Student T Test Calculator

Calculator Inputs

Test Type

Input Mode

Alternative Hypothesis

Significance Level (alpha)

Confidence Level (%)

Hypothesized Mean

Hypothesized Difference

Summary Statistics

Sample Mean

Sample Standard Deviation

Sample Size

Group 1 Mean

Group 1 Standard Deviation

Group 1 Size

Group 2 Mean

Group 2 Standard Deviation

Group 2 Size

Mean of Paired Differences

Standard Deviation of Differences

Number of Pairs

Raw Values

Sample A Values

Use commas, spaces, or new lines.

Sample B Values

For paired tests, both series must have equal length.

Example Data Table

Scenario	Recommended Test	Example Inputs	Use Case
Single class average vs target score	One-sample	Mean 72.4, SD 8.6, n 20, null mean 70	Checks whether one sample differs from a benchmark.
Two independent classes	Independent equal variances	Group 1: 78.2, 9.1, 18; Group 2: 71.5, 10.4, 16	Compares average scores from different groups.
Different spreads between groups	Welch two-sample	Group 1 SD 6.2, Group 2 SD 15.1	Handles unequal variances more safely.
Before and after tutoring scores	Paired	Differences mean 4.2, SD 6.1, pairs 14	Measures change within matched observations.

Formula Used

One-Sample Student t Test

t = (x̄ - μ₀) / (s / √n)

Use this when one sample mean is compared with a known or hypothesized population mean.

Independent Student t Test with Equal Variances

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

t = [(x̄₁ - x̄₂) - Δ₀] / [s_p √(1/n₁ + 1/n₂)]

Use this when two independent groups likely share the same variance.

Welch Two-Sample t Test

t = [(x̄₁ - x̄₂) - Δ₀] / √(s₁²/n₁ + s₂²/n₂)

Welch’s version is preferred when group variances or sizes differ noticeably.

Paired Student t Test

t = (d̄ - Δ₀) / (s_d / √n)

Here, d̄ is the average paired difference and s_d is the standard deviation of differences.

Confidence intervals are built with the estimate ± critical t × standard error. The calculator also reports effect size to show practical importance, not only statistical significance.

How to Use This Calculator

Select the correct t test based on your data structure.
Choose summary statistics or raw values mode.
Enter alpha, confidence level, and the null mean or difference.
Fill in one sample, two independent groups, or paired inputs.
Press the calculate button to see results above the form.
Review the table, interpretation, graph, and export options.

FAQs

1. When should I use a one-sample t test?

Use it when one sample is compared against a known or hypothesized mean. It checks whether the sample average is significantly different from that benchmark.

2. What is the difference between Student and Welch tests?

The equal-variance Student test assumes both groups have similar population variances. Welch’s test relaxes that assumption and is usually safer when spreads or sample sizes differ.

3. When is a paired t test the correct choice?

Use a paired test when observations are matched, such as before-and-after scores or repeated measurements on the same subjects.

4. What does the p value mean here?

The p value shows how likely your result would be if the null hypothesis were true. Smaller values indicate stronger evidence against the null.

5. Why is the confidence interval important?

It gives a plausible range for the sample mean or mean difference. It helps you judge magnitude and precision, not just significance.

6. What if my raw datasets have different lengths?

For independent tests, different lengths are fine. For paired tests, each value must have a matching partner, so both lists must contain the same count.

7. Does this calculator report effect size?

Yes. It reports Cohen’s d for one-sample and paired designs, and Hedges’ g for two-sample designs, with a simple magnitude label.

8. Can I export the result?

Yes. After calculation, use the CSV button for spreadsheet-friendly output or the PDF button for a printable result summary.