Correlation
We usually come across situations where it is important to identify the relationship between two variables. This relationship, or association, is also called a correlation. So, correlation is nothing but an association between the variables. In other words, correlation occurs when the change in one variable affects the change in another variable.
If an increase (or a decrease) in one variable simultaneously increases (or decreases) the other variable, then the correlation is said to be positive or direct. If, on the other hand, the decrease (or increase) in one variable increases (or decreases) the other variable, then the correlation is said to be negative or diverse. Correlation is said to be perfect only if a corresponding change in one variable simultaneously causes proportional change in the other variable.
A British biometrician named Karl Pearson invented a formula to measure the intensity or the degree of correlation between two variables. This formula has been named after him as Karl Pearson Correlation Coefficient. Karl Pearson Correlation Coefficient is a numerical measure of linear relationship between data. Mathematically, Karl Pearson Correlation Coefficient can be defined as the ratio between the covariance of two variables, say X and Y, and the product of the square root of their respective variances.
Numerically, the value of the correlation coefficient should not exceed unity. If the value of the correlation coefficient is ‘+1,’ then the variables are said to be in positive correlation. On the other hand, if the value of correlation coefficient is ‘-1,’ then the variables are said to be in negative correlation.
There are two points which one should remember while dealing with correlation. The first is that the value of the correlation coefficient is independent of the change in origin and scale. Secondly, the two independent variables are said to not be in correlation if the value of the covariance of the variable is zero. However, the converse of this property is not true. That is, the two variables that are not in correlation are not necessarily independent.
The following assumptions underlie correlation coefficient:
Correlation coefficient assumes that the two variables under study should have a linear correlation.
Correlation coefficient 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, the value of the correlation coefficient must be zero. If the value of the correlation coefficient is not zero, then such correlations are often termed as chance correlation or spurious correlation.
For example, the correlation between the income of a person and the height of a person is a spurious correlation. Additionally, the correlation between people’s shoe size and their intelligence is a spurious correlation.
A pearsonian coefficient of correlation between the ranks of the two variables, say x and y, is called rank correlation coefficient between that group of variables.
Correlation is a kind of statistical technique that can explain whether or not a pair of variables is related. Correlation also explains how strongly the pair of variables is related.
Correlation usually works for quantifiable data. The quantifiable data should be meaningful while performing the statistical technique of correlation. By meaningful, we mean that while conducting correlation, the data should not be purely categorical data.
Most researchers do not generally perform correlation with rating scales, but if the researcher performs correlation with rating scales, then the researcher should perform correlation with rating scales very carefully.
