T-Test Calculator

One-sample, two-sample (Welch or pooled), and paired t-tests with APA write-up.

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About this tool

Paste one or two samples and pick one-sample, independent two-sample (Welch or pooled) or paired. You get t, df, p, the mean difference, a confidence interval and Cohen's d.

How to use

1
Step 1
Choose the test type and enter the sample values.
2
Step 2
Set the null value (default 0), tail and confidence level.
3
Step 3
For two samples pick Welch or pooled variance, then press Calculate.

How it works

Welch's test does not assume equal variances and uses a fractional df. Paired mode tests the mean of the differences between matched observations. The p-value is the chance of a t at least this extreme if the null were true; the confidence interval shows the plausible range for the mean difference.

Welch: t = (x̄₁ − x̄₂) ÷ √(s₁²/n₁ + s₂²/n₂)      one-sample: t = (x̄ − μ₀) ÷ (s/√n)

Worked example

Two groups of eight scores

Input
A: 88,92,79,95,85,90,83,97 B: 81,86,78,90,80,84,76,89 (Welch, two-tailed)
Output
t(13.56) = 2.00, p = .066; mean difference 5.625; 95% CI [−0.43, 11.68]; d = 1.00
Walkthrough
Means 88.625 and 83.0; variances 37.41 and 26.0; SE = √(37.41/8 + 26/8) = 2.815; t = 5.625 ÷ 2.815 = 1.998. The CI spans zero, matching p >.05.

Limitations

  • Needs raw data, not summary statistics.
  • Assumes roughly normal samples; very small or skewed samples call for a non-parametric test.

Questions

When should I use Welch instead of pooled?
Use Welch unless you have a good reason to assume equal variances; it is safe either way.
What is the paired t for before-and-after 70,75,80,68,72 vs 72,78,83,70,75?
t(4) = −10.61, p =.0004, mean difference −2.6.
What is the one-sample t for 5.1,4.9,5.6,5.8,6.0,5.2 against 5?
t(5) = 2.46, p =.057.
Does a p of.066 mean no difference?
No, only that the data do not reach the 5% threshold; the CI shows the effect could still be sizeable.

Features

  • One, two and paired
  • Confidence interval
  • Cohen's d

Guides

Related resources

Guides and videos from around the web—opens on YouTube or the publisher’s site.

  • Finding mean, median, and mode

    Khan Academy

    Baseline summary stats for coursework checkoffs.

    Watch on YouTube

  • Mean, Variance and Standard Deviation

    StatQuest with Josh Starmer

    Descriptive stats behind table and test tools.

    Watch on YouTube

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