Theory question 113
StatisticsIn a research to determine the relationship between performance of students in an entrance examination and subsequent school performance, the results of ten randomly selected students were obtained as follows:
Students: A, B, C, D, E, F, G, H, I, J
Performance in Entrance Examination: 11, 12, 8, 13, 6, 15, 10, 14, 17, 16
School Performance: 5, 10, 9, 7, 4, 8, 6, 14, 11, 12
(a) Calculate the Spearman's rank correlation coefficient. (b) What would be the researcher's conclusion from the result in 13(a)?
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(a) Ranks (highest = 1): Entrance 7, 6, 9, 5, 10, 3, 8, 4, 1, 2; School 9, 4, 5, 7, 10, 6, 8, 1, 3, 2.
Σd² = 4 + 4 + 16 + 4 + 0 + 9 + 0 + 9 + 4 + 0 = 50.
ρ = 1 − 6(50)/990 ≈ 0.70.
(b) There is a fairly strong positive relationship: students who do well in the entrance examination tend to do well in school.
Rank each set, find the differences, then use ρ = 1 − 6Σd²/(n(n² − 1)).