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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
9 years ago

Dear Jinish,

In statisticsSpearmans 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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