How to Calculate and Interpret Correlation Coefficients

• \(x\) and \(y\) are two variables

• \(Σx\) and \(Σy\) are the sum of \(x\) and \(y\) values, respectively

• \(Σxy\) is the sum of the product of \(x\) and \(y\) values

• \(Σx^2\) and \(Σy^2\) are sums of squares of \(x\) and \(y\) values, respectively

Calculate Spearman’s Rho

The following formula is used to calculate Spearman’s Rho:

rho\(=1-\frac{6∑d^2}{n^3-n}\)

where:

• \(n\) is equal to the number of data points

• \(D\) is the difference between the ranks of two variables (\(x\) and \(y\)).

You can interpret the correlation coefficient using the following tips:

• When the correlation coefficient is \(+1\), it is a complete positive linear relationship, that is, as the value of one variable increases, the value of the other variable also increases.

• When the correlation coefficient is \(-1\), a negative linear relationship is complete; as the value of one variable increases, the value of the other variable decreases.

• A correlation coefficient of \(0\) does not indicate a linear relationship between two variables.

• The correlation coefficient between \(0\) and \(1\) (excluding \(0\)) indicates a positive linear relationship between the variables, the higher the coefficient, the stronger the relationship. Also, the correlation coefficient between \(0\) and \(-1\) (excluding \(0\)) indicates a negative linear relationship between variables, a lower coefficient makes the relationship stronger.

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