An optometrist is interested in the effects of different brands of eye drops. She desires to know if different drops affect the accuracy of standard vision test. Some researchers think that Brand A may have more adverse effects on individual's capability to correctly report the letters in the vision test than Brand B or Brand C. There is also some speculation that effect of drops on vision differs dramatically for individuals who are far-sighted compared to those who are near-sighted.
The optometrist hires you to design experiment which tests the effect of the eye drops on test performance. You tell her there are two possible approaches to take: a randomized comparative approach or matched pairs design.
Discuss how you would use each design to test the effect of the eye drops on test performance on a random sample of patients. Remember, there is a concern about the effects for near vs. far-sighted patients. As much as possible, use diagrams instead of words to summarize your experimental design.