Use to evaluate the equivalence between a test mean and a reference mean using paired observations. For example, suppose that you want to determine whether 2 blades are equally good at cutting  through leather. Because pieces of leather vary in grain and toughness, you decide to take a pair of measurements from each piece, one using the test blade and one using the reference blade. Because both measurements are affected by the toughness of the particular piece, they are dependent.

If the observations are not paired, but instead are independently selected from two populations, use the 2-sample equivalence test procedure.

You can also evaluate whether the test mean is greater than or less than the reference mean.

You developed a new cleaning solution for contact lenses. You want to verify that your new solution cleans lenses as well as the leading brand. You have 14 participants wear contact lenses for a day, and then clean the lenses. Each participant cleans one lens in your solution and the other lens in the leading brand. By pairing the observations, you reduce the amount of variability that is caused by differences between participants. Finally, you assess the cleanliness of each lens by measuring the angle of contact for a drop of fluid on the lens. The angle of contact is affected by film or deposits on the lens.

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