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### Spearman Rank Correlation Coefficient

```
Date: 08/26/97 at 13:44:58
From: Lawrence Binek
Subject: Spearman's Rank

I would like to get a clear definition of Spearman's Rank and how it
is used. What data do I use to find the correlation, what formula do
I have to use?
```

```
Date: 08/30/97 at 11:20:50
From: Doctor Anthony
Subject: Re: Spearman's Rank

Rank correlation can be used to give a quick approximation to the
product moment correlation coefficient.  It is also used when only
ranking values can be given.  If we have n comparisons of paired data
(x,y) and if D is the difference in rank of x and y for a particular
pair, then we calculate SUM(D^2) over all n pairs.  The Spearman rank
correlation coefficient is calculated from:

6.SUM(D^2)
r =  1 - ------------
n(n^2 - 1)

For perfect positive correlation SUM(D^2) = 0 and the correlation
coefficient is 1.  For perfect negative correlation the coefficient
works out as -1.  When correlation is not perfect, r lies between -1
and +1.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Statistics

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