_power)^2 x (s1^2 + s2^2 / r) / delta^2

n2 = r x n1

For two groups with a standardized effect, it uses:

n1 = (z_alpha + z_power)^2 x (1 + 1 / r) / d^2

Dropout adjustment is n_recruit = n_analyzable / (1 - dropout). Finite population correction is n_fpc = n0 / (1 + (n0 - 1) / N).

How to Use This Calculator

Select the t test design that matches your research question.
Choose one tailed or two tailed testing.
Enter alpha and desired statistical power.
Use a known effect size, or enter a mean difference and standard deviation.
Set the allocation ratio for two group studies.
Add expected dropout and any known finite population size.
Press the calculate button and review the sample target.
Download the CSV or PDF report for records.

Planning a t Test Study

A sample size plan protects a study before data collection starts. It links the expected mean difference, standard deviation, alpha, power, and design. A t test can compare one mean, paired changes, or two independent groups. Each design needs enough observations to detect the target effect. Small samples may miss useful differences. Very large samples may waste time and money.

What This Calculator Estimates

This calculator estimates the minimum sample size for common t test planning. It supports one sample, paired, and two group designs. You can enter an effect size directly. You can also enter a mean difference and standard deviation. The tool then converts the information into a standardized effect. For two groups, it handles allocation ratios. That helps when one group is harder to recruit.

Why Alpha and Power Matter

Alpha is the chosen false positive risk. A common value is 0.05. Power is the chance of detecting the planned effect. A common target is 80% or 90%. Higher power needs more observations. A smaller alpha also needs more observations. Two tailed tests need more evidence than one tailed tests. That usually increases the sample size.

Design Choices

One sample and paired tests use the variability of one measurement or paired difference. Independent group tests use group standard deviations and group allocation. Dropout adjustment inflates the final recruitment target. This is useful when participants may leave the study. Finite population correction can reduce the target when the population is small. Use it only when sampling is without replacement from a known population.

Interpreting Results

Treat the output as a planning estimate. It uses a normal approximation for speed and clarity. Actual power can vary with nonnormal data, unequal variances, missing values, and protocol changes. Always document assumptions before collecting data. Sensitivity checks are also helpful. Try several effect sizes and dropout rates. This shows how fragile the plan may be. If the required sample is unrealistic, reconsider the effect, design, or measurement approach.

Practical Notes

Record every assumption in the report. Include the alpha level, tail direction, power target, effect size source, allocation rule, and dropout rate. This makes the analysis easier to review, share, and repeat later with research stakeholders.

FAQs

What is a sample size t test calculator?

It estimates how many observations are needed before running a t test. It uses expected effect, alpha, power, variance, tails, and design type.

Can I use it for paired data?

Yes. Choose the paired option. Enter the expected mean change and the standard deviation of paired differences, or enter a standardized effect size.

What does power mean?

Power is the chance of detecting the planned effect when it truly exists. Common targets are 0.80 and 0.90.

What effect size should I enter?

Use pilot data, prior studies, or a meaningful practical difference. Avoid choosing an effect only because it gives a convenient sample size.

Why does a two tailed test need more samples?

A two tailed test checks both directions. It splits alpha across both tails, so stronger evidence is needed for the same power.

How does dropout affect sample size?

Dropout increases the recruitment target. The calculator inflates the analyzable sample so enough complete observations remain after expected losses.

What is allocation ratio?

Allocation ratio is n2 divided by n1. A value of 1 means equal group sizes. A value of 2 means group 2 is twice as large.

Is this exact power analysis?

It is an advanced normal approximation. For final regulated studies, confirm assumptions with a statistician or exact software when required.