I'm stuck in my homework question. Do I use a sample size formula paired samples for the following problem? When I used paired sample formula, I got an answer of 63 participants. The solution given by this website used a sample size formula for one sample and gave an answer of 32. A study is being planned to assess whether a topical anti-allergic eye drop is effective in preventing the signs and symptoms of allergic conjunctivitis. In a pilot study, at an initial visit, participants are given an allergen challenge; that is, they are subjected to a substance that provokes allergy sign (e.g., cat dander) and their redness score is noted 10 minutes after the allergen challenge (visit 1 score). At a follow-up visit, the same procedure is followed, except that participants are given an active eye drop in one eye and the placebo in the fellow eye 3 hours before the challenge; a visit 2 score is obtained 10 minutes after the challenge. The mean and standard deviation for the data are shown below. Active Eye Change in average redness score -0.61 ± 0.70 (visit 2 - visit 1) Placebo eye Change in average redness score -0.04 ± 0.68 Change score in active eye - change score in placebo eye -0.57 ± 0.86 Suppose we want to estimate the number of participants needed in the main study so that there is a 90% chance of finding a significant difference between active and placebo eyes using a two-sided test with a significance level of 0.05. We expect the active eyes to have a mean redness score 0.5 units less than that of the placebo eyes. How many participants are needed in the main study?
I'm stuck in my homework question. Do I use a
A study is being planned to assess whether a topical anti-allergic eye drop is effective in preventing the signs and symptoms of allergic conjunctivitis. In a pilot study, at an initial visit, participants are given an allergen challenge; that is, they are subjected to a substance that provokes allergy sign (e.g., cat dander) and their redness score is noted 10 minutes after the allergen challenge (visit 1 score). At a follow-up visit, the same procedure is followed, except that participants are given an active eye drop in one eye and the placebo in the fellow eye 3 hours before the challenge; a visit 2 score is obtained 10 minutes after the challenge. The mean and standard deviation for the data are shown below.
Active Eye
Change in average redness score -0.61 ± 0.70 (visit 2 - visit 1)
Placebo eye
Change in average redness score -0.04 ± 0.68
Change score in active eye - change score in placebo eye
-0.57 ± 0.86
Suppose we want to estimate the number of participants needed in the main study so that there is a 90% chance of finding a significant difference between active and placebo eyes using a two-sided test with a significance level of 0.05. We expect the active eyes to have a mean redness score 0.5 units less than that of the placebo eyes. How many participants are needed in the main study?
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