Types of Correlation

TYPES OF CORRELATION

1. Simple (Linear) correlation (2 variables only) : The correlation between the given two variables. It is denoted by r_xy

2. Partial correlation (more than 2 variables): The correlation between any two variables while removing the effect of other variables. It is denoted by r_{xy.z …}

3. Multiple correlation (more than 2 variables) : The correlation between a group of variables and a variable which is not included in that group. It is denoted by R_y.(xz…)

In this chapter, we study simple correlation only, multiple correlation and partial correlation involving three or more variables will be studied in higher classes .

Simple correlation or Linear correlation

Here, we are dealing with data involving two related variables and generally we assign a symbol ‘ x ’ to scores of one variable and symbol ‘y ’ to scores of the other variable. There are five types in simple correlation. They are

1) Positive correlation (Direct correlation)

2) Negative correlation (Inverse correlation)

3) Uncorrelated

4) Perfect positive correlation

5) Perfect negative correlation

1) Positive correlation: (Direct correlation)

The variables are said to be positively correlated if larger values of x are associated with larger values of y and smaller values of x are associated with smaller values of y. In other words, if both the variables are varying in the same direction then the correlation is said to be positive. 

In other words, if one variable increases, the other variable (on an average) also increases or if one variable decreases, the other (on an average)variable also decreases.

For example,

i) Income and savings

ii) Marks in Mathematics and Marks in Statistics. (i.e.,Direct relationship pattern exists).

2) Negative correlation: (Inverse correlation)

The variables are said to be negatively correlated if smaller values of x are associated with larger values of y or larger values x are associated with smaller values of y. That is the variables varying in the opposite directions is said to be negatively correlated. In other words, if one variable increases the other variable decreases and vice versa.

For example,

i) Price and demand

ii) Unemployment and purchasing power

3) Uncorrelated:

The variables are said to be uncorrelated if smaller values of x are associated with smaller or larger values of y and larger values of x are associated with larger or smaller values of y. If the two variables do not associate linearly, they are said to be uncorrelated. Here r = 0.

Important note: Uncorrelated does not imply independence. This means “do not interpret as the two variables are independent instead interpret as there is no specific linear pattern exists but there may be non linear relationship”.

4) Perfect Positive Correlation

If the values of x and y increase or decrease proportionately then they are said to have perfect positive correlation.

5) Perfect Negative Correlation

If x increases and y decreases proportionately or if x decreases and y increases proportionately, then they are said to have perfect negative correlation.

Correlation Analysis

The purpose of correlation analysis is to find the existence of linear relationship between the variables. However, the method of calculating correlation coefficient depends on the types of measurement scale, namely, ratio scale or ordinal scale or nominal scale.

Statistical tool selection