One-Sample T-Test calculator

Compare your sample mean to a known population mean. Enter your data to calculate t-value, p-value, and confidence intervals online.

What it does

Tests whether the mean of a single sample differs from a reference value you specify — a published norm, a target, or a clinically meaningful threshold.

When to use it

You have one group of measurements and a number you want to compare them against, rather than a second group.

Cautions

• The reference value must come from outside your data. Testing against a number derived from the same sample is circular.
• A non-significant result does not show the mean equals the reference — use an equivalence test if that is the claim you want to make.

Alternatives

• Wilcoxon signed-rank — the data are skewed or ordinal, so the mean is not the summary you mean
• Paired t-test — the reference is another measurement on the same subjects, not a fixed number

How to read the output

Mean, SD and the test value μ₀

The sample mean against the value you nominated. The distance between them, in the outcome's units, is the finding. μ₀ must come from outside this dataset. Choosing it after looking at the mean guarantees the answer you were hoping for.

t-statistic and df

How many standard errors the sample mean sits from μ₀; df is n − 1.

p-value

How surprising a difference at least this large would be IF the groups really were identical on this measure. A small p means the data would be surprising under that assumption. It is not the probability that the result is due to chance, and not the probability that the groups are the same — those read the conditional backwards. It also answers 'would this be surprising?', never 'is this big enough to matter?': with a large sample a trivial difference returns a small p, and the result looks identical to an important one.

How this calculator is validated · Which statistical test should I use?