# Correlation Analysis

**Topics:**Spearman's rank correlation coefficient, Correlation and dependence, Pearson product-moment correlation coefficient

**Pages:**13 (3446 words)

**Published:**November 7, 2011

The correlation analysis refers to the techniques used in measuring the closeness of the relationship between the variables. The degree of relationship between the variables under consideration is measured through the correlation analysis. And the measure of correlation called as correlation coefficient or correlation index summarizes in one figure the direction and degree of correlation. Thus correlation is a statistical device which helps us in analyzing the covariation of two or more variables.

The problem of analyzing the relation between different series should be broken down nto 3 steps: * Determining whether a relation exists and, if it does, measuring it * Testing whether it is significant

* Establishing the cause and effect relation, if any.

A real life example:

An extremely high and significant correlation between the increase in smoking and increase in lung cancer would not prove that smoking causes lung cancer. The proof of a cause and effect relation can be developed only by means of an exhaustive study of the operating elements themselves.

Correlation and causation:

Correlation analysis helps us in determining the degree of relationship between two or more variables, it does not tell anything about cause and effect relationship. The explanation of a significant degree of correlation may be any one, or a combination of the following reasins: * Correlation may be due to pure chance, especially ina small sample The following example shall illustrate the point:

income (rs) : 5000 6000 7000 8000 9000 weight (lb) : 120 140 160 180 200 the above data show a perfectly positive relationship between income and weight as the income is increasing the weight is also increasing and the rate of change between two variables is the same * Both the correlated variables may be influenced by one or more other variables * Both the variables may be mutually influencing each other so that neither can be designated as the cause and other the effect.

Types of correlation:

Correlation is described in several different ways. Three of the most important ways of classifying correlation are: i. Positive or negative

ii. Simple, partial and multiple

iii. Linear and non linear

Positive and negative correlation:

Whether correlation is positive or negative it would depend upon the direction of change of variables. * If both the variables are varying in the same direction then is known as positive correlation * If the variables are varying in the opposite directions then it is known as negative correlation.

Examples:

Positive correlation: negative correlation:

X 10 12 15 18 20 X 20 30 40 60 80 Y 15 20 22 25 37 Y 40 30 22 15 10

Simple, partial and multiple correlation:

* When only two variables are studied then it is a problem of simple correlation. * When three or more variables are studied then it is a problem of partial or multiple correlation * In multiple correlations three or more variables are studied simultaneously.

Linear and nonlinear correlation:

The distinction between linear and nonlinear correlation is based upon the constancy ratio of change between the variables. * If the amount of change in one variable tends to be a constant ratio to the amount of change is the other variable then correlation is said to be linear. * If the amount of change in one variable does not bear a constant ratio to the amount of change in the other variable then correlation is said to be nonlinear.

The following two diagrams illustrate the...

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