T-Test Calculator
Calculate a one-sample t statistic from sample mean, hypothesized mean, standard deviation and sample size.
One-sample t-test
The t statistic compares a sample mean with a hypothesized population mean while accounting for sample variability and sample size.
How a T-Test Works
A t-test compares a sample mean with a reference value or compares means between groups while accounting for sample variability. The t statistic reflects the size of the difference relative to its estimated standard error.
T-Test Example
Suppose a sample mean is 52, the comparison value is 50 and the estimated standard error is 1. The resulting t statistic is 2, meaning the observed difference is two estimated standard errors from the reference value.
Important Assumptions
Interpretation depends on the type of t-test, independence of observations and whether the data are reasonably compatible with the assumptions used by the selected test. For small samples, severe non-normality can matter more.
Frequently Asked Questions
What does a larger absolute t value mean?
It means the observed difference is larger relative to the estimated uncertainty.
Is a t-test the same as a z-test?
No. T-tests use the t distribution and are commonly used when population variability is estimated from the sample.
Should I use a one-tailed or two-tailed test?
That depends on the hypothesis defined before analyzing the data.
Interpreting a T-Test
A t-test evaluates a difference relative to its estimated sampling variability. The appropriate formula depends on whether observations are paired or independent and whether equal variances are assumed. A t statistic alone is not an effect size; sample size, confidence intervals, assumptions and the corresponding p-value provide additional context.
Methodology, Assumptions and Interpretation
A t-test compares a mean difference with its estimated standard error. The correct form depends on one-sample, paired or independent samples, and Welch’s version is generally used when equal variances are not assumed; interpretation also depends on independence and distribution assumptions.