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# Difference Between Rank Coefficient and Karl Pearson’s Coefficient of Correlation

• Last Updated : 21 Jun, 2022

Rank Coefficient of Correlation is the method of determination of coefficient of correlation. It is also named Spearman’s Coefficient of Correlation. It measures the linear association between ranks assigned to individual items according to their attributes. Attributes are those variables that cannot be numerically measured such as intelligence of people, physical appearance, honesty, etc.

It is developed by British psychologist Charles Edward Spearman. It is used when the variables cannot be measured meaningfully as in the case of quantitative variables such as price, income, weight, etc. Basically, it is used when values are expressed qualitatively.

#### Formula:

Rank Coefficient of Correlation (rs)= 1 – 6ΣD2  / (N3–N)

#### Solution:

Here, n =  8

(rs)= 1 – 6ΣD2  / (N3–N)
= 1- 6 * 22 / 504
= 1- 132/504
= 0.74

Rank Coefficient of Correlation (rs)= 0.74

### Karl Pearson’s Coefficient of Correlation:

Karl Pearson’s Coefficient of Correlation (or Product moment correlation or simple correlation coefficient or covariance method ) is based upon the arithmetic mean and the standard deviation.

According to Karl Pearson, the correlation coefficient of two variables is obtained by dividing the sum of the products of the corresponding deviations of the various items of two series from the respective means by the product of their standard deviations and the number of pairs of observation. Basically, it is based on the covariance of the concerned variables.

#### Formula is:

Karl Pearson's Coefficient of Correlation  (r) = NΣXY−ΣX.ΣY / √NΣX2 - (Σx)2 √NΣY2 - (ΣY)2

#### Example:

Find the value of Karl Pearson’s coefficient correlation from the following table:

### Solution:

(r) = NΣXY−ΣX.ΣY / √NΣX2 - (Σx)2 √NΣY2 - (ΣY)2
(r) = 6(20,485) – (247 × 486) / [√[[6(11,409) – (2472)] × [6(40,022) – 4862]]]

Karl Pearson’s Coefficient of Correlation  (r) = 0.5298

### Difference between Rank Coefficient and Karl Pearson’s Coefficient of Correlation

The difference between Rank Coefficient and Karl Pearson’s Coefficient of Correlation is as follows:

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