Mathematical Details: Our treatment of the t-test has been limited. In particular, the mathematical details have been omitted. This site provides the general equations for using a t-test to compare two data sets, as well as for other types of t-tests. This site also provides useful details and an on-line calculator.
For further information, including a discussion of more esoteric (but important) considerations, such as one-tailed vs. two-tailed t-tests, type 1 vs. type 2 errors and paired t-tests consult the following textbook:
Miller, J. C.; Miller, J. N. Statistics for Analytical Chemistry, Ellis Horwood: Chichester
What if I have more than two data sets?: When you have more than two data sets, using a t-test to make all possible comparisons is not a good idea. Each t-test has a certain probability of yielding an incorrect result and when used multiple times, the probability increases that at least one conclusion will be incorrect. Instead, you should use an analysis of variance (ANOVA). This site provides a brief discussion of ANOVA and an on-line calculator.
This handout provides an explanation of the difference between paired and unpaired data.