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

Dear Jinish,

In statistics, Spearmans rank correlation coefficient or Spearmans rho, named after Charles Spearman and often denoted by the Greek letter  (rho) or as , 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,	Hours of TV per week,
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 . To do so we use the following steps, reflected in the table below.

1. Sort the data by the first column (). Create a new column  and assign it the ranked values 1,2,3,...n.
2. Next, sort the data by the second column (). Create a fourth column  and similarly assign it the ranked values 1,2,3,...n.
3. Create a fifth column  to hold the differences between the two rank columns ( and ).
4. Create one final column  to hold the value of column  squared.

IQ,	Hours of TV per week,	rank	rank
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  found, we can add them to find . The value of n is 10. So these values can now be substituted back into the equation,

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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