Calculation practice: Repeatability. The following anonymized data show the midterm and final exam grades (%) for eight undergraduate students from a biostatistics class at a major university. The partial ANOVA table provides sums of squares and mean squares. What is the repeatability of grade performance?

a. Calculate s_A² from the mean squares and the sample size. What variance component does this quantity estimate?

b. Calculate the repeatability using s_A² and MS_error .

c. Interpret the repeatability you just calculated. What fraction of the variance among test scores is estimated to reflect true differences among students in performance, and what fraction is measurement variance from test to test within students?

d. What assumptions are you making when estimating repeatability to test scores?

Individual 11 22 33 44 55 66 77 88 Midterm grade 7878 8484 9494 8282 5858 6262 8181 8080 Final exam grade 8181 6565 7575 6262 6060 8686 9292 8989