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Statistical hypothesis testing

T-Test Calculator

Calculate the t-statistic, degrees of freedom, p-value, confidence interval, and statistical significance for one-sample, independent, and paired t-tests.

  • Three test types
  • One or two-tailed tests
  • Instant p-value
  • No registration

Statistical Test Workspace

Select a test and enter your sample information.

Select the type of t-test
One-sample statistics
Independent sample statistics

Group 1

Group 2

Welch's test is usually safer when group variances or sample sizes differ.
Paired observations
Separate values with commas, spaces, or new lines.
Both lists must contain the same number of observations.
Test settings
T-test results
Statistically significant

Calculated p-value 0.0000
T-statistic 0.0000
Degrees of freedom 0
Mean difference 0.0000
Standard error 0.0000
One-Sample Test Compare one sample against a reference value.
Independent Groups Compare two unrelated sample means.
Paired Observations Analyze matched or repeated measurements.
Private Calculation Your data is processed directly in the browser.

How to Use the T-Test Calculator

This calculator helps you determine whether an observed difference is statistically significant. Choose the test that matches your research design, enter the required sample statistics, and review the calculated results.

1

Select a T-Test

Choose one-sample, independent, or paired based on the relationship between your data.

2

Enter Your Data

Add sample means, standard deviations, sample sizes, or paired raw values.

3

Interpret the Result

Compare the p-value with the selected alpha level to evaluate the null hypothesis.

What Is a T-Test?

A t-test is an inferential statistical method used to evaluate whether a sample mean differs from a reference value or whether two sample means differ from each other. It is commonly used when the population standard deviation is unknown.

The test produces a t-statistic that measures the size of the observed difference relative to its standard error. The calculator then uses the t-distribution and the degrees of freedom to estimate a p-value.

Understanding the P-Value

The p-value represents the probability of observing a result at least as extreme as the calculated result when the null hypothesis is assumed to be true.

  • A p-value below the significance level indicates evidence against the null hypothesis.
  • A p-value above the significance level means the available evidence is not strong enough to reject the null hypothesis.
  • Statistical significance does not automatically mean the difference is large or practically important.
General one-sample t-test formula
t = (x̄ − μ₀) ÷ (s ÷ √n)

In this formula, x̄ is the sample mean, μ₀ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Which T-Test Should You Use?

One-Sample T-Test

Use a one-sample t-test when you have one sample and want to compare its mean with a known, expected, or hypothesized value. For example, a manufacturer may test whether the average package weight differs from 500 grams.

Independent-Samples T-Test

Use an independent t-test when the observations in one group are unrelated to the observations in the second group. Examples include comparing test scores from two separate classrooms or comparing outcomes between a treatment group and a control group.

This calculator provides both Welch's t-test and the pooled variance Student's t-test. Welch's method does not require equal population variances and is often the preferred general option.

Paired-Samples T-Test

Use a paired t-test when each value in one list has a meaningful relationship with a value in the other list. Common examples include before-and-after measurements or matched participant pairs.

Important T-Test Assumptions

A correct mathematical calculation does not guarantee a valid research conclusion. Consider the following assumptions before interpreting the results:

  • Observations should be measured on a continuous or approximately continuous scale.
  • Observations should be independent, except for the intentional pairing used in a paired t-test.
  • The sample should not contain severe or unexplained outliers.
  • The data, or paired differences, should be approximately normally distributed when the sample is small.
  • The pooled independent t-test additionally assumes equal population variances.
This tool is intended for education, research planning, and general analysis. Important academic, medical, financial, or business decisions should be reviewed by a qualified statistician or relevant professional.

Frequently Asked Questions

A significant result means the calculated p-value is below the selected significance level. This provides evidence against the null hypothesis, but it does not measure practical importance or prove causation.

A significance level of 0.05 is common, but the correct value depends on the field, research plan, and cost of making a false-positive conclusion. Ideally, choose the level before examining the data.

Use a two-tailed test when differences in either direction matter. Use a one-tailed test only when a directional hypothesis was justified and selected before analyzing the results.

Welch's t-test allows the two groups to have different variances and uses adjusted degrees of freedom. The pooled test assumes equal variances and combines the variance estimates from both groups.

Yes. Enter matching before and after values in the same order. The calculator creates a difference for every pair and performs a one-sample t-test on those differences.

No. A small p-value concerns statistical evidence, not effect size. Large samples can produce small p-values for minor differences, so the mean difference, confidence interval, and subject context should also be considered.