The one-sample t-test compares the mean of one sample with a fixed reference value.
Why it matters
It answers "is our group different from a known standard?"
Key ideas
- Outcome: numeric
- One group, one reference value μ0
- t = (x̄ − μ0) ÷ (SD ÷ √n)
- df = n − 1
- Assumes roughly normal data (or n ≥ 30)
- Report mean difference, 95% CI, d
Real-life research example
Is the mean hemoglobin of 25 adolescent girls different from the reference 12.0 g/dL?
When to use
- One numeric variable vs a standard value
When NOT to use
- Don't use it for two groups
- Don't use with strong skew and small n
Mini example
Values: 11.2, 10.8, 12.1, 11.5, 10.9, 11.7, 11.0, 10.6 vs μ0 = 12
Quick takeaway
One group + one standard value = one-sample t-test.
Try it yourself
Run the example. Is the mean different from 12? Look at the CI as well as p.
Model answer
If the CI for the difference excludes 0, the mean differs from 12 at the 5% level. The CI also shows by how much.