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Can you provide me with examples of Spear man’s Rank Coefficient of Correlation for repeated & non repeated rank

Can you provide me with examples of Spear man’s Rank Coefficient of Correlation for repeated & non repeated rank

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1 Answers

Aman Bansal
592 Points
12 years ago

Dear Jinish,

In statistics, Spearmans rank correlation coefficient or Spearmans rho, named after Charles Spearman and often denoted by the Greek letter \rho (rho) or as r_s, is a non-parametric measure of statistical dependence between two variables. It assesses how well the relationship between two variables can be described using a monotonic function. If there are no repeated data values, a perfect Spearman correlation of +1 or −1 occurs when each of the variables is a perfect monotone function of the other.

Example

In this example, we will use the raw data in the table below to calculate the correlation between the IQ of a person with the number of hours spent in front of TV per week.

IQ, X_i Hours of TV per week, Y_i
106 7
86 0
100 27
101 50
99 28
103 29
97 20
113 12
112 6
110 17

First, we must find the value of the term d^2_i. To do so we use the following steps, reflected in the table below.

  1. Sort the data by the first column (X_i). Create a new column x_i and assign it the ranked values 1,2,3,...n.
  2. Next, sort the data by the second column (Y_i). Create a fourth column y_i and similarly assign it the ranked values 1,2,3,...n.
  3. Create a fifth column d_i to hold the differences between the two rank columns (x_i and y_i).
  4. Create one final column d^2_i to hold the value of column d_i squared.
IQ, X_i Hours of TV per week, Y_i rank x_i rank y_i d_i d^2_i
86 0 1 1 0 0
97 20 2 6 −4 16
99 28 3 8 −5 25
100 27 4 7 −3 9
101 50 5 10 −5 25
103 29 6 9 −3 9
106 7 7 3 4 16
110 17 8 5 3 9
112 6 9 2 7 49
113 12 10 4 6 36

With d^2_i found, we can add them to find \sum d_i^2 = 194. The value of n is 10. So these values can now be substituted back into the equation,

\rho = 1- {\frac {6\times194}{10(10^2 - 1)}}

which evaluates to ρ = −0.175757575... with a P-value = 0.6864058 (using the t distribution)

This low value shows that the correlation between IQ and hours spent watching TV is very low

Best Of luck

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Thanks

Aman Bansal

Askiitian Expert

 


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