The paired t-confidence interval and test procedures are used to analyze the differences between paired observations. The procedures are used to determine if the mean difference for the population is likely to be different from a reference value (usually zero).

Suppose you have job satisfaction data for a random sample of employees who each filled out a survey before and after a new break was added to their daily work schedule. You could use a paired t-procedure to determine if the break influences overall satisfaction ratings. Or, you may have hardness data for a sample of metal parts collected before and after a new hardening process. You could use a paired t-procedure to determine if the process affects hardness.

An advantage of analyzing paired observations rather than independent samples is that the variability in the observations that is due to differences between the people or objects sampled is factored out, resulting in a more powerful test.

To use the paired t-procedures, the distribution of the differences should be normally distributed. If this does not appear to be the case, you should consider using an appropriate nonparametric procedure. Also, the samples must be dependent, or paired.

A physiologist wants to determine whether a certain type of running program will have an affect on resting heart rate. The heart rates of 15 randomly selected people are measured. They are then placed on the running program and measured again one year later. Thus, the before and after measurements for each person constitute a pair of observations.

Data: Running.MTW (available in the Sample Data folder).