Two Sample T Test Calculator for Percentages

Calculator

Group 1 label

Group 2 label

Group 1 mean percent

Group 2 mean percent

Group 1 standard deviation

Group 2 standard deviation

Group 1 sample size

Group 2 sample size

Null difference

Confidence level

Alternative hypothesis

Variance assumption

Decimal places

Example Data Table

Example	Group 1 mean	Group 1 SD	Group 1 n	Group 2 mean	Group 2 SD	Group 2 n	Suggested method
Course completion	76.4%	11.8	42	70.1%	13.2	39	Welch
Quality score	88.2%	6.4	30	84.7%	6.1	30	Pooled
Survey rating percent	64.5%	18.3	55	59.0%	21.6	48	Welch

Formula Used

Difference: d = x̄₁ - x̄₂

Welch standard error: SE = sqrt(s₁² / n₁ + s₂² / n₂)

Test statistic: t = (d - d₀) / SE

Welch degrees of freedom: df = (a + b)² / [a² / (n₁ - 1) + b² / (n₂ - 1)]

Here, a = s₁² / n₁, and b = s₂² / n₂.

Pooled variance: s_p² = [(n₁ - 1)s₁² + (n₂ - 1)s₂²] / (n₁ + n₂ - 2)

Confidence interval: d ± t_critical × SE

How to Use This Calculator

Enter the mean percentage for each sample.
Enter each sample standard deviation in percentage points.
Enter both sample sizes.
Set the null difference. Use 0 for a usual equality test.
Choose two tailed, right tailed, or left tailed testing.
Select Welch unless equal variance is justified.
Press Calculate to view the result above the form.
Use CSV or PDF to save the report.

Overview

A two sample t test for percentages compares two group averages. Each average is written as a percent. The method treats those percentages as measured values, not simple counts. It is useful for test scores, completion rates from repeated periods, quality percentages, survey scale percentages, and similar summaries.

This calculator works with group means, standard deviations, and sample sizes. It can use Welch's method when group spreads differ. It can also use a pooled method when equal variance is a fair assumption. Welch's method is safer for many real projects.

Why Percentages Need Care

Percentages look simple, but they still vary. A group average of 72 percent is not enough by itself. You also need the sample size and the spread. A small sample can move a lot. A large sample gives a steadier estimate.

The result is shown in percentage points. A difference of five means five percentage points. That is not always the same as five percent relative change. The calculator also shows relative lift, so both views are clear.

Interpreting Results

The t value measures how far the observed difference sits from the null difference. It uses standard error as the scale. A larger absolute t value gives stronger evidence against the null. The p value then describes how unusual that t value is under the chosen assumption.

The confidence interval gives a practical range for the true difference. If the interval is wide, the data are uncertain. If it is narrow, the estimate is more precise. Effect size helps judge practical importance.

Good Practice

Choose a two tailed test when any difference matters. Choose a right tailed test when group one should be higher. Choose a left tailed test when group one should be lower. Decide this before looking at results.

Check the data source before reporting. Confirm that samples are independent. Confirm that percentages were measured the same way. Use the exported report for notes, records, or review.

Avoid using this test for one raw proportion. Use a proportion test for counts of successes and failures. Use this page when each group has an average percentage and a percentage standard deviation. That distinction keeps the model honest and easier to explain during peer review.

FAQs

What is a two sample t test for percentages?

It compares two average percentage values from independent groups. It uses the difference, standard deviations, sample sizes, and a t distribution to estimate evidence against a null difference.

Should I use Welch or pooled variance?

Use Welch when sample sizes or standard deviations differ. It is the safer default. Use pooled variance only when equal variation is reasonable from design, history, or strong evidence.

Is this the same as a two proportion z test?

No. A two proportion z test uses success counts and total counts. This page uses percentage means, percentage standard deviations, and sample sizes for two independent samples.

What does percentage point difference mean?

It is direct subtraction between percentages. If group one is 76% and group two is 70%, the difference is 6 percentage points, not automatically 6 percent relative growth.

What does the p value show?

The p value shows how unusual the observed t statistic is when the null hypothesis is assumed true. Smaller values give stronger evidence against the null.

Can I use this with unequal sample sizes?

Yes. Enter each sample size separately. Welch's method handles unequal sample sizes well, especially when the standard deviations are also different.

What confidence level should I choose?

Common choices are 90%, 95%, and 99%. A higher confidence level gives a wider interval. Use the level expected by your report, class, or study plan.

What should I report after calculating?

Report group means, standard deviations, sample sizes, method, t statistic, degrees of freedom, p value, confidence interval, and a short interpretation.