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## Kerala Plus One Economics Notes Chapter 17 Correlation

Correlation

The relationship between any two or more variables is referred to as correlation. Correlation studies and measures the intensity of relationships among variables.

Positive and Negative Correlation

When the values of two variables move in the same direction, the correlation is said to be positive; and when the values of two variables move in the opposite direction, the correlation is said to be negative. That is, if the value of one variable increases with an increase (and decreases with a decrease) of the value of the other variables, they are said to be in positive correlation. Likewise, if the value of one variable increases with a decrease (and decreases with an increase) of the value of the other variable, they are said to be in negative correlation.

Techniques of measuring correlation

Scatter Diagram: A scatter diagram is a useful technique for visually examining the form of relationship, without calculating any numerical value. In this technique, the values of the two variables are plotted as points on a graph paper. The cluster of points, so plotted, is referred to as a scatter diagram. From a scatter diagram, one can get a fairly good idea of the nature of the relationship. In a scatter diagram the degree of closeness of the scatter points and their overall direction enable us to examine the relationship. If all the points lie on a line, the correlation is perfect and is said to be unity. If the scatter points are widely dispersed around the line, the correlation is low. The correlation is said to be linear if the scatter points lie near a line or on a line.

Karl Pearson’s Coefficient of Correlation: This is also known as the product-moment correlation and simple correlation coefficient. It gives a precise numerical value of the degree of linear relationship between two variables X and Y. The linear relationship may be given by Y = a + bX.

This type of relationship may be described by a straight line. The intercept that the line makes on the Y-axis is given by a and the slope of the line is given by b. It gives the change in the value of Y for very small change in the value of X. On the other hand, if the relation cannot be represented by a straight line as in Y = X^{2} the value of the coefficient will be zero.

It clearly shows that zero correlation need not mean absence of any type of relation between the two variables.

Spearman’s Rank Correlation: Spearman’s rank correlation was developed by the British psychologist C.E. Spearman. It is used when the variables cannot be measured meaningfully as in the case of price, income, weight etc. Ranking may be more meaningful when the measurements of the variables are suspect. Consider the situation where we are required to calculate the correlation between height and weight of students in a remote village. Neither measuring rods nor weighing scales are available. The students can be easily ranked in terms of height and weight without using measuring rods and weighing scales.

Rank correlation coefficient and simple correlation coefficient have the same interpretation. Its formula has been derived from simple correlation coefficient where individual values have been replaced by ranks. These ranks are used for the calculation of correlation. This coefficient provides a measure of linear association between ranks assigned to these units, not their values. It is the Product Moment Correlation between the ranks.