Question

Find the Rank Correlation Coefficient for the following data.
Student Name 1 2 3 4 5 6 7 8 9
Rank in A 3 4 1 2 5 7 9 8 6
Rank in B 5 7 1 4 3 2 8 9 6​

Answer 1

Answer:

X Y Rank X Rank Y d d

2

35 40 1 2 1 1

54 60 2 3 1 1

80 75 4 5 1 1

95 90 8 6 2 4

73 70 3 4 1 1

73 75 3 5 2 4

35 38 1 1 0 0

91 95 7 7 0 0

83 75 6 5 1 1

81 70 5 4 1 1

∑d

2

=14

Sperman rank correlation coefficient =r=1−

n(n

2

−1)

6∑d

2

r=1−

10(100−1)

6(14)

r=1−

990

84

=1−.084=.915

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Solution To Question ID 675326

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SIMILAR QUESTIONS

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Following are the ranks of 10 students in Maths and Biology projects given by 2 professors. Find the rank correlation coefficient.

Maths 4 8 5 3 1 2 10 7 6 9

Biology 1 4 5 6 2 3 8 9 7 10

Hard

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>

If ∑d

i

2

=25, n=6 find rank correlation coefficient where d

i

is the difference between the ranks of i

th

values.

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Answer 2

Answer:The Rank Correlation Coefficient is -0.3

Step-by-step explanation:

The Rank Correlation Coefficient, also known as Spearman's rank correlation coefficient, is a measure of the correlation between two sets of ranks. To calculate the coefficient, we use the following formula:

$r = 1 - (6 * ∑d^2) / (n^3 - n)$

where d is the difference in ranks for each pair of data, and n is the number of pairs.

Using this formula, the calculation for the data provided would be:

Student Name 1 2 3 4 5 6 7 8 9

Rank in A 3 4 1 2 5 7 9 8 6

Rank in B 5 7 1 4 3 2 8 9 6

$d = |A - B| = |2|+|3|+|0|+|2|+|2|+|5|+|1|+|1|+|0| = 20$

$r = 1 - (6 * 20^2) / (9^3 - 9)$$= 1 - (6 * 400) / (728 - 9)$ $= 1 - 2400/719$ $= 1 -3.3 = -0.3$

The Rank Correlation Coefficient is -0.3, which indicates a weak negative correlation between the two sets of ranks. This means that as one set of ranks increases, the other decreases. The negative value represents a downward trend.

It may not have a strong correlation because ranking are based on different methodologies.

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