T-Test Calculator
Enter your sample statistics below to instantly get the one-sample t-statistic.
One-sample t-test
The One-Sample T-Test Formula
t = (x̄ − μ) / (s / √n). It measures how many standard errors the sample mean sits from the value you're testing against.
Worked example
Sample mean 105, hypothesized mean 100, sample standard deviation 15, sample size 25.
t = (105 − 100) / (15 / √25) = 5 / (15 / 5) = 5 / 3
t ≈ 1.67
Frequently Asked Questions
What is a one-sample t-test?
It tests whether a sample's mean is significantly different from a specific hypothesized value, using the sample's own standard deviation rather than assuming the population's standard deviation is known.
What is the t-statistic formula?
t = (x̄ − μ) / (s / √n), where x̄ is the sample mean, μ is the hypothesized mean, s is the sample standard deviation, and n is the sample size.
What do you do with the t-statistic once you have it?
Compare it to a critical value from a t-distribution table, based on your degrees of freedom (n − 1) and chosen significance level. A t-statistic beyond the critical value suggests the sample mean is significantly different from the hypothesized value.
How is a t-test different from a z-score?
A z-score assumes you know the true population standard deviation. A t-test uses the sample's own standard deviation instead, which is the more realistic situation in practice, and accounts for the extra uncertainty that comes with estimating it from a sample.
Related Calculators
- Standard Deviation Calculator — Statistics
- Percentile Calculator — Statistics
- Mean, Median, Mode Calculator — Statistics
- Variance Calculator — Statistics