Using the t-Test Calculator
Choose the design before entering data. One-sample compares sample A with the null mean; paired compares matched A minus B observations; Welch compares independent sample means without assuming equal variances. The null field refers to the mean or mean difference for that design.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- Test type
- One-sample
- Sample A
- 8, 9, 10, 11, 12
- Null mean / A−B difference
- 0
- Alternative hypothesis
- Two-sided
Example result
- Mean / mean difference
- 10
- t statistic
- 14.142136
- Degrees of freedom
- 4
- p-value
- 0.00014512817
- 95% two-sided CI lower
- 8.0367568
- 95% two-sided CI upper
- 11.963243
- Interpretation
- A small p-value is evidence against the specified null under the model assumptions, not proof of causation or practical importance.
Method and assumptions
Sample variances use n−1. One-sample and paired tests use n−1 degrees of freedom; paired tests operate on A−B differences. Independent samples use Welch-Satterthwaite degrees of freedom, without assuming equal variances. P-values come from the Student t distribution. Confidence intervals shown are always two-sided 95%, even for a one-sided hypothesis. Assumes appropriate independent sampling; paired differences / small-sample residuals should be reasonably normal. Does not correct multiple testing or infer causation.
Reference: itl.nist.gov — method and further reading
Check what the data represents
A statistical result is only meaningful in relation to the observations and assumptions behind it. Keep track of whether values describe a whole population or a sample, whether observations are independent, and which distribution the method uses. More decimal places cannot compensate for a sample that does not represent the question you are trying to answer.
Common question
Does a small p-value show that the effect is large?
No. A p-value concerns compatibility with the null under the test assumptions. Sample size, variability and the study design affect it. Inspect the estimated difference and confidence interval, and decide separately whether the effect matters in the real setting.