Correlation A correlation is a relationship between two

Correlation

A correlation is a relationship between two variables. The data can be represented by the ordered pairs (x, y) where x is the independent variable and y is the dependent variable.

Types of Correlation Positive correlation �High values of X tend to be associated with high values of Y. �As X increases, Y increases Negative correlation �High values of X tend to be associated with low values of Y. �As X increases, Y decreases No correlation

Linear Correlation y = dependent variable x = independent variable m = slope of the line c = y-intercept y m and c are unknown, therefore, are estimated from the data. Rise c m = Rise/Run x 4

Correlation Coefficient �The correlation coefficient is a measure of the strength and the direction of a relationship between two variables. �The range of the correlation coefficient is 1 to 1. If x and y have a strong positive linear correlation, correlation coefficient is close to 1. If x and y have a strong negative linear correlation, correlation coefficient is close to 1. If there is no linear correlation or a weak linear correlation, correlation coefficient is close to 0.

Different methods of calculating Correlation Coefficients Pearson’s Product Moment Correlation (Symbolized by r) Spearman Rank-Order Correlation Coefficient (ρ) Z-score method Point biserial correlation coefficient (rpb) Phi coefficient ( )

Pearson’s Product Moment Correlation Formula-

Calculating Pearson Product Moment Correlation Coefficient 1. Find the sum of the x-values. 2. Find the sum of the y-values. 3. Multiply each x-value by its corresponding y-value and find the sum. 4. Square each x-value and find the sum. 5. Square each y-value and find the sum. 6. Use the equation to calculate the correlation coefficient.

Calculate the correlation coefficient r for the following data- x 1 2 3 4 5 y – 3 – 1 0 1 2 xy – 3 – 2 0 4 10 x 2 1 4 9 16 25 y 2 9 1 0 1 4 There is a strong positive linear correlation between x and y.

Spearman Rank-Order Correlation Coefficient (ρ) Used with two ranked/ordinal variables

Example: Calculate the correlation coefficient ρ for the following data- X Y Rx Ry D=Rx~Ry D² 1 2 3 4 5 – 3 – 1 0 1 2 5 4 3 2 1 0 0 0 0 0 ∑D²=0

Here N=5 So, there is a strong positive linear correlation between x and y. v. It is about the same what we have got from the method of calculating Pearson Product moment correlation coefficient

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