A paired t test is used when you have two sets of Normally distributed values for each participant in a study (or other forms of matched data) and want to see if the two measures differ. Commonly this may be used for pre- and post-test scores to see if the intervention has made an improvement. The differences are computed and then the Student's t-test is used to see if they are significantly different from zero.
The paired t test is used for a within subjects experiment when the data is believed to be Normally distributed. It has greater statistical power than taking the two sets of pre- and post-test scores and comparing them using a plain t test. The Wilcoxon signed rank test is a nonparametric equivalent, but has less power when the data values are Normal.
Used in glossary entries: nonparametric statistics, Normal distribution, statistical power, Student's t-test, Wilcoxon signed rank test