T-Test Calculator: One-Sample, Two-Sample & Paired

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Formula at a glance

T-Test Calculator: Welch t — t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂). Example: Two groups → t statistic: 3.4359124 — How the T-Test Calculator works: Welch t — t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)

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📘 About the T-Test

A t-test checks whether a mean differs from a value, or two means differ from each other, taking the sample size and spread into account. Use the two-sample test for two separate groups (a new teaching method vs the old), the paired test when the same people are measured twice (before and after), and the one-sample test against a known value.

Paste the data, choose the test and the tail. The calculator gives t, the degrees of freedom, the p-value, the decision at your significance level, the confidence interval for the difference and Cohen’s d. Welch’s test is the default for two groups because it does not assume equal variances.

🧮 Formula

Welch t

t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)

Paired t

t = d̄ / (s_d/√n)

One-sample t

t = (x̄ − μ₀)/(s/√n)

✏️ Worked examples

Two groups

You enter
Test	Two independent samples (Welch)
Sample 1	23, 25, 28, 30, 32, 29, 27
Sample 2	19, 22, 24, 21, 26, 23
Hypothesised mean μ₀ (one-sample)	25
Test	Two-tailed (≠)
Significance level α	0.05 (95%)

You get
t statistic	3.4359124
p-value (two-tailed)	0.00558871
Degrees of freedom	10.9664
Decision	Significant at α = 0.05 — reject the null hypothesis (p = 0.00558871 < 0.05)
95% confidence interval for the difference	1.87286 to 8.55572
Test	Welch’s two-sample t-test (H₀: μ₁ = μ₂)
Effect size (Cohen’s d)	1.877

t = 3.4359124, p = 0.00558871.

Before and after (paired)

You enter
Test	Paired (before/after)
Sample 1	200, 190, 210, 220, 205
Sample 2	195, 185, 200, 210, 200
Hypothesised mean μ₀ (one-sample)	0
Test	Two-tailed (≠)
Significance level α	0.05 (95%)

You get
t statistic	5.7154761
p-value (two-tailed)	0.00463584
Degrees of freedom	4
Decision	Significant at α = 0.05 — reject the null hypothesis (p = 0.00463584 < 0.05)
95% confidence interval for the difference	3.59956 to 10.4004
Test	Paired t-test (H₀: mean difference = 0)

t = 5.7154761, p = 0.00463584.

🧭 How to use this calculator

What you enter

Test
Sample 1Separate numbers with commas, spaces or new lines.
Sample 2
Hypothesised mean μ₀ (one-sample)
Test
Significance level α

What you get

t statistic
p-value (two-tailed)
Degrees of freedom
Decision
95% confidence interval for the difference
Test
Effect size (Cohen’s d)

❓ Frequently asked questions

Which t-test should I use?

Two different groups: two-sample (Welch). The same subjects twice: paired. One group against a target: one-sample.

What does the p-value mean?

The probability of a difference at least this large if there were really no difference. Below 0.05 is usually called significant.

What assumptions does the t-test make?

Independent observations and roughly normal data (or samples of about 30 or more per group).

t T-Test Calculator (One-Sample, Two-Sample, Paired)