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

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