1. Suppose we are planning to collect paired data Xi,Yi with the goal of estimat
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Question
1. Suppose we are planning to collect paired data Xi,Yi with the goal of estimating EX -EY. We want to have 80% power to detect a raw effect size EX -EY = 1, and based on previous experience we are confident that SD(X) ˜ 2 and SD(Y ) ˜ 3. However we do not know much about the correlation between X and Y .(a) What sample size is required if cor(X, Y ) = 0.3?
(b) If we perform the study using the sample size from part (a), and the correlation coefficient is actually 0.5, then what power do we actually have?
Explanation / Answer
Suppose we are planning to collect paired data Xi,Yi with the goal of estimating EX -EY. We want to have 80% power to detect a raw effect size EX -EY = 1, and based on previous experience we are confident that SD(X) = 2 and SD(Y ) =3. a) cor(X,Y) = 0.3 cov(x,y)/(sd(x)*sd(y)) = 0.3 cov(x,y) = 0.3(6) cov(x,y) =1.8 Apply the covariance formulae and will be solved
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