MedStatica
Calculators · §4
Form MS-C4
One-sample t-test · exact noncentral t

Sample size for one mean vs a reference value

How many participants to show your group's average differs from a fixed benchmark — a guideline target, a historical norm, a device specification.

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Means calculations use the exact noncentral t distribution (Lenth 1989), so small samples are handled correctly. A planning estimate, not a substitute for a statistician.

Method & formula

The one-sample t-test compares a single group's mean to a fixed reference value. The required n depends on the standardized difference δ/σ; this calculator searches with the exact noncentral t distribution on n−1 degrees of freedom (matching R's power.t.test(type = "one.sample")) rather than the normal approximation, which matters at the small samples this design often ends up with.

One caution: comparisons against historical or external references inherit the biases of the reference — a concurrent control group is stronger evidence whenever it is feasible.

Source: Lenth RV. Algorithm AS 243. Appl Statist 1989;38:185–89.

Inputs, explained

Meaningful difference from reference
The smallest gap between your group's true mean and the reference value that would matter.
Standard deviation (SD)
The expected SD of the outcome within your group.

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