Nonparametric Statistics Spearman\'s Rank Correlation Coefficient 1. This is the

Question

Nonparametric Statistics Spearman's Rank Correlation Coefficient 1. This is the nonparametric alternative to the Pearson's Product Moment Correlation 2. Assumption: The n ordered pairs of data form a random sample and the variables are ordinal or numerical. 3. The null hypothesis that we test is "there is no correlation between the two rankings". The alternative is "there is a correlation between the two variables". Assignment 8: Four judges rank 10 contestants in the Shelby Beauty contest with 10 being the highest and 1 being the lowest. Their rankings are given below: Contestant 1 2 34 5 6 7 10 0 Judge A59 Judge B 4 10 65S Judge C 6 4 8 3 79 5 7 4 Judge D 9 8989 10 6 7 8 Calculate Spearman's Rho for each pair of judges Which 2 judges are the most closely related? Which 2 judges are the least closely related? Which judge was the kindest? a. b. c.

Explanation / Answer

part a)

A = c(5,9,3,8,6,7,4,8,4,6)
B = c(7,8,6,7,8,5,10,6,5,8)
C = c(6,8,4,8,3,7,9,5,7,4)
D =c(9,8,9,8,9,10,6,7,8,7)

r1 = cor.test(A, B, method="kendall")

r1

Kendall's rank correlation tau

data: A and B

z = 0.27886, p-value = 0.7803

alternative hypothesis: true tau is not equal to 0

sample estimates:

tau

0.07412493

r2 = cor.test(A, C, method="kendall")

r2

Kendall's rank correlation tau

data: A and C

z = 0.64115, p-value = 0.5214

alternative hypothesis: true tau is not equal to 0

sample estimates:

tau

0.1666667

r3 = cor.test(A, D, method="kendall")

r3

Kendall's rank correlation tau

data: A and D

z = -0.093604, p-value = 0.9254

alternative hypothesis: true tau is not equal to 0

sample estimates:

tau

-0.02503131

r4 = cor.test(B, C, method="kendall")

r4

Kendall's rank correlation tau

data: B and C

z = 0.27886, p-value = 0.7803

alternative hypothesis: true tau is not equal to 0

sample estimates:

tau

0.07412493

r5 = cor.test(B, D, method="kendall")

r5

Kendall's rank correlation tau

data: B and D

z = -1.519, p-value = 0.1288

alternative hypothesis: true tau is not equal to 0

sample estimates:

tau

-0.4156195

r6 = cor.test(C, D, method="kendall")

r6

Kendall's rank correlation tau

data: C and D

z = -0.93604, p-value = 0.3493

alternative hypothesis: true tau is not equal to 0

sample estimates:

tau

-0.2503131

part b) B and D are most closely related where r = -

-0.4156195.

A and D are the least closely related , where r = -0.02503131 .

part c) the judge D is the kindest who has given the good ranking to the contestant.

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