Approach (paired t-test)

Testing whether two paired measurements, X and Y, have equal means is done in terms of the differences

D = Y - X

The test is then expressed as

H0:   µD = 0

HA:   µD ≠ 0

or a one-tailed variant. The hypotheses are therefore assessed with a standard univariate t-test using test statistic

This is compared to a t distribution with n - 1 degrees of freedom to find the p-value.

Example

The diagram below illustrates a 2-tailed test for equal means, based on n = 15 paired observations.

From the p-value, we conclude that there is very strong evidence that the means for Y and X are different.