Rank correlation, Applied Statistics

Assignment Help:

Rank Correlation

Sometimes the characteristics whose possible correlation is being investigated, cannot be measured but individuals can only be ranked on the basis of the characteristics to be measured. We then have two sets of ranks available for working out the correlation coefficient. Sometimes the data on one variable may be in the form of ranks while the data on the other variable are in the form of measurements which can be converted into ranks.

Thus, when both the underlying variables are ordinal or when the data are available in the ordinal form irrespective of the type of variable, we use the rank correlation coefficient to find out the extent of relationship between the two variables.

This rank correlation coefficient is also known as Spearman's rank correlation coefficient. Rank correlation is a non-parametric technique for measuring strength of relationship between paired observations of two variables when the data are in a ranked form.

Rank Correlation measures the degree of agreement between the two sets of ranks.

Rank Correlation Coefficient R is

  1153_rank correlation.png

where,   n   =      Number of individuals ranked

             Di   =       Difference in the ranks of the ith individual

             i     =       1, 2, ........ n

 

             Di   =       Difference in the ranks of the ith individual

             i     =       1, 2, ........ n

Example

The ranks of 8 students are given according to their marks in English and History.

Student No.

1

2

3

4

5

6

7

8

English

2

8

1

7

6

4

5

3

History

7

3

2

6

5

8

4

1                                          

 

We want to know whether or not students who are good in English are also good in History. For this the calculations are:

1531_rank correlation1.png

 

Here

1509_rank correlation2.png

= 74 and n = 8

 

R

  706_rank correlation3.png
  = 0.119  

The correlation between the ranks is seen to be low.


Related Discussions:- Rank correlation

Mode, Mode The mode is the value which occurs most frequ...

Mode The mode is the value which occurs most frequently in a set of observations on the point of maximum frequency and around which other items of the set cluste

Theoretical yield and actual yield, Write down the symbols and unit for the...

Write down the symbols and unit for the following: mass, molar mass, molar and molarity Write down the relationship between mass and molar mass and show that the units match.

Explain graph theory, For each of the following scenarios, explain how grap...

For each of the following scenarios, explain how graph theory could be used to model the problem described and what a solution to the problem corresponds to in your graph model.

Caveat, Caveat We must be careful when interpreting the meaning of asso...

Caveat We must be careful when interpreting the meaning of association. Although two variables may be associated, this association does not imply that variation in the independ

Find the relation between two substance, Find the Relation between two subs...

Find the Relation between two substance: The following table shows the results obtained in experiments aimed to determine how solubility of water in benzene depends on tempera

STATISTICS, Ask 3. Precision Manufacturing has a government contract to pro...

Ask 3. Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircraft. Each rod is required to be 20 millimeters in diameter. Each

Semiaverages and least square, how can we graph a trend line by semiaverage...

how can we graph a trend line by semiaverages and least square method?

Kurtosis and skew, how to interpret results, a good explanation to help me ...

how to interpret results, a good explanation to help me understand.

Calculate the one year interest rate, A.The coupon rate of Erie-Chicago Rai...

A.The coupon rate of Erie-Chicago Rail is 7%. The interest rate of Florida municipal bond with equal risk is 6%.  At what tax rate the two bonds are as good as each other B.Supp

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd