Question

what value does a correlational analysis have in attempting to understand if two variables are causally related? Use citations and references.

Answer 1

often we come acrosssituations in which our focus is simultaniously on two or more variables & invariably, we observe that movements in one variable are accompanied by movements in other variable.For example, brother's age & sisters's age move together , scores on an I.Q test move with scores in college examinations.similarly, studies in income & expendicture on households or price & demand of commodities , exhibit accompaning movement of two variables .

The above statements are not enough to draw any conclusion.SO, we need a quantitative measure & a statistical form of the relationship between two variables .

Meaning of Correlation: If the change in one variable affects a change in the other variable, the variables are said to be correlated. correlation can be positive or negative.

Scatter Diagram: It is a diagrammatic representation of bivariate data. For bivariate distribution (); i=1,2,....,n, if the values of the variables X & Y are plotted along the x-axis & y-axis respectively in the plane. This dotted diagram is known as scatter diagram. If the points in the diagram are dense then we will get a very good correlation & if the points in the diagram are wide apart from each other then we will get a poor correlation.

KARL PEARSON'S COEFFICIENT OF CORRELATION: To measure the degree of linear relationship between two variables , Karl Pearson(1867-1936) developed a formula called Correlation Coefficient.It is denoted by r(X,Y) or

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

where = x bar , = y bar

The correlation coefficient lies between -1 & +1. If r = +1 , the correlation is perfect & positive and if r = -1 , correlation is perfect & negative. If r=0 , then there is no correlation .

Uses of correlation coefficient : 1 . The series of height & weight of individuals over a period of time

2. The amount of rainfall & the rate of agricultural production in a country . etc

In the above diagram all the different type of scatter diagrams are mentioned.