Coefficient of Correlation (r)

from

raw scores

(when deviations are taken from zero)

AND

Rank Difference Correlation Coefficient **(**
**ρ )**

Formulae:

r =[ Σxy - N * M_{x}M_{y }] /√[
(ΣX^{2} - NM^{2}_{x})*(ΣY^{2} - NM^{2}_{y})]
-----(1)

**σ _{x }**= √[(ΣX

**σ _{y }**= √[(ΣY

* by subtraction of fixed amount from X and Y.

r* = (NΣX'Y' - ΣX'^{*}ΣY^{' })
/ (√([NΣX^{'2} - (ΣX' )^{2}] *√[NΣY^{'2} - (ΣY' )^{2}]
) ----(2)

where X'=X-a and Y'=Y-b;

Equn. 1 & Equn.2 are alternate forms.

**Correlation coefficient from Ranking score (not tied ) :** ρ
=1 - [6 * ΣD^{2} / N( N^{2}-1 )] where D
= x - y;

When in stead of absolute x-score or y-score, Judge X and Judge Y give a ranking score for traits A, B,C etc such as rank 1,2,3,4,5,........ a coefficient of correlation is found out

provided rank for similar trends are not tied, such that say for trait A, both Judge X & Judge Y scores are 2. If one treats the ranked data as absolute data, one gets the r under *

When ranks are treated as scores and there are no ties, ρ = r . ρ provides a quick and convenient way of estimating the correlation when N is small or when we only have ranks.

In case of large N, the ρ is still useful for exploratory purpose.