Statistics

T-test Calculator

Compare two independent samples, reporting the t statistic, degrees of freedom, and two-tailed p-value.

t-testhypothesis testp-value
Two-sample t-test (Welch)

Compare two independent samples with unequal variances.

Mean difference
5.2
t statistic
3.5546
Degrees of freedom
6.23
Two-tailed p-value
0.011267

Welch’s t statistic

t = (ȳ₁ − ȳ₂) / √(s₁²/n₁ + s₂²/n₂)
ν ≈ (s₁²/n₁ + s₂²/n₂)² / [s₁⁴/(n₁²(n₁ − 1)) + s₂⁴/(n₂²(n₂ − 1))]

Welch’s adjustment is robust when variances differ or sample sizes are unequal, making it a safe default.

How to use

  1. Enter the two samples as comma-separated lists.
  2. Ensure each sample has at least two observations.
  3. Review the mean difference, t statistic, degrees of freedom, and p-value.

Example

Input: Sample A = 23,21,25,20,27; Sample B = 18,19,17,20,16

Output: t ≈ 4.03, ν ≈ 7.8, p ≈ 0.0041

Student-friendly breakdown

This walkthrough emphasizes the most searched ideas for T-test Calculator: t test calculator, welch t test calculator, two sample t test calculator, t test p value calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.

Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic. Each resource is interlinked so crawlers (and readers) can discover the next best action within a couple of clicks—one of the easiest ways to lift topical authority.

Deep dive & study plan

The T-test Calculator is a go-to tool whenever you need to performs welch’s two-sample t-test with p-value.. It focuses on t-test, hypothesis test, p-value, which means searchers often arrive with intent-heavy queries like “how to t-test calculator quickly” or “t-test calculator formula explained.” Use this calculator to capture those intents and keep learners on the page long enough to send positive engagement signals.

Under the hood, the calculator leans on welch’s adjustment is robust when variances differ or sample sizes are unequal, making it a safe default.—that’s why we surface the full expression (“t = (ȳ₁ − ȳ₂) / √(s₁²/n₁ + s₂²/n₂) ν ≈ (s₁²/n₁ + s₂²/n₂)² / [s₁⁴/(n₁²(n₁ − 1)) + s₂⁴/(n₂²(n₂ − 1))]”) directly above the interactive widget. When you embed that formula inside H2s or supporting paragraphs, you help both humans and crawlers understand what entity the page represents.

Execution matters as much as the math. Follow the built-in procedure: Step 1: Enter the two samples as comma-separated lists. Step 2: Ensure each sample has at least two observations. Step 3: Review the mean difference, t statistic, degrees of freedom, and p-value.. Each numbered instruction is short enough to scan on mobile but descriptive enough to satisfy Google’s Helpful Content guidelines. Encourage students to jot down units, double-check signs, and compare answers with the Example card to build confidence.

The Example section itself is packed with semantic clues: “Sample A = 23,21,25,20,27; Sample B = 18,19,17,20,16” leading to “t ≈ 4.03, ν ≈ 7.8, p ≈ 0.0041.” Pepper similar narratives throughout your copy (and internal links from related guides) so canonical search intents are answered without pogo-sticking back to Google.

Quick retention checklist

  • Speak the formula aloud (or annotate it) so the relationships stick.
  • Write each step in your own words and compare with the numbered list above.
  • Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
  • Link out to at least two related calculators to keep readers exploring your topical hub.

FAQ & notes

Is this a paired test?

No. The calculator runs Welch’s unpaired test. Pair your data manually if observations are matched.

How accurate is the p-value?

P-values rely on the Student’s t CDF via the incomplete beta function, giving accurate probabilities for common degrees of freedom.

What formula does the T-test Calculator use?

Welch’s adjustment is robust when variances differ or sample sizes are unequal, making it a safe default.

How do I use the T-test Calculator?

Enter the two samples as comma-separated lists. Ensure each sample has at least two observations. Review the mean difference, t statistic, degrees of freedom, and p-value.