# Calculating Correlation

## Calculating Correlation

**Understanding Correlation**

**Correlation**is a statistical measure that indicates the extent to which two or more variables fluctuate together.- A
**positive correlation**means that as one variable increases, the other also increases; and as one decreases the other also decreases. - A
**negative correlation**represents the opposite; when one variable increases, the other decreases. - Correlation coefficients range from -1 to 1. A value of +/- 1 indicates a perfect degree of
**linear association**between two variables.

**Calculating the Correlation Coefficient**

- The correlation coefficient, often denoted by
**r**, is a measure that determines the degree to which two variables’ movements are associated. - It is calculated using the
**Pearson Product-Moment Correlation formula**. - A correlation coefficient near to +1 or -1 shows a strong correlation, while a correlation coefficient near to 0 shows a weak correlation.
- To calculate the correlation coefficient, first calculate the covariance of the two variables, then divide by the product of their standard deviations.

**Interpreting Correlation Coefficients**

- A correlation coefficient
**between 0 and 0.3 (or 0 and -0.3)**shows a weak correlation. - A correlation coefficient
**between 0.3 and 0.7 (-0.3 and -0.7)**shows a moderate correlation. - A correlation coefficient
**between 0.7 and 1.0 (-0.7 and -1.0)**shows a strong correlation.

**Properties of the Correlation Coefficient**

- The correlation coefficient is
**symmetric**, meaning correlation from X to Y is the same as correlation from Y to X. - The correlation coefficient has the
**unitless**property, which allows you to compare correlation coefficients across different pairs of variables. - The
**sign (+/-)**of the correlation coefficient represents the direction of the relationship between two variables. - Correlation does not imply causation. A high correlation between two variables X and Y does not mean that changes in X cause changes in Y (and vice versa).

**Spearman’s Rank Correlation Coefficient**

- When the normal Pearson Product-Moment Correlation might not reflect the true relationship between two variables, we can use the
**Spearman’s rank correlation coefficient**. - It is used when the relationship between the variables is
**nonlinear**or when the variables are both ranked. - This rank version of correlation coefficient is calculated the same way as the standard correlation coefficient, but with ranked values.