Correlation: Correlation COMPILED BY Arpita somani Shruti gupta Kriti bhargava Tanya gupta
INTRODUCTION OF CORRELATION: INTRODUCTION OF CORRELATION Correlation is the relationship that exists between two or more variables. If variables are related in such a way that change in one creates a corresponding change in the other then the variable are said to be correlated. When the relationship is of a quantitative nature, the appropriate statistical tool for discovering and measuring the relationship and expressing it in a brief formula is known as correlation.
Example: Example Correlation is a measure of association between two numerical variables. Example (positive correlation) Typically, in the summer as the temperature increases people are thirstier.
What is the need of correlation ?: What is the need of correlation ? Correlation help in study of economic theory and business studies, it help in establishing relationship between variable like price and quantity demanded, advertising and sales promotion measures. Correlation analysis helps in deriving precisely the degree and direction of such relation. The effect of correlation is to reduce the range of uncertainty of our prediction. The prediction based on correlation analysis will be more reliable and near to reality. The measure of coefficient of correlation is relative measure of change.
On the basis of Direction : On the basis of Direction Positive correlation: if both the variables vary in same direction, correlation is said to be positive correlation .if one variable increase, the other also increases or, if one variable decreases, the other variable is said to be a positive correlation. Negative correlation: if both the variable vary in opposite direction, the correlation is said to be negative. In other word if one variable increases, but other variable decreases or, if one variable decreases but the other variables increases, than correlation between two variables is said to be negative correlation.
Methods of studying correlation: Methods of studying correlation
KARL PEARSON’S COEFFICIENT OF CORRELATION: KARL PEARSON’S COEFFICIENT OF CORRELATION Karl Pearson’s method popularly known as Pearsonian Coefficient of Correlation. It is denoted by symbol ‘r’. Formula: In case of Actual Mean Method- r=∑ xy/N x . y
ASSUMED MEAN METHOD WHEN DEVIATIONS ARE TAKEN: ASSUMED MEAN METHOD WHEN DEVIATIONS ARE TAKEN Formula: r= ∑d x d y - ( ∑d x . ∑d y ) N √ ∑d x 2 – (∑d x ) 2 /N √∑d y 2 – (∑d y ) 2 /N Where as: d x is calculation of deviation from assumed mean of X i.e . d x =X-A . d y is calculation of deviation from assumed mean of Y i.e. d y =Y-A.
Example of Karl Pearson: Example of Karl Pearson
Continued: Continued x=√∑x 2 /N = √60/9 =2.58 y=√∑y 2 /N = √60/9 =2.58 r = ∑xy = 57 Nxy = +0.951 Hence both the variables are highly positively correlated.
Spearman’s rank correlation: Spearman’s rank correlation R = 1- 6∑D 2 / N 3 –N Where as: R = Rank Correlation Coefficient D = Difference of the ranks between paired items in two series. N = Number of pairs of ranks
Cont…….: Cont……. In case of tied ranks R=1- 6(∑D 2+ m 3- m..) 12 N 3 - N
Example of spearman’s method: Example of spearman’s method R s = 1 – 264-990 = 1 – 0.267 = 0.733
Concurrent Deviation Method: Concurrent Deviation Method Formula r c = √+-(2C-N/N) Where r c : Coefficient of Concurrent Deviation C: No. of positive signs after multiplying the direction of change of X series & Y sries . N= No. of pairs of observation compared.
CONCURRENT DEVIATION EXAMPLE: CONCURRENT DEVIATION EXAMPLE r c = √+-(2C-N/N) C=5 , N=7 r c = √+-(2.5-7/7) r c = √+-(3/7) r c = + 0.6546