Answer to Question #290819 in Statistics and Probability for saia

Question

The following represent the scores of a group of students on two tests. calculate spearman rs and kendall's tau for these data.

Test 1 - 36, 34, 33, 29, 29, 28, 28, 28, 24, 22, 19, 12

Test 2 - 18, 26, 24, 18, 15, 12, 14, 13, 12, 10, 8,9

Answer 1

Test 1 Test 2 Rank Test 1 Rank Test 2 d d$^2$ Concordant Discordant

36 18 1 3 2 4 8 2

34 26 2 1 1 1 10 0

33 24 3 2 1 1 9 0

29 18 4 3 1 1 8 0

29 15 4 5 1 1 7 0

28 12 6 8 2 4 3 2

28 14 6 6 0 0 5 0

28 13 6 7 1 1 4 0

24 12 9 8 1 1 3 0

22 10 10 10 0 0 2 0

19 8 11 12 1 1 0 1

12 9 12 11 1 1

$spearman~rank=1-\frac{6\sum d^2}{n(n^2-1)}\\ \sum d^2=16\\n=12\\ spearman~rank=1-\frac{6\times 16}{12(12^2-1)}\\ =1-\frac{96}{1716}\\ =1-0.5594\\ =0.4406\\ Kendall's~Tau=\frac{C-D}{C+D}\\ C=sum~of~concordant\\ D=sum~of~discordant\\ =\frac{59-5}{59+5}\\ =\frac{54}{64}=0.8438\\$