# SPEARMAN RANK CORRELATION COEFFICIENT

## About "Spearman rank correlation coefficient"

Spearman rank correlation coefficient :

When we need finding correlation between two qualitative characteristics, say, beauty and intelligence, we take recourse to using rank correlation coefficient.

Rank correlation can also be applied to find the level of agreement (or disagreement) between two judges so far as assessing a qualitative characteristic is concerned.

As compared to product moment correlation coefficient, rank correlation coefficient is easier to compute, it can also be advocated to get a first hand impression about the correlation between a pair of variables.

Spearman’s rank correlation coefficient is given by where rR denotes rank correlation coefficient and it lies between –1 and 1 inclusive of these two values.

dᵢ =  xᵢ - yᵢ  represents the difference in ranks for the i-th individual and n denotes the number of individuals.

In case u individuals receive the same rank, we describe it as a tied rank of length u. In case of a tied rank, the above given formula is changed to  ## Spearman rank correlation coefficient - Practice problems

Problem 1 :

Compute the coefficient of rank correlation between sales and advertisement expressed in thousands of dollars from the following data: Solution :

Let the rank given to sales be denoted by x and rank of  advertisement be denoted by y.

We note that since the highest sales as given in the data, is 95, it is to be given rank 1, the second highest sales 90 is to be given rank 2 and finally rank 8 goes to the lowest sales, namely 68.

We have given rank to the other variable advertisement in a similar manner. Since there are no ties, we can apply the formula given below. Computation of Rank correlation between Sales and Advertisement. Since n  =  8 and  ∑d²  =  4, apply the above formula, we get

r  =  1 - 6 d² / n(n² - 1)

r  =  1 - 6x4 / 8(8² - 1)

r  =  1 - 0.0476

r  =  0.95

The high positive value of the rank correlation coefficient indicates that there is a very good amount of agreement between sales and advertisement.

Problem 2 :

Compute the coefficient of rank correlation between Eco. marks and statistics marks as given below : Solution :

This is a case of tied ranks as more than one student share the same mark both for Economics and Statistics.

For Eco. the student receiving 80 marks gets rank 1 one getting 62 marks receives rank 2, the student with 60 receives rank 3, student with 56 marks gets rank 4 and since there are two students, each getting 50 marks, each would be receiving a common rank, the average of the next two ranks 5 and 6 i.e. (5+6) / 2  =  5.50 and lastly the last rank..

7 goes to the student getting the lowest Eco marks.

In a similar manner, we award ranks to the students with stats marks.

Computation of Rank Correlation Between Eco Marks and Stats Marks with Tied Marks For Economics mark there is one tie of length 2 and for statistics mark, there are two ties of lengths 2 and 3 respectively. After having gone through the stuff given above, we hope that the students would have understood "Spearman rank correlation coefficient".

Apart from the stuff given above, if you want to know more about "Spearman rank correlation coefficient", please click here.

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments... WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6