BYTETOOLS

T-Test Calculator

Run a one-sample, paired or two-sample t-test from raw data. Get t, degrees of freedom, exact p-values, the critical value, Cohen's d and a confidence interval.

-1.86081
t statistic
17.7765
df
0.079394
p (two-tailed)
0.039697
p (one-tailed)

Welch's two-sample t-test

Fail to reject the null hypothesis (p > α = 0.05)

2.10282
Critical t (±, α = 0.05)
-0.8322
Effect size (Cohen's d)
-3.3655 to 0.2055
95.0% CI

Cohen's d = (x̄₁ − x̄₂) / √((s₁² + s₂²)/2)

Working

n₁ / n₂10 / 10
Mean x̄₁0.75
Mean x̄₂2.33
Variance s₁²3.200556
Variance s₂²4.009
Standard error0.849091
Welch–Satterthwaite df17.7765
Difference of means (x̄₁ − x̄₂)-1.58

p-values come from the regularized incomplete beta function, so they match statistical software rather than a rounded printed table.

What is the T-Test Calculator?

The ByteTools T-Test Calculator runs the three t-tests you actually get set: one-sample against a hypothesised mean, paired samples for before-and-after data, and two independent samples with either Welch's unequal-variance correction or the classic pooled-variance version.

  • One-sample, paired and two-sample tests in a single tool
  • Welch–Satterthwaite degrees of freedom or pooled variance
  • Exact p-values from the incomplete beta function, not a table
  • Cohen's d effect size and a confidence interval for the difference
  • Working table showing means, variances and the standard error
  • 100% private — the numbers never leave your browser

How to use the T-Test Calculator

  1. 1

    Choose one-sample, paired samples or two independent samples.

  2. 2

    Paste your numbers into the sample boxes, separated by spaces, commas or new lines.

  3. 3

    For a one-sample test, enter the hypothesised population mean; for two samples, pick Welch or pooled variance.

  4. 4

    Select the significance level alpha, which also sets the confidence interval.

  5. 5

    Read t, df, the one- and two-tailed p-values, Cohen's d and the interval, then click Copy results.

About the T-Test Calculator

The ByteTools T-Test Calculator runs the three t-tests you actually get set: one-sample against a hypothesised mean, paired samples for before-and-after data, and two independent samples with either Welch's unequal-variance correction or the classic pooled-variance version. Paste your numbers, pick the test, and the full result appears immediately.

As well as t and the p-value it reports the degrees of freedom (including the Welch–Satterthwaite fraction), the critical t at your alpha, Cohen's d effect size and a confidence interval for the difference. A working table underneath shows the means, variances and standard error the answer was built from, so you can check each step rather than trusting a single number.

All of the arithmetic happens locally in your browser using a hand-written regularized incomplete beta function for the t tail. Your data is never uploaded, never logged and never leaves the page, which makes the tool safe for unpublished research or confidential coursework, and it carries on working with no internet connection at all.

Frequently asked questions

When should I use Welch's t-test instead of the pooled version?

Welch's test is the safer default for two independent samples because it does not assume the two groups share a variance. The pooled version is slightly more powerful when the variances really are equal and the samples are similar in size, but Welch loses very little when they are, so most statisticians recommend it routinely.

What is the difference between a paired and a two-sample t-test?

A paired test is used when each value in one sample is naturally matched to one in the other, such as the same person measured twice. It works on the differences within each pair, which removes person-to-person variation. A two-sample test treats the groups as independent and compares their means directly.

How big does Cohen's d need to be to matter?

The rough conventions are 0.2 for a small effect, 0.5 for medium and 0.8 for large, but they are only rules of thumb. What counts as a meaningful effect depends entirely on your field and what the measurement means in practice, so read d alongside the confidence interval rather than on its own.

Can I run a t-test on a small sample?

Yes, the t-distribution was designed for small samples and the tool works from two values upward. With very small samples the test has little power to detect a real difference and relies more heavily on the data being roughly normal, so treat a non-significant result as inconclusive rather than as evidence of no effect.

Why is my Welch degrees of freedom not a whole number?

The Welch–Satterthwaite formula estimates the degrees of freedom from the two sample variances, and that estimate is almost never an integer. Statistical software keeps the fractional value and so does this tool, which is why the p-value matches R or SPSS exactly.

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