**Correlation**

Correlation refers to the associations between variables. When an association exists between two variables, it means that the average value of one variable changes as there is a change in the value of the other variable

**Kinds of correlation:- **

- Positive and Negative correlation.
- Linear and non – linear correlation.
- Simple and multiple correlations.

**Positive correlation:** If two variables change in the same direction (i.e. if one increases the other also increases, or if one decreases, the other also decreases), then this is called a positive correlation. For example: Advertising and sales. Some other examples of series of positive correlation are:

(i) Heights and weights;

(ii) Household income and expenditure;

(iii) Price and supply of commodities;

(iv) Amount of rainfall and yield of crops.

**Negative correlation: –** If two variables change in the opposite direction (i.e. if one increases, the other decreases and vice versa), then the correlation is called a negative correlation. For example: T.V. registrations and cinema attendance.

**Linear Correlation: –** When two variables change in a constant proportion.

**Non- linear correlation: –** When two variables do not change in the same proportion.

**Simple correlation –** Relationship between two variables are studied.

**Multiple Correction –** Relationship between three or more than three variables are studied.

** Degrees of Correlation:**

**Perfect Correlation –**When values of both variables changes at a constant rate

**Types – **

**(a) Perfect positive correlation –** when values of both variables changes at a constant ratio in the same direction correlation coefficient value (r) is + 1

**(b) Perfect negative correlation –** When values of both the variables change at a constant ratio in opposite direction. Value of coefficient of correlation is -1

**Absence of correlation :**If two series of two variables exhibit no relations between them or change in one variable does not lead to a change in the other variable, then we can firmly say that there is no correlation or absurd correlation between the two variables. In such a case the coefficient of correlation is 0. 3. Limited degrees of correlation.

**Limited degree correlation :**If two variables are not perfectly correlated or there is a perfect absence of correlation, then we term the correlation as Limited correlation.

**Types –** a) High : r his between ± 0.7 & 0.999

- b) Moderate = r lies between ± 0.5 and + 0.699
- c) Low: r < ± 0.5

** Different methods of finding correlation **

- a) Karl Pearson’s coefficient method
- b) Rank method / Spearman’s coefficient method
- c) Scatter Diagram

**(A)Karl Pearson’s Method:-** It gives the precise numerical expression for the measure of correlation. It is denoted by ‘r’. The value of ‘r’ gives the magnitude of correlation and its sign denotes its direction.

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**Merits of Karl Pearson’s Method **

- Helps to find direction of correlation
- Most widely used method

** Demerits of Karl Pearson’s method **

- Based on large number of assumptions
- Affected by extreme values

**(B) Spearmans’s Rank Correlation Method:-** This method is based on the ranks of the items rather than on their actual values. The advantage of this method over the others in that it can be used even when the actual values of items are unknown. For example if you want to know the correlation between honesty and wisdom of the boys of your class, you can use this method by giving ranks to the boys. It can also be used to find the degree of agreements between the judgments of two examiners or two judges.

**Merits of Spearman’s Rank Correlation **

- Simple and easy to calculate
- Not affected by extreme values

** Demerits of Spearman’s Rank Correlation **

- Not Suitable for grouped data
- Not based on original values of observations.

**(C) Scatter Diagram** – Scatter Plots (also called scatter diagrams) are used to graphically investigate the possible relationship between two variables without calculating any numerical value. In this method, the values of the two variables are plotted on a graph paper. One is taken along the horizontal (X-axis) and the other along the vertical (Y-axis). By plotting the data, we get points (dots) on the graph which are generally scattered and hence the name ‘Scatter Plot’..

**Merits of Scatter Diagram **

- Most simplest method.
- Not affected by size of extreme values.

Demerits 1. Exact degree of correlation cannot be found.