Suppose that Kim is a participant in a study that compares several coaching methods to see how they affect math SAT scores. The grand mean of math SAT scores for all participants in the study is 550. The group that Kim participated in had a mean math SAT of 565. Kim’s score on the Math SAT was 610.
a. What was the estimated residual component (ij) of Kim’s score, that is, the part of Kim’s score that was not related to the coaching method? (Both parts of this question call for specific numerical values as answers).
b. What was the “effect” (αj) component of Kim’s score?