Question

Suppose that you were interested in investigating the effect of a drug that is to be used in the treatment of patients who have glaucoma in both eyes. A comparison between the mean reduction in eye pressure for this drug and for a standard treatment is desired. Both treatments are applied directly to the eye. a. Describe how you would go about collecting data for your investigation. b. Does your method result in paired data? c. Can you think of a reasonable method of collecting data that would result in independent samples? Would such an experiment be as informative as a paired experiment? Comment.

Short answer

a) You would conduct a randomised controlled trial, assigning one treatment to each patient randomly and compare the mean reduction in eye pressure. b) The data collected would not be paired, as each patient received only one type of treatment. c) You could collect independent samples by assigning one treatment to each eye randomly, but this would not be as informative as a paired experiment since the variation between patients might affect the comparison.

Step-by-step solution

Designing The Study

For part a, you could conduct a randomised controlled trial, where patients are randomly assigned to receive either the new drug or the standard treatment. The reduction in eye pressure would be measured for all patients, and the mean reductions for the two groups would be compared. Care would be taken to ensure that the groups are as similar as possible in all relevant aspects (e.g., age, severity of glaucoma, etc.) except for the treatment they receive. This would help to isolate the effect of the treatment.

Determining The Type Of Data

For part b, the method described in step 1 would not yield paired data, as each patient only receives one type of treatment. The data pairs in a paired data set typically come from the same subject or related subjects. Since in this experiment every patient receives one type of treatment, the data from different patients are independent rather than paired.

Suggesting An Alternative Method

For part c, you could collect independent samples by randomly assigning one treatment to each eye of a patient. Since each eye is treated differently, the response (reduction in eye pressure) of one eye would be independent of the other. While this experiment would involve independent samples, it would not be as informative as a paired experiment. In a paired experiment, by applying both treatments to the same patient, we eliminate the variation between patients, which allows us to precisely measure the difference in effectiveness of the two treatments. In contrast, in an experiment with independent samples, variations between patients can confound the comparison of the treatments.