Correlation - Mrs. Salini Viswom

CORRELATION – ITS INTERPRETATION AND IMPORTANCE

INTRODUCTION

.

In the foregoing units we have discussed those statistical measures that we use for a single variable i.e. the distributions relating to one quantitative variable. Now we shall study the problem of describing the degree of simultaneous variation of two variables. The data in which we secure measures of one variable for each individual is called aunivariate distribution. If we have pairs of measures on.two variables of each individual, the joint presentation of the two sets of scores is called a bivatiate distribution. We come across a number of situations involving the study of two or more variables. For example, consider the scores of five students in mathematics and physics as under :

Students

1 2 3 4 5

Scores in Maths (X) 40 !7 29 36 25

Scores in Physics (Y) 38 16 30 32 24

Here each student has values on two variables X and Y i.e. the scores in Mathematics and

Physics respectively; hence the distribution is called bivariate distribution.

Similarly,' the distr~butioninvolving more than two variables are called multivariate distributions. In the present unit we will deal with bivariate distribution;. In a bivariate distribution the pair of scores made by the same set of individuals on two variables are given. 

Statistical Techniques of Analysis

THE CONCEPT OF CORRELATION

To illustrate what we mean by a relationship between two variables, let us use the example cited in \6.1 i.e. the scores of 5 students in mathematics and physics. What pattern do youfind in the data ?You may notice that in general those students who score well in mathematics also get high scores in physics. Those who are average in mathematics, get just average scores in physics and those who are poor in mathematics get low scores in physics. In short, in this case there is a tendency for students to score at par on both variables. Performance on the two variables is related; in other words the two variables are related, hence co-vary. If the change in one variable appears to be accompanied by a change in the other variable, the two tariables are said to be co-related and this inter-dependence is called correlation.

CO-EFFICIENT OF CORRELATION

To measure the degree of association or relationship between two variables quantitatively, an index of relationship is used and is termed as co-efficient of correlation.

Co-efficient of correlation is a single number that tells us to what extent the two variables are related and to what extent the variations in one variable changes with the variations in the other.

Symbol ~f co-efficient of correlation

The co-efficient of correlation is always symbolized either by r or p (Rho). The notion 'r' is known as product moment correlation co-efficient or Karl Pearson's Coefficient of Correlation.  The symbol 'P' (Rho) is known as Rank Difference Correlation Coefficient or Spearman's Rank Correlation Coefficient.

 

MAXIMUM RANGE OF VALUES OF CO-EFFICIENT

OF CORRELATION

The measurement of correlation between two variables results in a maximum value that ranges from -1 to + I , through zero. The k 1 values denote perfect coefficient of correlation. 

TYPES OF CORRELATION

In a bivariate distribution, the correlation may be :

1. Positive, Negative or Zero; and

2. Linear or Curvilinear (Non-Linear)

16.6.1 Positive, Negative and Zero Correlation

When the increase in one variable (X) is followed by a c~rresponding

increase in the other variable (Y); the correlation is said to be positive correlation. The positive correlations range from 0 to + l ; the upper limit i.e. +1 is the perfect positive co-efficient of correlation. The perfect positive correlation specifies that, for every unit increase in one variable, there is proportional increase in the other. For example "Heat" and "Temperature" have a perfect

positive correlation. If, on th.e other hand, the increase in one variable (X) results in a corresponding decrease in the other variable (Y), the correlation is said to be negative correlation. The negative correlation ranges from 0 to -1; the lower limit giving the perfect negative correlation. The perfect negative correlation indicates that for every unit increase in one variable, there is proportional unit decrease in the other. . Zero correlation means no relationship between the two variables X and Y;i.e. the change inone variable (X) is not associated with the change in the other variable (Y). For example, body weight and intelligence, shoe size and monthly salary; etc. The zero correlation is-the mid-point of the range -1 to +l.