The Paired t-Test Involving
Two Related Means

If the variables are paired, then we are interested in the change between the first set of data and the second.  Let one set of variables equal x , and the other equal y. the difference of a set n (dn) would equal xn  minus yn :

d = x-y

To conduct a paired t-test of the mean, we need two values: First, the mean of the differences of all of the pairs, which is easily computed with the equation.  Keep in mind that n  equals the number of pairs.

Second, we require the standard deviation of the difference:

We now have the raw data needed to conduct a paired t-test of means.