Theory of Correlation and Types of Correlation

            Correlation is a statistical terminology which connotes the movement of one variable with respect to another one.  In short, it brings out the relationship of one variable with reference to another and the terms by which one variable is allied or affiliated to another variable. 

If there is variation in one variable, there is a corresponding disparity in another such that it is either in the negative or positive direction, meaning that both vary together, for example, with the increase in magnitude of one variable, another also exhibits a rise or they may vary in opposition, with one variable decreasing in value with corresponding increase in the other variable.

There are three types of correlation based on the increasing together, analogous increase and decrease and no change at all.  The types of correlation are positive, negative and no correlation. 

A positive correlation is one in which both the variables are equivalent to one another and change corresponding to the other in the same direction, exhibiting either increment or decrement  in values.  For example, when the age of children increase, their heights also increase, thus showing a case of positive correlation.

A negative correlation showcases a negative trend, in which, with the increase in one variable, the other decreases, thus manifesting a negative trend.  For example, with the increase in the price of a commodity, the demand decreases, with few people capable of affording to buy the product. 

With the concept of no correlation between two variables, the increase or decrease of one will have no influence and will not affect any change in the other variable.  For example, the rise in intelligence of people is not related to the number of people watching television as television viewing is not related to intelligence among the viewers. 

If the strength between two variables and their orientation, which means the direction of their movement, whether in the same direction or opposite direction are measured, it involves the calculation of correlation co-efficient.  This is denoted by the alphabet 'r' and signifies how the relationship between two variables varies. 

There are also other forms of correlations available namely, partial correlation, in which the interconnection between two variables is indicated and studied by keeping all other variables constant.  For example, the study on the effect of obesity on Diabetes Mellitus by keeping other factors like smoking, heart ailments and blood glucose as constant factors. 

Linear Correlation is one in which as one value or the variable changes, the other variable changes in a particular ratio and when plotted will provide a linear graph.  For example, income and expenditure pattern in families.

Zero order Correlation corresponds to the correlation co-efficient assuming zero as the relationship between two variables. If it is a -1, then it is a perfect negative correlation, while if it is +1, it denotes a perfect positive correlation between the two variables. 

Problems Encountered in Solution to Correlation and Types of Correlation problems

Correlation and Types of Correlation problems are most of the time tricky to solve by students as they have to incur wide knowledge on the topic before embarking on the task of solving problems.  Not only they should be aware of the types of correlation, and the various formulae in solving the problems, but also familiarize themselves with the ways in which each variable is negatively or positively correlated or not correlated at all from the given set of data.

It might be complicated to know about the correlation co-efficient and its influence on the magnitude and direction of movement of two variables, with values ranging from -1 to +1 determined by the calculations made and the solutions arrived at.

The scrupulous manner in which the students make the task of solving problems efficiently is mainly achieved through rigorous practice and following numerous correlations involving several variables. 

The types of correlation should be made decipherable through intensive, methodical and painstaking efforts by students in order to solve the problems pertaining to correlation.  For example, for imbibing knowledge on Zero Order Correlation, students should know the significance of correlation coefficient and how practically a zero correlation coefficient leads to the Zero Order Correlation. 

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