Correlation Analysis : Meaning-Definition-Types- Methods

 

-Watch The Video Given Above For Detailed Explanation -

Meaning -

If two series vary in such a way, that Fluctuation in one variable is accompanied by the fluctuation in other variable, these variables are said to be correlated.

Like -

  • Rise in price of a commodity reduces its demand and vice – versa.
  • Relationship between rainfall and production.

# The term correlation refers to the study of relationship between two or more variables.

Correlation Definitions -

# If two or more quantities vary, so that movement in one tend to be accompanied by corresponding movements in other then they are said to be correlated.
- L.R.Connor

# Correlation means that between two series or groups of data there exist some casual connection.
- W.I King

# Correlation analysis  attempts to determine the degree of relationship between variables.
- Cowden

Types :-
  • Positive and Negative Correlation
  • Linear and Non- linear Correlation
  • Simple Correlation
  • Partial Correlation
  • Multiple Correlation
1. Positive and Negative Correlation
If changes in two connected series is in the same direction, i.e. increase in one variable is associated with increase in other variable, the correlation is said to be positive (+).
For e.g.- Increase In Fathers age , increase in Son’s age. 
&
If two related series changes in the opposite direction i.e. increase in one variable is associated with the corresponding decrease in other variable, the relation is said to be negative (-).
For e.g.- rise in price of a commodity reduces its demand and vice – versa.

2. Linear and Non- linear Correlation
If the amount of change in one variable tends to bear constant ratio of change in other variable, the correlation is said to be linear. We get a straight line if the variables of these series are marked on graph paper.
For e.g.- Increase In rainfall will increase in production.
&
Correlation would be called non-linear or curve-linear, if the amount of change in one variable does not bear constant ratio to the amount of change in other variable. We get a straight line if the variables of these series are marked on graph paper.
For e.g.- If we Double the amount of rainfall the production would not necessarily be doubled.

3. Simple Correlation
When only two variables are studied, it is called simple correlation.
For e.g. If we study the effect of rain on potato production per acre.

4. Partial Correlation
In partial correlation we recognize more than two variables, but consider only two variable to be influencing each other, the effect of other variable being kept constant.
For e.g. If we study the effect of rain, soil, temperature on potato production but consider only the effect of rain and temperature.

5. Multiple Correlation
If the common effect of two or more independent variables on one dependent data series is studied, it is called multiple correlations.
For e.g. If we study the effect of rain, soil, temperature on potato production per acre.

METHODS :-
  • Scatter Diagram
  • Karl Pearson Coefficient of correlation
  • Spearman's Rank Correlation
METHOD I -  Scatter Diagram
A scatter plot, scatter graph, and correlation chart are other names for a scatter diagram. We draw this graph with two variables. The first variable is independent and the second variable depends on the first. other charts use lines or bars to show data, while a scatter diagram uses dots. This may be confusing, but it is often easier to understand than lines and bars.

Types :-

  • Scatter Diagram with Perfect Correlation
  • Scatter Diagram with Moderate Correlation
  • Scatter Diagram with No Correlation
1. Scatter Diagram with Perfect Correlation

This is also known as “Scatter Diagram with a High Degree of Correlation”.In this diagram, data points are close to each other and you can draw a line by following their pattern. In this case, you say that these variables are closely related.


2. Scatter Diagram with Moderate Correlation

Here, the data points are a little closer and you can see that some kind of relationship exists between these variables. This is also known as “Scatter Diagram with a Low Degree of Correlation.

3. Scatter Diagram with No Correlation

Here, the data point spread is so random that you cannot draw a line through them.Therefore, you can say that these variables have no correlation.This is also known as “Scatter Diagram with Zero Degree of Correlation”.



METHOD II - Karl Pearson Coefficient of correlation

It is an assumption of Karl Pearson’s coefficient of correlation that linear relations exist in both the series. This method is considered as the best method because it provides the knowledge of directions and change in data i.e. positive or negative and also shows the degree of correlation which should always lie between +1 and -1.

Formula : 

   OR

Degree of Correlation

The interpretation of co-efficient of correlation is based on the degree of correlation.

The coefficient may be in the following degrees:-

  1. Perfect Correlation
  2. Absence of Correlation or No Correlation
  3. Limited degree of Correlation
1.  Perfect Correlation

  • Perfect positive correlation (r) = +1
  • Perfect negative correlation (r) = -1

2. Absence of Correlation or No Correlation

r = 0

3. Limited degree of Correlation

  • Low degree of positive or negative Correlation r = 0 to + 0.25
  • Moderate degree of positive or negative Correlation r = + 0.25 to 0.75
  • High degree of positive or negative Correlation r = + 0.75 to 1

Standard Error and Probable Error

Formulas:-

            &  

Here -
S.E = Standard Error
P.E = Probable Error
   r  = Coefficient of Correlation
  N = No. of items 

Interpretation of Coefficient of Correlation

  • If the coefficient of correlation is more than 6 times of Probable Error (r > 6 P.E), it is significant.
  • If r is less than P.E (r < P.E), it is insignificant.

NUMERICAL :

Watch the video given Above to know - How to solve a numerical with Karl Pearson’s Coefficient of Correlation (r) Method...

METHOD III - Spearman's Rank Correlation

If we want to find correlation between Two Qualitative characters such as colour, fragnence, intelligence, etc. then we use Searman’s Rank Correlation Method.

Charles Edward Spearman (1904), developed a formula which helps in obtaining the correlation coefficient between ranks of ‘n’ individuals in two characteristics.

Formula:-

              OR 

Numerical

Watch the video given Above to know - How to solve a numerical with Spearman's Rank Correlation – p(Rho) Method...

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