A researcher conducted experiments to compare memory performance between serial and free recall. A total of 72 participants were randomly assigned to different treatment groups. Each participant viewed 11 letters on a computer screen, completed a movement task, and then recalled the presented letters. Each participant attended one session and repeated the entire procedure four times, with different sets of letters each time. The outcome measure is the average number of correctly recalled letters out of the first 5 presented. You can download the data file at the following link. http://www.auburn.edu/~zengpen/teaching/STAT-7010/datasets/letters.csv The meaning of the variables are as follows. Time Meaning 1 8:00 -- 10:00 session 2 10:00 -- 12:00 session 3 12:00 -- 2:00 session 4 2:00 -- 4:00 session Memory Meaning 1 serial recall 2 free recall Movement Meaning 1 turn two glasses upside down 2 move two cylinders from an upper shelf to a lower shelf 3 move one cylinder from an upper shelf to a lower shelf Answer questions based on a model with all main effects, two-factor interactions, and three- factor interactions of time, memory, and movement. All effects are fixed effects.

Calculate the sum of squares for the following 3 contrasts for time, respectively. 1 = 1 + 2 3 4 , 2 = 1 2 , 3 = 3 4 .