# Calculate the Spearman’S Rank Correlation Coefficient for the Following Data and Interpret the Result: - Mathematics

Sum

Calculate the Spearman’s rank correlation coefficient for the following data and interpret the result:

 X 35 54 80 95 73 73 35 91 83 81 Y 40 60 75 90 70 75 38 95 75 70

#### Solution

To determine Spearman’s Rank Correlation:

 X Y R1 R2 d = R1 - R2 d2 35 40 9.5 9 0.5 0.25 54 60 8 8 0 0 80 75 5 4 1 1 95 90 1 2 -1 1 73 70 6.5 6.5 0 0 73 75 6.5 4 2.5 6.25 35 38 9.5 10 -0.5 0.25 91 95 2 1 1 1 83 75 3 4 -1 1 81 70 4 6.5 -2.5 6.25 Total ∑d2 = 17

r = 1 - (6[sum"d"^2 + sum (("t"^3 - "t")/12)])/("N"("N"^2 - 1))

where t is the number of individual involved in a tie.

Here, ∑d2 = 17, N = 10 , t = 3,2,2,2

sum("t"^3-"t")/12 = ((3)^2 - 3)/12 + 3 xx ((2)^3 - 2)/12

= (27-3)/12 + 3 xx (8 - 2)/12

= 24/12 + 18/12 = 42/12 =7/2 = 3.5

r = 1 - (6[17 + 3.5])/(10(100 - 1))

=1 - 123/990

= (990-123)/990

= 867/990 = 0.876

Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
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