Page 173 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 11: Rank Correlation Method
Dilfraz Singh, Lovely Professional University

Unit 11: Rank Correlation Method Notes

CONTENTS
Objectives
Introduction
11.1 Rank Correlation Method
11.2 Merits and Limitations of the Rank Method
11.3 Summary
11.4 Key-Words
11.5 Review Questions
11.6 Further Readings

Objectives

After reading this unit students will be able to:
• Explain Rank Correlation Method.
• Know the Merits and Limitations of Rank Method.
Introduction

When a group of individuals are arranged according to their degree of possession of a character, they
are said to be ranked. The ordinal number of an individual in the arrangement is called its rank the
arrangement as a whole is called a ranking.
When there are two series of ranks for the same set of individuals, corresponding to two different
characters or two judges assigning ranks for the same character, one may be interested to know if the
two series are associated. The association between two series of ranks for the same set of individuals
is called rank correlation.
11.1 Rank Correlation Method

This method of finding out covariability or the lack of it between two variables was developed by the
British psychologist Charles Edward Spearman in 1904. This measure is especially useful when
quantitative measures for certain factors (such as in the evaluation of leadership ability or the judgment
of female beauty) cannot be fixed, but the individuals in the group can be arranged in order thereby
obtaining for each individual a number indicating his (her) rank in the group. In any event, the rank
correlation coefficient is applied to a set of ordinal rank numbers, with 1 for the individual ranked
first in quantity, or quality, and so on, to n for the individual ranked last in a group of n individuals
(or n pairs of individuals). Spearman’s rank correlation coefficient is defined as:

∑
6D 2
R = −1
N 3 − N
where R denotes rank coefficient of correlation and D refers to the difference of ranks between paired
items in two series.

The association between two series of ranks for the same set of individuals is called
rank correlation.

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