Correlation :Bivariate data, meaning and types of correlation.

 

Correlation

Bivariate Data ©

A set of observation on a single character is referred as univariate data. A set of observations on two characters of every unit in a sample group is known as bivariate data. Examples of bivariate data are: (i) Height and weight of students (ii) the monthly income & expenditure of several families etc. In the above examples the characters are of quantitative nature, known as variables and will be denoted by X and Y. Thus the bivariate data will consist of n pairs of observations (Xi, Yi), i=1, 2, 3,…. of variables X and Y. When the bivariate data are considerably large, they may be grouped by using a two-way frequency table known as bivariate frequency distribution.

Correlation

If bivariate data are given on two variable X and Y then the correlation means the study of the inter relationship between two variables X and Y.  In general, we say that two variables are correlated when the change (an increase or decrease) in the values of one variable cause the change in the corresponding values of other variable. The mutual relationship between such variables is called correlation.

Typical examples for correlation analysis will be the relation between height of father and height of son, between age of husband and age of wife, between score in Statistics and score in Economics etc. But if we measure the amount of rain fall (X) in Mumbai and number of babies born in New Delhi (Y), in this case the study of inter-relationship would be meaningless. Thus in correlation study we consider only those two variables which has cause and effect relationship. The relationship is considered to be the linear type.

Types of Correlation

1. Positive Correlation (Direct correlation)

If an increase (or decrease) in the value of one variable is followed by increase (or decrease) in the value of other variable then we say that there is a positive correlation between two variables. Thus positively correlated variables change in the same direction. For example-income and expenditure, height and weight of group of people are positively correlated variables.

 

2. Negative Correlation (inverse correlation)

If an increase (or decrease) in the value of one variable is accompanied by decrease (or increase) in the value of other variable then we say that, there is a negative correlation between two variables. That is negatively correlated variables change in the opposite direction. For example, Supply and Price of the commodity, Volume and pressure of a perfects gas, Criminal attitude and education are negatively correlated variables.

3. Perfect Positive Correlation

If the change in the values of the variables is in same direction and is proportional then the correlation between these two variables is said to be perfect positive correlation. For example, the circumference of a circle increases in a definite ratio with an increase in the length of its diameter.

4. Perfect Negative Correlation

If the change in the values of the variables is in opposite direction and is proportional then the correlation between these two variables is said to be perfect negative correlation. For example, from Boyle's law of gases the volume (V) varies inversely with the pressure (P) i.e. PV = constant. The correlation between volume & pressure is perfect negative correlation.

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