# Correlation

Quantitative Results
Statistical Analysis

Correlation, as the name suggests, depicts a relationship between two or more variables under study. It is generally categorized into two types, namely Bivariate and Partial.

Bivariate is the one that shows an association between two variables. Partial is the one that shows the association between two variables while keeping control or adjusting the effect of one or more additional variables.

A Correlation is a degree of measure, which means that it can be negative, positive, or perfect. A positive Correlation is a type in which an increase changes the other variable. In other words, if there is an increase (or decrease) in one variable, then there is a simultaneous increase (decrease) in the other variable. A negative Correlation is a type where if there is a decrease (or increase) in one variable, then there is a simultaneous increase (or decrease) in the other variables.

A perfect Correlation is that type where a change in one variable affects an equivalent change in the other variable.

A British biometrician named Karl Pearson developed a formula to measure the degree of the Correlation, called the Correlation Coefficient. This is generally depicted as ‘r.’ In mathematical language, it is defined as the ratio between the covariance of the two variables and the product of the square root of their individual variances. The range generally lies between -1 to +1. If the value is ‘+1,’ then the variable is said to be positively correlated. If, on the other hand, the value of the Correlation Coefficient is ‘-1,’ then the variable is said to be negatively correlated.

The value of the Correlation Coefficient does not depend upon the change in origin and the change in the scale.

If the value of the Correlation Coefficient is zero, then the variables are said to be uncorrelated. Thus, the variables would be regarded as independent. If there is no Correlation in the variables, then the change in one variable will not affect the change in the other variable at all, and therefore the variables will be independent.

However, the researcher should note that the two independent variables are not in any Correlation if the covariance of the variables is zero. This, however, is not true in the opposite case. This means that if the covariance of the two variables is zero, then it does not necessarily mean that the two variables are independent.

There are certain assumptions that come along with the Correlation Coefficient:

It assumes that the variables under study should be linearly correlated.
It assumes that a cause and effect relationship exists between different forces operating on the items of the two variable series. Such forces assumed by the correlation coefficient must be common to both series.

For the cases where operating forces are entirely independent, then the value of the correlation coefficient must be zero. If the value is not zero, then in such cases, correlation is often termed as chance or spurious. For example, the correlation between the income of a person and the height of a person is a case of spurious correlation. Another example of spurious correlation is the correlation between the size of the shoe and the intelligence of a certain group of people.