Short Questions with Answers: Correlation - 2

Q.16. What is the nature of correlation if the value of r is -1?
Ans. When r = -1, there is a perfect negative (inverse) correlation between the two variables. This means all observations lie exactly on a straight line with a negative slope, so an increase in one variable corresponds to a proportional decrease in the other.
Q.17. What is the value of r if the two variables are not related?
Ans. When the two variables have no linear relation, r = 0. This indicates no linear correlation between them; however, a non-linear relationship may still exist even when r = 0.
Q.18. State the merits of Karl Pearson's correlation coefficient.
Ans. The merits of Karl Pearson's correlation coefficient are:
(i) It is a real and precise measure of linear association because it is based on arithmetic mean and standard deviation, giving a numerical value for the strength of association.
(ii) It shows both the direction (positive or negative) and the degree (magnitude) of linear correlation between two continuous variables.
(iii) It is a unit-free measure, allowing comparison of correlation values across different data sets and units.
(iv) It is widely used and well understood, making interpretation and communication of results straightforward.
Q.19. What are the demerits of Karl Pearson's correlation coefficient.
Ans. The demerits of Karl Pearson's correlation coefficient are:
(i) The value of the coefficient is unduly affected by extreme values (outliers), which can distort the measure of association.
(ii) It assumes a linear relationship between variables; if the true relation is non-linear, the coefficient may be misleading.
(iii) There is a risk of misinterpretation - correlation does not imply causation, and results require careful analysis in context.
(iv) Calculation can be time-consuming for large data sets unless aided by calculators or software, and care is needed in computation.
Q.20. How does Spearman's rank correlation measure relation between variables?
Ans. Spearman's rank correlation measures the strength and direction of association by using the ranks of observations rather than their original values. It assesses how well the relationship between two variables can be described by a monotonic function, and is especially useful when data are ordinal or when assumptions required for Pearson's coefficient are not met.
Q.21. Name some qualitative variables.
Ans.Qualitative variables are attributes or qualities that cannot be measured numerically. Examples include beauty, wisdom, bravery, dedication and honesty.
Q.22. Who developed Spearman's rank correlation?
Ans. Spearman's rank correlation was developed by the British psychologist Charles E. (C. E.) Spearman.
Q.23. When is rank correlation preferred to Pearsonian coefficient?
Ans. Rank correlation is preferred to the Pearsonian coefficient when the data contain extreme values (outliers), when the variables are ordinal, or when the assumptions of Pearson's coefficient (such as linearity and interval measurement) are not satisfied.
Q.24. What are the merits of rank correlation coefficient?
Ans. The merits of rank correlation coefficient are:
(i) It is easier to calculate and understand since it uses ranks rather than raw measured values.
(ii) It is appropriate for qualitative or irregular data and for situations where measurement scales are ordinal rather than interval or ratio.
(iii) It can be used even when the actual numerical data are not available; correlation can be found simply from the ranks assigned to values.
Q.25. Write the demerits of rank correlation coefficient.
Ans. The demerits of rank correlation coefficient are:
(i) The method is less precise than measures based on actual values, so it may not reflect small differences accurately.
(ii) It becomes impractical for a very large number of items, as assigning and handling ranks can be cumbersome.
(iii) It is applicable mainly to individual (paired) series and cannot be directly used for grouped frequency distributions without special adjustments.