If ranks can be assigned to pairs of observations for two variables X and Y, then the correlation between the ranks is called the rank correlation coefficient.
RANK CORRELATION
Spearman’s
rank correlation coefficient
If
ranks can be assigned to pairs of observations for two variables X and Y, then
the correlation between the ranks is called the rank correlation coefficient.
It is usually denoted by the symbol ρ
(rho). It is given by the formula
where
D =
difference between the corresponding ranks of X and Y
and N is the total number of pairs of observations of
X and Y.
Problem 5
Alpha
Recruiting Agency short listed 10 candidates for final selection. They were
examined in written and oral communication skills. They were ranked as follows:
Find out whether there is any correlation between
the written and oral communication skills of the short listed candidates. Solution: Take
X = Written Communication Skill and Y = Oral Communication Skill.Inference: From the value of r, it is
inferred that there is a high, positive rank correlation between the written
and oral communication skills of the short listed candidates. Problem 6The
following are the ranks obtained by 10 workers in abc company on the basis of
their length of service and efficiency.Find out whether there is any correlation between the
ranks obtained by the workers as per the two criteria.Inference: The rank
correlation coefficient is not high. Problem 7 (conversion of scores
into ranks)Calculate
the rank correlation to determine the relationship between equity shares and
preference shares given by the following data on their price. From the given data on share price, we have to find
out the ranks for equity shares and preference shares. Step 1. First,
consider the equity shares and arrange them in descending order of their price
as 1,2,…,8. We have the following ranks:Step 2. Next,
take the preference shares and arrange them in descending order of their price
as 1,2,…,8. We obtain the following ranks:Step 3. Calculation
of D2:Fit the given data with the correct rank. Take X =
Equity share and Y = Preference share. We have the following table:Inference: From the value of ρ, it is
inferred that the equity shares and preference shares under consideration are
negatively correlated. However, the absolute value of ρ is 0.29 which is not
even moderate. Problem 8 Three
managers evaluate the performance of 10 sales persons in an organization and
award ranks to them as follows:Determine which two managers have the nearest
approach in the evaluation of the performance of the sales persons.Inference: Comparing the 3 values of ρ, it
is inferred that Mangers I and ii have the nearest approach in the evaluation
of the performance of the sales persons.
Tags : Research Methodology - Correlation And Regression Analysis
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