a). Coefficient of correlation is between -1 and +1 . How would you express it arithmetically?
b). define Karl pearson's method of calculating coefficient of correlation and spearman's rank difference method.
c). What are limits of correlation coefficient r ?
d). If r = +1 in one situation and r = -1 in the other, what kind of relationship exist between the variables X and Y ?
e). What are the limits of coefficient of rank correlation ?
f). If thje values of X and Y have been ranked and we compute correaltion between ranks of Xand Y, will this correlation be equal to the value of coefficient of rank correlation ?
b. Karl Pearson's correlation coefficient acts as an important tool to measure the linear quantitative relationship between two variables X and Y. It only measures the degree and intensity of the relationship between the two variables and not the cause and effect relationship between them. This is most commonly known as Pearsonian correlation of coefficient and is represented as 'r'. It is ascertained by dividing the sum of the products of deviations of different items of X and Y series from their respective means by product of the number of observations and standard deviations of X and Y series. Rank correlation coefficient is used to measure the correlation between the two qualitative variables which cannot be expressed quantitatively. The attributes of the qualitative variables such as, beauty, honesty, etc. are assigned different ranks (that can be expressed quantitatively) on the basis of preferences.
c. , The limits of Karl Pearson's coefficient is between -1 to +1.
d. When r = -1, it implies that there exists negative linear correlation between the two variables. On the other hand, when r = +1, it implies that there exists positive linear correlation between the two variables.
e., the limits of Rank Correlation coefficient is between -1 to +1.
f. No, the two correlation coefficients would not be same. Rank correlation coefficient is generally lower or equal to Karl Pearson’s coefficient. This is because the rank correlation coefficient uses ranks instead of the full set of observations that leads to some loss of information. If the precisely measured data are available, then both the coefficients will be identical.