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.
