...one of the most highly
regarded and expertly designed C++ library projects in the
world.

— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

Imagine that we have a before and after reading for each item in the sample: for example we might have measured blood pressure before and after administration of a new drug. We can't pool the results and compare the means before and after the change, because each patient will have a different baseline reading. Instead we calculate the difference between before and after measurements in each patient, and calculate the mean and standard deviation of the differences. To test whether a significant change has taken place, we can then test the null-hypothesis that the true mean is zero using the same procedure we used in the single sample cases previously discussed.

That means we can:

- Calculate confidence intervals of the mean. If the endpoints of the interval differ in sign then we are unable to reject the null-hypothesis that there is no change.
- Test whether the true mean is zero. If the result is consistent with a true mean of zero, then we are unable to reject the null-hypothesis that there is no change.
- Calculate how many pairs of readings we would need in order to obtain a significant result.