T Statistic Calculator

What Is the T-Statistic?

The t-statistic measures how far a sample mean falls from a hypothesized population mean, measured in standard errors:

$$t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$$

It is the test statistic for Student's t-test when population variance is unknown. Related tools: Hypothesis Testing Calculator and Degrees of Freedom Calculator.

Example

With $\bar{x} = 15$, $\mu = 10$, $n = 36$, and $s = 6$, the t-statistic is $(15-10)/(6/\sqrt{36}) = 5$.

Frequently Asked Questions

How is t different from z?

The z-statistic uses known population standard deviation. The t-statistic uses sample standard deviation and follows a t-distribution with $n-1$ degrees of freedom.

What are the degrees of freedom?

For a one-sample t-statistic, degrees of freedom equal $n - 1$.

Can t be negative?

Yes. A negative t means the sample mean is below the hypothesized population mean.

Does this calculator run the full t-test?

It computes the t-statistic and standard error. Use the Hypothesis Testing Calculator or P Value Calculator for p-values and decisions.

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T Statistic Calculator

What Is the T-Statistic?

Example

Frequently Asked Questions

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