Correlation Significance

The study of the correlation is of immense use in the practical life because of the following reasons:

1. Most of the variables represent some kind of relationship. For e.g., there is relationship between income and expenditure, price and supply, etc. With the help of correlation analysis we can evaluate in one figure the degree of relationship existing between the variables.

2. Once we know that two variables are closely related, we can estimate the value of one variable given by the value of another. This is known with the help of the regression analysis.

So far we have studied problems relating to only one variable, in practice we come across a large number of problems including the use of two or more than two variables. If two quantities vary in such a way that the movements in one are accompanied by the movements in the other, there quantities are correlated, for e.g., there exists some relationship between age of wife and age of husband,  price of commodity and amount demanded, Increase in rainfall up to a point and number of cinema goers, etc. the degree of relationship between variables under consideration is evaluated  through correlation analysis. The measure of correlation is known as the correlation coefficient. The correlation index summarizes in one figure i.e. the degree and direction of correlation. The correlation analysis refers to the methods used in measuring the closeness of the relationship between the variables.

The problem of analyzing the relation between different series should be split into three steps:

1. To determine whether a relation exists and, if it does measuring it.

2. Testing whether it is significant or not.

3. Establishing the cause & affect relation, if any.

Here only the first aspect will be discussed, for the second aspect a reference may be made on the tests of Significance. The third aspect is the analysis that of establishing the cause-effect relation, is difficult to be treated statistically. An extremely high and significant correlation between the increase in smoking & increase in lung cancer would not prove that smoking causes lung cancer. The proof of cause & effect relation can be developed only by means of an exhaustive study of the operative elements themselves.

It must be noted that the detection and analysis of correlation (i.e. co variation) between the two statistical variables requires relationship of some sort which associates the observation in pairs, one of each pair being a value of each of the two variables. In normal, the pairing relationship may be of almost any nature, like observations at the time or place or over a period of time or different places.

The computation concerning the degree of closeness is totally based on the regression equation. However it is possible to perform the correlation analysis without actually having a regression equation.

In business, the correlation analysis enables the executive to estimate sales, costs, prices and other variables on the basis of some other series with which these sales, costs or prices may be functionally related. Some of the guesswork can be eliminated from decisions when the relationship between a variable to be estimated and the one or more other variables on which it depends are close and reasonably invariant.

However, it must be noted that the coefficient of correlation is one of the most widely used and also one of the most widely abused statistical measure. It is abused in the sense that one sometime overlooks the fact that the correlation measures are nothing but the strength of linear relationship and that it does not necessarily imply a cause effect relationship.

The Progressive development in the methods of science and philosophy has been characterized by increase in the knowledge of relationship or correlations. In nature one also finds multiplicity of the interrelated forces.

The effect of correlation is to decrease the range of uncertainty. The prediction based on the correlation analysis is to be more valuable and near to reality.