Given two paired sets and of measured values, the paired -test determines whether they differ from each other in a significant way under the assumptions that the paired differences are independent and identically normally distributed.

To apply the test, let

			(1)
			(2)

then define by

(3)

This statistic has degrees of freedom.

A table of Student's t-distribution confidence intervals can be used to determine the significance level at which two distributions differ.

Goulden, C. H. Methods of Statistical Analysis, 2nd ed. New York: Wiley, pp. 50-55, 1956.

CITE THIS AS:

Weisstein, Eric W. "Paired t-Test." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Pairedt-Test.html