(a) kg/feet

(b) percentage

(c) non-existent

(a) 0 to infinity

(b) minus one to plus one

(c) minus infinity to infinity

(a) when Y increases X increases

(b) when Y decreases X increases

(c) when Y increases X does not change

(a) linearly related

(b) not linearly related

(c) independent

(a) Karl Pearson’s coefficient of correlation

(b) Spearman’s rank correlation

(c) Scatter diagram

(a) more accurate than rank correlation coefficient

(b) less accurate than rank correlation coefficient

(c) as accurate as the rank correlation coefficient

* The correlation coefficient (r) has no unit.

* The correlation coefficient is independent of origin as well as scale.

* When the Measurements of the Variables are Suspect e.g., in a remote village where measuring rods or weighing scales are not available, height and weight of people cannot be measured precisely but the people can be easily ranked in terms of height and weight.

* When Data is Qualitative It is difficult to quantify qualities such as fairness, honesty etc. Ranking may be a better alternative to quantification of qualities.

* When Data has Extreme Values Sometimes the correlation coefficient between two variables with extreme values may be quite different from the coefficient without the extreme values. Under these circumstances rank correlation provides a better alternative to simple correlation.

* Qualitative variables such as beauty, intelligence, honesty, etc.

* It is also difficult to measure subjective variables such as poverty, development, etc which are interpreted differently by different people.

* If r = 0 the two variables are uncorrelated. There is no linear relation between them. However, other types of relation may be there and hence the variables may not be independent.

* If r= 1 the correlation is perfectly positive. The relation between them is exact in the sense that if one increases, the other also increases in the same proportion and if one decreases, the other also decreases in the same proportion.

* If r = -1 the correlation is perfectly negative. The relation between them is exact in the sense that if one increases, the other decreases in the same proportion and if one decreases, the other increases in the same proportion.

* Rank correlation coefficient is generally lower or equal to Karl Pearson’s coefficient.

* Rank correlation coefficient is preferred to measure the correlation between qualitative variables as these variables cannot be measured precisely.

* The rank correlation coefficient uses ranks instead of the full set of observations that leads to some loss of information.

* If extreme values are present in the data, then the rank correlation coefficient is more precise and reliable.

As the value of r is zero, so there is no linear correlation between X and Y.

As the correlation coefficient between the two variables is + 1, so the two variables are perfectly positive correlated.

Last Updated on: Aug 23, 2022