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One-sample t-test calculator

Tests whether the mean of one sample differs from a known or hypothesized value μ. Returns t, df, the two-sided p-value and Cohen’s d.

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Your data

One column of numbers — separated by spaces, commas or new lines. Use a dot as the decimal separator.

n = 0

The hypothesized population mean to compare against (e.g. the scale midpoint, a norm value, or zero).

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When to use this

Use a one-sample t-test when you have one group of measurements and want to know whether its mean differs from a fixed reference value: a published norm (do our patients sleep less than the recommended 7 hours?), a scale midpoint (is average agreement above the neutral point of 3?), or a target value in quality control. It is the simplest member of the t-test family — one sample, one comparison value, one p-value.

Key assumptions

  • Observations are independent of each other (one measurement per participant).
  • The variable is approximately normally distributed — or the sample is large enough (n ≳ 30) for the central limit theorem to make the test robust.
  • The data are interval or ratio scaled.
  • The test value μ is chosen before looking at the data.

Common mistakes

  • Choosing μ after inspecting the sample mean — that invalidates the p-value.
  • Using it for paired before/after data; that calls for a paired-samples t-test on the differences.
  • Reporting significance without an effect size — always include Cohen’s d so readers can judge whether the difference matters.

Frequently asked questions

What does the test value μ mean?
μ (mu) is the fixed value you compare your sample mean against — a population norm, a theoretical midpoint, or a benchmark. The test asks: if the true population mean were exactly μ, how surprising would a sample mean like ours be?
How large should Cohen’s d be?
Conventional benchmarks are 0.2 (small), 0.5 (medium) and 0.8 (large). Here d = (M − μ) / SD, i.e. the difference expressed in standard-deviation units. Context matters more than the labels — a “small” d can be important in medicine.
Is the p-value one-sided or two-sided?
Two-sided: it tests whether the mean differs from μ in either direction. If you have a strong directional hypothesis specified in advance, you can halve the reported p-value for a one-sided test.

Related free tools

Sample size calculatorSample size for two groupsEffect size (Cohen's d)Descriptive statisticsIndependent t-testPaired t-testOne-way ANOVAz-table (standard normal)t-table (critical values)Chi-square table

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